Experiment, Time and Theory

Home , Alfred Bucherer, Emil Cohn, Heinz London

Faculty of Arts Thesis for the degree of Doctor in Philosophy at the University of Antwerp to be defended by

Jan Potters

Experiment, Time and Theory

On the Scientiﬁc Exploration of the Unobservable

Antwerp 2019

Supervisor: Prof. Dr. Bert Leuridan

Faculteit Letteren & Wijsbegeerte Verhandeling neergelegd voor de graad van Doctor in de Wijsbegeerte Aan de Universiteit Antwerpen Verdedigd door

Jan Potters

Experiment, Tijd en Theorie

Over de wetenschappelijke exploratie van het onobserveerbare

Antwerpen 2019

Promotor: Prof. Dr. Bert Leuridan

L’anthropologie est làpour nous le rappeler, le passage du temps peut s’interpréterde multiples fa¸cons,comme cycle ou comme décadence, comme chute ou comme instabilité,comme retour ou comme présence continuée.Appelons temporalité l’interprétationde ce passage pour bien la distinguer du temps. Les modernes ont pour particularitéde comprendre le temps qui passe comme s’il abolissait réellement le passé derrière lui. Ils se prennent tous pour Attilla derrière qui l’herbe ne repoussait plus. Ils ne se sentent pas éloignésdu Moyen Ageˆ par un certain nombre de siècles,mais séparésde lui par des révolutionscoperniciennes, des coupures épistémologiques, des ruptures épistémiquesqui sont tellement radicales que plus rien ne survit en eux de ce passé– que plus rien ne doit survivre en eux de ce passé.

Nous n’avons jamais et´ e´ modernes Bruno Latour

Contents

Contents v

Acknowledgments vii

Introduction 1

1 Manipulation and the Realist Anthropology 3 1.1 Introduction ...... 3 1.2 Hacking’s Anthropological Origin-Myth ...... 4 1.3 Realism and its arguments ...... 6 1.3.1 Putnam’s No Miracles-Argument ...... 6 1.3.2 The Underdetermination Argument ...... 10 1.3.3 Van Fraassen and Inference to the Best Explanation ...... 12 1.3.4 Laudan and the Pessimistic Meta-Induction ...... 15 1.3.5 Scientiﬁc Realism: Anthropology, Strategy and Hypothesis . . 18 1.4 Manipulability and the Realist Strategy ...... 19 1.4.1 Ian Hacking: Manipulating the Unobservable ...... 19 1.4.2 Nancy Cartwright: Constructing Nomological Machines . . . . 22 1.4.3 Manipulability and the Realism-Issue ...... 28 1.5 Manipulability and its Relation to Theory ...... 32 1.5.1 Margaret Morrison: Manipulability and Theory ...... 33 1.5.2 Michela Massimi: Manipulability and Phenomena ...... 34 1.5.3 Theodore Arabatzis: Manipulability and History ...... 36 1.6 Research Question ...... 37

2 Experiment and the Electron’s Velocity-Dependence of Mass 41 2.1 Introduction ...... 41 2.2 Kaufmann’s First Experiments and the Electromagnetic Electron . . 43 2.3 Lorentz’s Deformable Electron and the Principle of Relativity . . . . 57 2.4 Kaufmann’s Final Run of Experiments ...... 66 2.5 Early Relativistic Responses to Kaufmann’s Experiments ...... 71 2.6 Discussing Kaufmann’s Experimental Set-Up ...... 78 2.7 Planck’s Dynamics: Quanta, Relativity and the Electron ...... 93 2.8 Einstein and von Laue on the Electron ...... 107 2.9 Investigating the Electron’s Dynamics ...... 125

3 Experiment and the State of Magnetization of Superconductors 129 3.1 Introduction ...... 129 3.2 Lippmann’s Theorem, Perfect Conductors and Frozen In Fields . . . 132

v Contents

3.3 Kamerlingh Onnes and Tuyn’s Experiments ...... 134 3.4 Overturning the Classical Electron ...... 143 3.5 Experiment and Superconducting Phenomena ...... 152 3.6 Superconductors and Phenomenological Theories ...... 170 3.7 Superconductors, Diamagnetism and Experiment ...... 183 3.8 Investigating the State of Magnetization ...... 193

4 Manipulation and an Epistemology of Exploration 197 4.1 Introduction ...... 197 4.2 Exploration in Experimentation and Modeling ...... 199 4.2.1 Steinle and Exploratory Experimentation ...... 199 4.2.2 Massimi and Exploratory Modeling ...... 201 4.2.3 Uljana Feest and the Process of Stabilization ...... 203 4.3 Stabilization, Exploration and Experimental Inferences ...... 206 4.3.1 Exploration and the Electron’s Velocity-Dependent Mass . . . 208 4.3.2 Exploration and Superconductivity’s State of Magnetization . 218 4.3.3 Manipulability, Exploration and Stabilization ...... 229 4.3.4 Exploration and the Realist Anthropology ...... 235

Conclusion 241

Appendix A Experimental Inferences and Interpretations 251

Bibliography 255

Abstract 275

vi Acknowledgments

According to the views elaborated in this dissertation, research is to be characterized as exploration. Such exploration happens in a space of possibilities, and the subject of this dissertation concerns the epistemological factors that shape and constrain this space. But, of course, research does not happen in an epistemological vacuum. Material and social factors equally well play an important role in shaping, constraining and sustaining the way in which research is carried out. While I have not been able, unfortunately, to pay much attention to these factors in what is to follow, I cannot let those that have sustained my research go unnoticed. The first person who I would like to thank is my supervisor, Bert Leuridan. Over the years, he has given me space to explore and elaborate my own thoughts, while sustaining me at every moment by means of comments, remarks, criticism and support. My work has improved tremendeously thanks to him, and I am sure that without his clear and analytic eye this dissertation would have been at least twice as long without containing more information. Besides Bert, there are many other wonderful people in the Antwerp philosophy department that have made my time there a pleasure. I would like to thank them not only for providing an intellectually stimulating environment, but equally well for all the pleasant, non-philosophical lunch breaks we had. My gratitude goes out to Sydney, Thomas, Raoul, Marco, Jasper, Farid, Jan, Ludger, Karim, Erik, Els, Henk, Thomas, Laura, Katrien, Nele, Leen, Zuzanna, Hannah, Jo and many others. I have been fortunate to be able to go beyond Antwerp as well. From Ghent, I would like to acknowledge Fons, Pieter, Wim, Laura, Boris, Barnaby, Sylvia, Fien, and Inge. From my time in Cambridge, I would like to thank Hasok Chang, Richard Staley, Joe Martin, Matt Farr, Jeremy Butterfield, Catarina Madruga, Caterina Schürch, George Vardulakis, Melissa Mouthaan and Lorien Sabatino. From my visits to Tübingen,I want to extend my gratitude to Marco Giovanelli, Harvey Brown, Dennis Lehmkuhl, Thomas Ryckman, Jeroen van Dongen and Daniel Olson. From conferences throughout the years, there are too many people to mention, although a few deserve one: Massimiliano Simons, Brandon Boesch, and Philipp Haueis. Luckily, life is more than philosophy. I have had the great luck to have friends that reminded me often enough that there are other things to do than write or read: Pieter, Bart, Joshua, Wesley, Jef, Wout, Bob, Senne, Seppe, Raf, Gert, Jonas, Nick, Kristof, Michael, Bob, Jan, Lander, Jan, Beth, Emmanuelle, Ben, Griet, Sophie, Renate, Victor, Quinten, Maarten, Nelis, Tomas, Na¨ım, Camille, Jesse, Florian, Mathijs, Freek, Jonathan, Elisabeth, Katrin, Hanne, Karen, Joris, Niels, Sanne, Sander, Nick, Eefke, David, Tom, Thomas, Dorien, Ruth, Merel, Bernard, Adèle, Emilien, Caroline, Filip, Yentl, Stijn, Kamiel, Josip, Frederik, Jan, Lucas, Siemen and many others. Some people are more important for the writing of a dissertation than others.

vii Contents

Besides Bert, I want to give a special thanks to Fons, Pieter, and Joshua, who read parts of this work. Further, I want to thank my family, my sisters Marie and Ren´ee,my brother Jef, and especially my parents from the bottom of my heart, for supporting me and for providing a warm and loving home. Finally, there is one person whom I cannot thank enough, since she has been with me every step of the way: lots of love to Veerle, to whom I dedicate this work.

viii Introduction

This dissertation is concerned with an investigation of how we are to conceptualize the success of scientiﬁc experiments, in the sense of experiments providing information about what is investigated, if we do not characterize them purely in terms of observation. In chapter 1, I will present a discussion of one particular non-observation- focused approach to scientiﬁc experimentation, namely Nancy Cartwright’s and Ian Hacking’s manipulability-idea. Elaborating how this idea emerged, how Cartwright and Hacking saw it as a solution to problems that plagued observation-focused proposals, and how their alternative in turn was problematized, will lead me to the formulation of the research question that is to guide and structure this dissertation:

[Research Question]: How are we to characterize the information provided by experimental manipulations?

In chapters 2 and 3, I will then investigate this question by means of a discussion of two historical episodes involving experimental manipulations that were, for a certain time, seen as successful, but which were later reconceptualized in such a way that the experiments were no longer seen as providing the information assumed earlier. On the basis of these investigations, I will then elaborate in chapter 4 what I will call an epistemology of exploration for experimental manipulations, to be developed on the basis of work by Friedrich Steinle, Michela Massimi and Uljana Feest. Before proceeding, however, I will provide a short overview of where this dissertation comes from, since, as will become clear near the end of this work, a part of research concerns conceptualizing and reconceptualizing its own history. The original goal of my PhD was to investigate how a naturalistic approach to metaphysics was possible from a practice-based view on science. As I put it in my research proposal: “My main objective is to develop a framework for naturalistic metaphysical inquiry that can give naturalistic metaphysicians a better understanding of what is metaphysically useful about scientific practice and how it can constrain their inquiry”. As one can already see from the few paragraphs written above, this goal has shifted quite a lot over the years. A first transformation that can be identified is that my work no longer concerns metaphysical inquiry in general, but rather the philosophical debate on scientific realism, i.e. the debate on the existence of unobservable entities and the truth of scientific theories. I will focus, more specifically, on one particular contribution to it, namely Hacking’s and Cartwright’s realist proposal, often called entity realism. Whether or not the issue on scientific realism is a metaphysical issue, is itself a topic of philosophical debate. But in any case, my aim here is not primarily to formulate a particular position within the realism-debate, but rather to investigate in what way the realism-issue can be tackled within the historical-philosophical study of science. For, as we will see, the realism-issue does not just concern the existence of

1 Introduction unobservable entities or the truth of scientific theories: it touches upon the whole of scientific practice. A second transformation is that I no longer call this work ‘naturalistic’. The reason for this is that calling a philosophical account naturalistic is often taken to mean that it tries to reduce philosophical issues to questions that can be addressed in terms of established scientific results. In what is to follow, however, I will argue that what counts as a scientific result – e.g. something that can be taken to be established by successful experimentation – is itself subject to scientific dispute, and will change over time, depending on what scientists take to be other results. As such, insofar as this dissertation can be taken to provide an argument that there are no scientific facts or results in isolation, it is not naturalistic in this sense. One could argue that I should not give up on the predicate ‘naturalistic’, but rather try to change what we understand by it. I take that to be a valuable point, and insofar as my dissertation is concerned with the philosophical study of science, and thus provides an example of how I think that philosophers can, and maybe should, study science, one could call it a contribution to the debate on what counts as naturalistic philosophy. This work, I would say, is still concerned with the philosophical study of scientific practice, or more specifically, with how we are to conceptualize the way in which scientists are guided in their scientific work. The practice-turn is often characterized as a shift in focus from what scientists say in their theories to what scientists do through their actions.1 Part of the research presented here is indeed concerned with what scientists do: a lot will be said about experimental manipulations, for example. Most of it is concerned, however, with how scientists talk about what they and others do: how do scientists themselves conceptualize such experimental manipulations, and how do these conceptualizations fare over time? In order to make sense of what scientists do, I will argue, we need to take into account what their theories say about their actions and those of others. As such, this work can be read as an attempt to conceptualize how we are to understand scientific practices. As a consequence of what I take to be the central issue in the realism debate, i.e. how to understand the historical stability of scientific successes, this conceptualization will be historical in nature. As such, I do not see my work as a turn away from theory towards practice, but rather as an attempt to investigate, in a way that integrates history and philosophy of science, how practices and their theories come into being and disappear. Now that I have outlined what this work is and is not concerned with, let us turn to a discussion of experimentation and the scientific realism debate.

1 See, for example, the mission statement of the Society for Philosophy of Science in Practice (consultable at www.philosophy-science-practice.org/about/mission-statement), or L´ena Soler’s, Sjoerd Zwart’s, Vincent Israel-Jost’s and Michael Lynch’s introduction to their book on the practice turn in philosophy of science (2014).

2 Chapter 1

Manipulation and the Realist Anthropology

1.1 Introduction

The topic of this dissertation concerns how we are to conceive of the functioning and success of experiments, if we are to conceptualize them in a way that is not observation-focused. The starting point of what is to follow will be the work of Ian Hacking and Nancy Cartwright, who have argued extensively against such an observation-focused conceptualization of experimentation. This will inform us about why this focus on observation is problematic, and how Cartwright and Hacking proposed an alternative approach to the conceptualization of experimentation, which they formulated in terms of manipulation. It will then be shown that, as it stands, the manipulation-approach in turn suﬀers its own issues, which arise, I will argue then, because Cartwright and Hacking conceptualize the information provided by experimental manipulations in terms of factual knowledge. This will then lead to the formulation of the following research question, which is to guide and structure the rest of this dissertation:

[Research Question]: How are we to characterize the information provided by experimental manipulations?

How this question arises will be elaborated in this chapter, by means of a discussion of how Cartwright and Hacking proposed their manipulability-idea as a way to overcome the focus on observation that they took to dominate the scientiﬁc realism- debate at the time. We will start, in section 1.2, with a discussion of Hacking’s views on what he calls the representationalist anthropology underlying the realism- debate. The state of this debate at the time of Hacking’s and Cartwright’s work will then be discussed in section 1.3. There, we will discuss Putnam’s work on the topic (section 1.3.1) as well as some of the arguments that were raised against it: Willard van Orman Quine’s underdetermination argument (section 1.3.2); the pessimistic meta-induction as it was formulated by Larry Laudan (section 1.3.4); and Bas van Fraassen’s deconstruction of inference to the best explanation (section 1.3.3). This will also show that the realism-debate was indeed observation-focused at the time. Section 1.4 will then be concerned with how Hacking (section 1.4.1) and Cartwright (section 1.4.2) attempted to shift the debate from observation to manipulability, and how this led to the development of an alternative realist approach,

3 Chapter 1. Manipulation and Realism known in the literature as entity realism. This proposal as well has been challenged, as we will see in section 1.5, in ways that are very comparable to the issues raised with Putnam’s approach to scientiﬁc realism. The reason for this, as I will argue in section 1.6, is that Hacking and Cartwright still conceptualize the epistemology of manipulation in terms of the anthropology that, according to Hacking, underlies the standard scientiﬁc realist position. This will then show how the research question formulated above arises.

1.2 Hacking’s Anthropological Origin-Myth

Science, one can often hear, is in the business of, or at least aims at, uncovering what is real. So why is there the debate about scientiﬁc realism within philosophy? What is it that brings philosophers to argue about the claim that science studies reality? And what could philosophers contribute more, than adding to what scientists have said that it is really real?2 What is the realism-issue about, and how did it arise as a problem to which philosophers saw themselves required to answer? It is these questions that Hacking addresses in the chapter titled ‘Reals and Representations’ that forms the intermezzo between the Representing and the Intervening parts of his (1983) book Representing and Intervening. In this chapter, Hacking (1983, p. 130 – 146) investigates these questions, more speciﬁcally, in terms of what he calls a philosophical anthropology, i.e. a philosophical account of what it means to be a human being.3 His reason for approaching the issue in this way is that “[r]eality is just a byproduct of an anthropological fact[. . . ;] the concept of reality is a byproduct of a fact about human beings” (Hacking, 1983, p. 131). What we call real, on Hacking’s view, is thus dependent on what we take to be characteristic of mankind.4 After discussing earlier proposals for such a philosophical anthropology, such as ‘man is essentially something that lives in cities’, ‘mankind is characterized by its capacity to invent tools’, or ‘humanity is distinguished from the rest in terms of its ability to speak’, Hacking turns to the idea that “[h]uman beings are representers [. . . ]. People make representations” (1983, p. 132). These representations are public entities accessible to the senses, e.g. physical

2 This point was expressed very poignantly by Arthur Fine: “What then of the realist, what does he add to his core acceptance of the results of science as really true? My colleague, Charles Chastain, suggested what I think is the most graphic way of stating the answer – nameley, that what the realist adds on is a desk-thumping, foot stamping shout of ‘Really!’ So, when the realist and the antirealist agree, say, that there really are electrons and that they carry a unit negative charge and really do have a small mass (of about 9.1×10−28 grams), what the realist wants to add is the emphasis that all this is really so. ‘There really are electrons, really’.” (Fine, 1984, p. 97). 3 Hacking himself admits that the account he offers is more a fantasy than an actual empirical claim, but he does not see this as a problem: “Let us, as philosophers, welcome fantasies. There may be more truth in the average a priori fantasy about the human mind than in the supposedly disinterested observations and mathematical model-building of cognitive science” (Hacking, 1983, p. 131). 4 At this point, this will probably seem like a rather strange approach to the conceptualization of ‘the real’. As will become clear, however, there is a certain way in which it makes good sense to address the question in these terms: most scientific realist positions, for example, will elaborate their conceptualization of reality on the basis of how scientific practice, according to them, approaches the real: our conceptualization of reality is dependent on how we take mankind to study, and engage with, reality.

4 Experiment, Time and Theory objects or pictures, that were taken by humans to be likenesses of things in reality. What radically changed the epistemological status of these representations, according to Hacking’s discussion of the realist anthropology, was the appearance of language, since it was because of this that the idea of ‘the real’ emerged. Humans could start to say about a representation that it depicts something as it is, by comparing the likeness with what was observed. In this way, Hacking’s anthropological account continues, people could start reasoning about what is real: since this representation is like reality in those aspects, this suggests that reality also has these other aspects of the representation. But the emergence of language not only allowed people to start reasoning about reality, it also gave rises to disputes about reality, since what emerged were multiple possible representations:

When there were only undiﬀerentiated representations then, in my fantasy story about the origin of language, ‘real’ was unequivocal. But as soon as representations begin to compete, we had to wonder what is real. Anti-realism makes no sense when only one kind of representation is around. Later it becomes possible. (Hacking, 1983, p. 139)

Whenever we have more than one representation of something, the debate on which one is real is open. This state of aﬀairs in itself does not yet provide us what we would now call the philosophical issue of realism. For this, a second element needs to be added, namely the supposition that reality goes beyond what our senses tell us: “[t]hings [. . . ] have an inner constitution, a constitution that can be thought about, perhaps even uncovered” (Hacking, 1983, p. 140). In this way, what is real is no longer conﬁned to what is observed directly: that is the domain of the appearances. The idea also begins to form that while we can have multiple representations compatible with the appearances, there has to be one that gets at the truth behind the appearances. As such, the search is open for principles and criteria that distinguish realistic representations from those that are not. In this way, Hacking claims, we see the emergence of the philosophical and metaphysical enterprise that is the realism-issue:

As soon as what we would now call speculative physics had given us alternative pictures of reality, metaphysics was in place: Metaphysics is about criteria of reality. Metaphysics is intended to sort good systems of representation from bad ones. Metaphysics is put into place to sort representations when the only criteria for representations are supposed to be internal to representation itself. (Hacking, 1983, p. 142)

At first, it was believed that science would provide such criteria, since it seemed to offer us a historical progression towards better representations of reality. It soon turned out, however, that within science as well “there might be several ways to represent the same facts” (Hacking, 1983, p. 143).5 And Kuhn’s work on the historical movement of scientific theories showed, according to Hacking, that we would never find theory-independent scientific criteria for distinguishing real from apparent representations, since every possible observation that could decide the issue is

5 Hacking sees this appear, for example, in Heinrich Hertz’s work on mechanics, which provided three diﬀerent ways to represent the then available knowledge of moving bodies (1983, p. 143 – 144).

5 Chapter 1. Manipulation and Realism already loaded with a particular theory. In this way, scientific realism has been transformed from a philosophical question into an impasse: the history of science itself seems to show that there is no scientific criterion that tells us what it is about true scientific representations that distinguishes them from others: “[t]here are – in the extremes of reading Kuhn – no criteria for saying which representation of reality is best. Representations get chosen by social pressures” (Hacking, 1983, p. 144). According to Hacking, however, this realism-impasse arises because the debate is based on a misguided conceptualization of how science approaches reality. The debate implicitly assumes that our representations can be true or false about the reality behind what we observe. But this assumption applies the truth-predicate to a domain to which it should not be applied, since the representations that we construct in science are not like everyday truths about what is observable, such as e.g. Hacking’s typewriter: “[t]here is a final truth of the matter about the typewriter. In physics there is no final truth of the matter, only a barrage of more or less instructive representations” (Hacking, 1983, p. 145). It is in this way that the realism-issue has become an impasse: By attending only to knowledge as representation of nature, we wonder how we can ever escape from representations and hook-up with the world. [. . . ] In our century John Dewey has spoken sardonically of a spectator theory of knowledge that has obsessed Western philosophy. If we are mere spectators at the theatre of life, how shall we ever know, on grounds internal to the passing show, what is mere representation by the actors, and what is the real thing? If there were a sharp distinction between theory and observation, then perhaps we could count on what is observed as real, while theories, which merely represent, are ideal. But when philosophers begin to teach that all observation is loaded with theory, we seem completely locked into representation, and hence into some version of idealism. (Hacking, 1983, p. 130) Because of this, Hacking argues, we need to get away from observation, and focus instead on what he calls manipulation. Before we turn to how Hacking and Cartwright elaborated this idea, however, let us first turn to how the realism-debate was carried out at the time. This will then provide us with the philosophical framework that led Hacking to his claim that the realism-debate was stuck in an impasse because of its observation-focused anthropology.

1.3 Realism and its arguments

1.3.1 Putnam’s No Miracles-Argument While Hacking presents his discussion of the realism-issue as an anthropological fantasy, there are certain very interesting parallels with the realism-debate as it was going on around the time Hacking published his fantasies. To argue for this, I will start with a discussion of the work of Hillary Putnam (1975; 1978), who is often taken to have provided the primary argument in favour of realism, the no miracles-argument [NMA].6 Putnam himself describes his strategy for approaching

6 For a discussion of some other formulations of the argument, by Grover Maxwell, J.J.C. Smart and Richard Boyd, see (Psillos, 1999, p. 70 – 81).

6 Experiment, Time and Theory the realism issue in the following terms: The strategy I followed [. . . ] is to view the language-speaker as constructing a symbolic representation of his environment. He cannot do this unless he causally interacts with his environment, and the accuracy or inaccuracy of his representation will affect the viability and success of his efforts in dealing with his environment; thus such an account of the relation of language-speakers to the world is part of a causal model of human behaviour. In so far as the assumed correspondence between the representations in the speaker’s mind and their external referents is part of the model, realism thus becomes an empirical hypothesis. (Putnam, 1978, p. 4) What Putnam states here is what we could call, in line with Hacking’s claims discussed above, a philosophical anthropology. According to Putnam, this anthropology offers us realism as an empirical hypothesis, in the sense that we can investigate the realist truth of representations in certain fields by searching for a successful interaction with the environment. Putnam then elaborates such a realist hypothesis for the fields of mathematics and logic. The successful interaction in both cases, he argues, runs via science, and it is in this context that he formulates his [NMA].

Realism with respect to mathematics It is often assumed, Putnam argues, that our mathematical claims are obtained by means of a priori proofs from postulates and axioms that have no connection at all with our physical environment (1975, p. 61). In fact, however, we often make use in mathematics of what he calls quasi-empirical methods.7 Many of our mathematical concepts, he argues, find their origin in the sciences: they were developed there in response to particular issues, and once they showed their fertility, the postulates and axioms that govern these concepts received quasi-empirical confirmation through their successful application in the context of science (1975, p. 61 – 69). This is prevalent throughout the history of mathematics, Putnam argues by means of different examples, even though it has rarely received much attention (1975, p. 67). It is in the use of these quasi-empirical methods that we can find the realist correspondence, according to Putnam, between our representations and our environment, and its success shows that we need to be realists with respect to our mathematical claims: “a reasonable interpretation of the application of mathematics to the physical world requires a realistic interpretation of mathematics” (Putnam, 1975, p. 74; original emphasis).8 In fact, it is the only interpretation of our mathematical statements, Putnam claims, that does not make this success a miracle. In this way, there

7 Putnam describes such methods as follows: they are “methods that are analogous to the methods of the physical sciences except that the singular statements which are ‘generalized by induction’, used to test ‘theories’, etc., are themselves the product of proof or calculation rather than being ‘observation reports’ in the usual sense” (1975, p. 62). 8 This does not mean, according to Putnam, that we have to believe in the existence of a separate mathematical realm. Rather, the objects studied by mathematicians are abstractions of the material objects that are to be found in physical reality. Set theory, for example, is an abstract theory of the possible behaviour of sets of objects, and according to Putnam, the same claim can be made for (almost) all mathematical objects: “[n]ot only are the ‘objects’ of pure mathematics conditional upon material objects; they are, in a sense, merely abstract possibilities. Studying how mathematical objects behave might better be described as studying what structures are abstractly possible and what structures are not abstractly possible” (Putnam, 1975, p. 60).

7 Chapter 1. Manipulation and Realism is a very strong analogy to be drawn between mathematics and science, for in the case of our scientiﬁc theories as well, the only way we can make sense of their success is in terms of a realist correspondence between our theoretical representations and our environment, as he puts it in his (1975) formulation of his [NMA]:9

The positive argument for realism is that it is the only philosophy that doesn’t make the success of science a miracle. That terms in mature scientific theories typically refer [. . . ], that the theories accepted in a mature science are typically approximately true, that the same term can refer to the same thing even when it occurs in different theories – these statements are to be viewed by the scientific realist not as necessary truths but as parts of the only scientific explanation of the success of science, and hence as part of any adequate scientific description of science and its relations to objects. (Putnam, 1975, p. 73)

Realism with respect to truth A similar approach is employed by Putnam in his (1978) book, which collects his 1976 John Locke lectures titled Meaning and Knowledge. He there presents an elaboration of a realist position with respect to the field of logic. His focus is, more specifically, on how we are to conceptualize a realist correspondence between our environment and Tarski’s theory of truth. What a realist interpretation with respect to truth comes down to, according to Putnam, is an acceptance of claims about truth and falsity of the form “A statement can be false even though it follows from our theory (or from our theory plus the set of true observation sentences)” (1978, p. 34 – 35).10 This claim forms a realist interpretation of the notions of truth and falsity, since it connects these concepts with our environment: it is not theory but the environment that determines what is true and false. That we are to regard this realist interpretation as acceptable or at least plausible is then argued for by means of an argument very similar to the one just discussed, namely by looking at how we use our logical concepts in our interaction with the environment. The interaction that Putnam directs his attention to, more specifically, is the formulation of theories by scientists. This activity is characterized, according to Putnam, by what he calls the convergence of scientific knowledge, which comes down to “preserving the mechanisms of the earlier theory as often as possible, which is what scientists try to do” (1978, p. 20).11 This convergence is something that calls for an explanation, Putnam claims, since it is not something that we would normally expect: trying to preserve mechanisms of earlier theories as much as possible is in fact the most difficult way to formulate a successful new theory, way more difficult than only trying to preserve the confirmed observation sentences that the earlier theory entailed. Still, Putnam claims, we do observe this in scientific practice, and in fact, such attempts to preserve earlier theories have often led to important discoveries (1978, p. 20). This behaviour can be explained, according to Putnam, by means of the following realist hypothesis, which he borrows from Richard Boyd:

9 Besides this positive argument for realism, there is also a negative one, according to Putnam, which comes down to the claim that various anti-realist, i.e. verificationist or idealist, attempts to reinterpret scientific statements have been unsuccessful (1975, p. 72). 10 With our theory, Putnam here means “a formalization of present knowledge” (1978, p. 35). 11 Putnam does not specify what he means by mechanisms, but it seems that he is concerned with the causal mechanisms that, according to scientific theories, underly what is observable.

8 Experiment, Time and Theory

Boyd tries to spell out realism as an over-arching empirical hypothesis by means of two principles:

1. Terms in a mature science typically refer. 2. The laws of a theory belonging to a mature science are typically approximately true.

What he attempts to show in his essay is that scientists act as they do because they believe (1) and (2) and that their strategy works because (1) and (2) are true. (Putnam, 1978, p. 20 – 21)

If scientists believe (1) and (2), then we would expect them to formulate their theories in such a way that these preserve the referential terms and the true laws of their predecessors. On this hypothesis, “my knowledge of (1) and (2) enables me to restrict the class of candidate-theories I have to consider, and thereby increases my chance of success” (Putnam, 1978, p. 21). Now, what is signiﬁcant about this realist hypothesis is that “if it is correct, the notions of ‘truth’ and ‘reference’ have a causal-explanatory role” (Putnam, 1978, p. 21). It is the scientist’s belief in the truth of a theory’s laws and the referential nature of a theory’s terms, which has emerged out of the scientist’s interactions with her environment, that constrains the scientist in the construction of a successor theory. In this way, the realist hypothesis sketched above would, if true, also show how the sought-after realist correspondence between our environment and our representations of truth and reference emerges out of our interaction with our environment. And the truth of this hypothesis is, again, argued for by means of the [NMA]. It is only if we are realists with respect to science that the success and convergence of our scientiﬁc theories does not turn into a miracle:

[I]f these objects [i.e. the gravitational ﬁeld or the metric structure of space-time] don’t really exist at all, then it is a miracle that a theory which speaks of gravitational action at a distance successfully predicts phenomena; it is a miracle that a theory which speaks of curved spacetime successfully predicts phenomena; and the fact that the laws of the former are derivable ‘in the limit’ from the laws of the latter theory has no methodological signiﬁcance. (Putnam, 1978, p. 19)

Realism as a philosophical strategy We have seen how Putnam’s philosophical anthropology, which conceptualizes humans as beings that construct representations, allows him to present realism with respect to mathematics and logic as an empirical hypothesis. Because of our causal interaction with our environment, we come to expect a realist correspondence between this environment and our mathematical and logical representations. The [NMA] then allows Putnam to argue for the truth of these hypotheses. In fact, there are two central elements to this realist hypothesis: the correspondence between the accuracy of our representations and the success of our interactions with the environment, and the increase of this accuracy over time, i.e. the convergence of knowledge. The realist hypothesis concerns the historical stability of a connection between representations and reality. In what follows, we will see that Quine, van Fraassen and Laudan raise issues with all three elements of this realist hypothesis. Quine’s work will address the

9 Chapter 1. Manipulation and Realism way in which scientists construct representations. Van Fraassen will raise questions about our connection with reality. And Laudan will be concerned with the presumed historical stability of the realist connection between representations and reality. Cartwright and Hacking, we will see then, will use their manipulability-idea to reconceptualize these three elements of the realist hypothesis, in such a way that it leads, they claim to a viable realist position.

1.3.2 The Underdetermination Argument The first argument to be considered, the underdetermination argument [UA], will be discussed in terms of Willard Van Orman Quine’s (1975) paper, ‘On Empirically Equivalent Systems of the World’. His goal there is explicitly to analyze in how far the argument forms a worry for scientific realists. The argument is often taken to lead to the conclusion that “[i]f all observable events can be accounted for in one comprehensive theory [. . . ] then we may expect that they can all be accounted for equally, in another conflicting system of the world” (Quine, 1975, p. 313). The argument for this conclusion is based on the way in which scientists practice their work. They do not rest on the level of the observable, but rather propose hypotheses concerning things that go beyond the observable. Given that “science [forms] a con- siderably integrated system of the world even now” (1975, p. 314), this claim would entail that “natural science is empirically under-determined; under-determined not just by past observation but by all observable events” (1975, p. 313). It is Quine’s goal to investigate how we are to understand this argument exactly, and what it entails.

Observation and theory In order to carry out his analysis of the [UA], Quine first needs to clarify the central terms involved, namely observation and theory. Observation, Quine argues, should not be taken in its sense of a private, sensory experience. Quine’s concern is rather with observation terms and sentences, which can be distinguished from other kinds of statements, according to Quine, by the following criterion: “[o]bservational expressions are expressions that can be learned ostensively” (1975, p. 316). When we can point to something and connect this with a word or a sentence, this means that that something is public and shared, and in this way, the problem of the privacy of our observational experiences is sidestepped: “witnesses will agree on the spot in applying an observation term, or in assenting to an observation sentence” (Quine, 1975, p. 315). The question that now needs to be addressed, in order to clarify the [UA], is how theoretical statements relate to observation sentences. A first, important difference between these two kinds of statements, according to Quine, is that while the truth of particular observation sentences varies with time and place, the truth or falsity of our theoretical statements is supposed to be invariable. In order to bring these two in line, we therefore need to add spatio-temporal coordinates to our observation sentences: such observation sentences Quine calls ‘pegged observation sentences’ (1975, p. 316). This then turns them into statements whose truth-value is invariable. It also constitutes, however, “an abrupt ascent from observation into theory”, since the establishment of a system of coordinates already requires mathematics and knowledge of the physical world (Quine, 1975, p. 317). Moreover, even then we are not yet able to derive possible observation sentences from our theory, for theories normally

10 Experiment, Time and Theory work with general expressions, and in order to derive a particular statement from the theory, we need to assume that other particular observation statements hold (boundary conditions). Only then are we able to derive an observation sentence from our theory in such a way that the theory can be tested with respect to observation, on the condition that the boundary conditions hold. As such, Quine argues, our theories in fact entail what he calls observational conditionals (Quine, 1975, p. 318). For Quine, however, this is not yet satisfactory, since while we now have clarified what we take to be observation, we have not yet said anything about what we take to be theory. The question that needs to be addressed, more specifically, is how we are to identify and differentiate theories, since in order to make sense of the [UA], we need a clear criterion of when two theories are equivalent. Common usage has been to identify a theory with a single sentence, the theory’s core (i.e. a conjunction of all the axioms of the theory), and all the logical consequences of this conjunction. This entails that “[a] single theory, in this sense, admits of many formulations: all that is required is that they be logically equivalent” (Quine, 1975, p. 318). But this criterion for the identity of theories will not do here, as Quine argues with an example of a new theory formulation obtained from an existing one by consistently switching two theoretical terms (t1 and t2): t1 everywhere replaces t2 and vice versa. This new theory formulation will be logically incompatible with the original one, since it proclaims very different things about t1 than the original theory does. The theories are, however, empirically equivalent: since the terms switched were purely theoretical, the theories imply exactly the same observation conditions. The difference between the two theories seems to be merely terminological, and Quine therefore proposes to drop logical equivalence as the criterion of identity. Instead, he proposes that “two formulations express the same theory if they are empirically equivalent and there is a reconstrual of predicates that transforms the one theory into a logical equivalent of the other” (Quine, 1975, p. 320).

Underdetermination and practice Now that the two central elements in the [UA], observation and theory, are clarified, Quine proposes the following formulation of the underdetermination claim: “under-determination says that for any one theory formulation there is another that is empirically equivalent to it but logically incompatible with it, and cannot be rendered logically equivalent to it by any reconstrual of predicates” (Quine, 1975, p. 322). The example involving t1 and t2 thus does not constitute a case of actual underdetermination. Another example, involving a theory formulation according to which the cosmos is infinite and one that conceptualizes the cosmos as finite but with objects shrinking in proportion as they move away from the center, also does not offer a case of actual underdetermination, for the two theories are empirically equivalent but they can also be rendered logically equivalent by switching predicates. This shows, according to Quine, that more is required for underdetermination to form an actual issue for science than different, empirically equivalent but logically incompatible theories that cannot be rendered logically equivalent by predicate reconstrual: “we need to show not only that such branching alternatives exist, but that they are inevitable” (Quine, 1975, p. 322 – 323). According to Quine, such branching is, however, never inevitable. We can always identify a theory T as the theory formulation consisting of a single sentence TOBS

11 Chapter 1. Manipulation and Realism conjoining all the theory’s observation conditionals, which is also a consequence 0 0 of every theory T1,..., Tn that is empirically equivalent with the theory T , and 0 which can never conflict with any one of these empirically equivalent theories T1, 0 ..., Tn. What this shows, according to Quine, is that if we would be able to check the truth of all the observation conditionals that would make up the conjunction TOBS, we would not require any theory, and hence we would not be confronted with branching alternatives. As such, Quine claims, “[i]n its full generality, the thesis of under-determination thus interpreted is surely untenable” (1975, p. 323). This analysis of the [UA] does teach us something about actual scientific practice, according to Quine. We are never in a position to check the truth of such a list of observation conditionals TOBS. This is why we formulate theories: they function as “a device for remote control and for mass coverage. The theory formulation serves to specify en masse the observation conditionals we are rightly or wrongly taking to be true” (Quine, 1975, p. 324). And this opens up the possibility of a form of underdetermination that, while logically weaker than the one discussed above, can show itself in scientific practice:

Underdetermination lurks where there are two irreconcilable formulations each of which implies exactly the desired set of observation conditionals plus extrateneous theoretical matter, and where no formulation affords a tighter fit. [. . . ] Here, evidently, is the nature of underdetermination. There is some infinite lot of observation conditionals that we want to capture in a finite formulation. Because of the complexity of the assortment, we cannot produce a finite formulation that would be equivalent merely to their infinite conjunction. Any finite formulation that will imply them is going to have to imply also some trumped-up matter, or stuffing, whose only service is to round out the formulation. There is some freedom of choice of stuffing, and such is the underdetermination. (Quine, 1975, p. 324)

What Quine’s (1975) work on the [UA] thus shows, is that because of our limitations as human beings, it cannot be excluded that scientists will end up with different theories that are logically incompatible but empirically equivalent: turning the infinite collection of observation conditionals that a theory is supposed to cover into a finite formulation requires stuffing, as Quine puts it, and in this there is always a certain freedom of choice. As such, the [UA] poses a problem for scientific realism insofar as it gives us reason to doubt that the stuffing used to construct a theory is true.

1.3.3 Van Fraassen and Inference to the Best Explanation Scientific realism and constructive empiricism The second challenge is to be found in Bas van Fraassen’s (1980) book, The Scientific Image. He there presents a deconstruction of the inference rule on which, he claims, many defences of the scientific realist position rely: inference to the best explanation [IBE]. Before out- lining his central claim, however, van Fraassen turns to a consideration of what we are to understand exactly under scientific realism. The position he will consider should not be identified with the na¨ıve statement that “the picture which science gives us of the world is a true one, faithful in its details, and the entities postulated

12 Experiment, Time and Theory in science really exist: the advances of science are discoveries, not inventions” (1980, p. 6 – 7). This statement does not do full justice to the scientific realist position, according to van Fraassen, since given that our earlier scientific theories have been replaced over time, it would entail that the claims of earlier realists would be refuted merely through these scientific advances.12 Instead, on the basis of a discussion of how different realists have characterized their position, he proposes the following statement:

Science aims to give us, in its theories, a literally true story of what the world is like;13 and acceptance of a scientiﬁc theory involves the belief that it is true. (van Fraassen, 1980, p. 8)

The advantage of this formulation is that it does not necessarily commit the realist to holding one particular scientific theory to be true. The statement rather concerns the reasons for the construction and acceptance of scientific theories. As such, the statement ascribes to the realist a belief about the epistemological practice of science, rather than a direct belief about what science tells us about the world.14 As an alternative position, van Fraassen proposes what he calls constructive empiricism, which does not take science to be primarily in the business of constructing a literally true story of what the world is like. On this view, science only aims for theories that are empirically adequate, which means that “what it says about the observable things and events in this world, is true – exactly if it ‘saves the phenomena”’ (van Fraassen, 1980, p. 12). Acceptance of a theory then involves the belief that the theory is empirically adequate. The distinction between the realist and the anti-realist constructive empiricist thus comes down to the kind of truth that science is concerned with: truth about the world, or only about those things within the world that are observable. The criterion offered by van Fraassen for distinguishing the observable from the unobservable is the following:

The human organism is, from the point of view of physics, a certain kind of measuring apparatus. As such it has certain inherent limitations – which will be described in detail in the ﬁnal physics and biology. It is these limitations to which the ‘able’ in ‘observable’ refers – our limitations, qua human beings. (van Fraassen, 1980, p. 17)15

12 Van Fraassen does not really elaborate this, but it seems that he has in mind here scientific advances that involve theory change without radical discontinuity. 13 Van Fraassen illustrates what he takes to be a literally true story by means of a contrast with how he takes positivists to read scientific theories. On the positivist view, the meaning of terms figuring in theoretical statements only depends on their connection with the observable, which entails that two theories can contradict each other while saying the same thing, i.e. if their observable consequences are the same. This positivist reading of theories offers, on van Fraassen’s view, a non-literal reading: “two theories which contradict each other in such a way can ‘really’ be saying the same thing only if they are not literally construed. Most specifically, if a theory says that something exists, then a literal construal may elaborate on what that something is, but will not remove the implication of existence” (van Fraassen, 1980, p. 11). 14 Important here is that while it is the aim of science to find true theories, this aim is not to be necessarily identified with the motives that individual scientists can have to formulate theories. It rather gives us the standard for success within the scientific enterprise: “What the aim is determines what counts as success in the enterprise as such; and this aim may be pursued for any number of reasons” (van Fraassen, 1980, p. 8). 15 Important to stress is that this criterion of observability does not constrain the constructive

13 Chapter 1. Manipulation and Realism

Inference to the best explanation Van Fraassen then turns to one of the arguments offered by different realists in favour of their position, namely “that the canons of rational inference require scientific realism. If we are to follow the same patterns of inference with respect to this issue as we do in science itself, we shall find ourselves irrational unless we assert the truth of the scientific theories we accept” (van Fraassen, 1980, p. 19), or, in an alternative formulation of Wilfrid Sellars, “to have good reason for holding a theory is ipso facto to have good reason for holding that the entities postulated by the theory exist” (van Fraassen, 1980, p. 19). The general idea behind these arguments is that, in both everyday and scientific situations, if we have good reasons for accepting a theory, then we have good reasons for believing that theory to be true. Accepting the theory while not taking it to be true would be irrational. The canon of rational inference that is pointed at here is [IBE], which van Fraassen sketches as follows: suppose we have some evidence E, and we have different hypotheses H1,H2,...,Hn that could explain this evidence; we should then infer that Hj rather than the other hypotheses exactly if Hj is a better explanation of E than the others are. Now, the best, or even only explanation for the success of our use of [IBE] in both everyday and scientific situations, the realist argument goes, is that there is indeed a connection between a hypothesis’ explanatory power and its truth. Hence, we are led to the conclusions that our best scientific theories are indeed true and that the entities they postulate do exist. Van Fraassen then points out that this inference rule can indeed be applied in many ordinary cases.16 But he then argues that such uses of [IBE] in themselves provide no reason for believing that the unobservable entities postulated by our scientific theories exist. To argue for this, he first considers what we could mean when we say that someone follows a rule such as [IBE]. After rejecting a few proposals, he settles on the claim that “to be following a rule, I must be willing to believe all conclusions it allows, while definitely unwilling to believe conclusions at variance with the ones it allows – or else, change my willingness to believe the premisses in question” (van Fraassen, 1980, p. 20). On the realist argument sketched above, following [IBE] would then mean that I am willing to believe that the theory which best explains the evidence is true. But van Fraassen’s constructive empiricism offers him a rival hypothesis for the realist’s claim that using [IBE] in science necessarily means that one is willing to believe that the best explanation is true. For we can equally well equate acceptance of a theory or claim with the belief that it is empirically adequate. And hence, for those cases where the realist sees the use of [IBE] as an argument for realism, the constructive empiricist sees an argument for constructive empiricism. What she sees in these situations, more specifically, is that “we are always willing to believe that empiricist to only those phenomena that are actually observed, but rather to all possible phenomena observable by us, since “the term ‘observable’ classifies putative entities, and has logically nothing to do with existence” (van Fraassen, 1980, p. 18). On van Fraassen’s view, a phenomenon is thus by definition something that is observable. Alternative conceptualizations of phenomena, which do not take them to be necessarily observable, will be discussed in section 1.4.3, where Hacking’s notion will be discussed, and in chapter 4, where Uljana Feest’s elaboration of Bogen and Woodward’s (1988) conceptualization of phenomena will be discussed. 16 He gives the following example: “I hear scratching in the wall, the patter of little feet at midnight, my cheese disappears – I infer that a mouse has come to live with me. Not merely that these apparent signs of mousely presence will continue, not merely that all the observable phenomena will be as if there is a mouse; but that there really is a mouse” (van Fraassen, 1980, p. 19 – 20).

14 Experiment, Time and Theory the theory which best explains the evidence, is empirically adequate (that all the observable phenomena are as the theory says they are)” (van Fraassen, 1980, p. 20). This alternative equally well provides an account for the cases of theory acceptance in science, according to van Fraassen, and hence we cannot take the use of [IBE] as an argument for scientiﬁc realism, for we have no way to decide whether the use of [IBE] in science with respect to the unobservable is motivated by an aim for truth or by an aim for empirical adequacy. Hence, we should not take the realist’s assumed connection between explanatory success and truth for granted: “there is no open-and-shut argument from common sense to the unobservable. Merely following the ordinary patterns of inference in science does not obviously and automatically make realists of us all” (1980, p. 23).

1.3.4 Laudan and the Pessimistic Meta-Induction The ﬁnal argument to be discussed, the pessimistic meta-induction [PMI], is often ascribed to Larry Laudan in his (1981) article, ‘A Confutation of Convergent Realism’.17 His concern there is with what he describes as the suggestion, which was increasingly common, that epistemological realism “is an empirical hypothesis, grounded in, and to be authenticated by its ability to explain the workings of science” (1981, p. 19). Laudan characterizes this realist hypothesis, which he calls convergent epistemological realism (CER), as consisting of a collection of theses that more or less correspond to the diﬀerent points that Putnam raised in the papers discussed above:18

1. Scientiﬁc theories (at least in the ‘mature’ sciences) are typically approximately true and more recent theories are closer to the truth than older theories in the same domain; 2. The observational and theoretical terms within the theories of a mature science genuinely refer (roughly, there are substances in the world that correspond to the ontologies presumed by our best theories); 3. Successive theories in any mature science will be such that they ‘preserve’ the theoretical relations and the apparent referents of earlier theories (i.e., earlier theories will be ‘limiting cases’ of later theories). 4. Acceptable new theories do and should explain why their predecessors were successful insofar as they were successful.

17 This is not completely correct, however, since Putnam (1978) himself already raised a similar kind of argument as posing an actual problem for his realist position with respect to truth, one that, according to him, was already formulated by Kuhn. If it would turn out, Putnam argues, that in the past there have been many successful theories that, from our point of view, are not approximately true and do not genuinely refer, then we would have no reason to take the success of our contemporary theories to indicate any kind of approximate truth or genuine reference: “eventually the following meta-induction becomes overwhelmingly compelling: just as no term used in the science of more than ﬁfty (or whatever) years ago referred, so it will turn out that no term used now (except maybe observation terms, if there are such) refers” (Putnam, 1978, p. 25). I have chosen to follow Laudan’s formulation of the argument since it is the most extensive one, and because it is the one that is most often discussed in the literature. 18 Laudan notes that while no philosopher of science has explicitly subscribed to all of the claims that make up (CER), most of them have been defended in one way or another by Putnam, Boyd and others (1981, p. 20 – 21).

15 Chapter 1. Manipulation and Realism

5. Theses (1)-(4) entail that (‘mature’) scientiﬁc theories should be successful; indeed, these theses constitute the best, if not the only, explanation for the success of science. The empirical success of science (in the sense of giving detailed explanations and accurate predictions) accordingly provides striking empirical conﬁrmation for realism. (Laudan, 1981, p. 20 – 21)

In general, Laudan claims, realists now make use of two abductive arguments to argue for the claims that make up (CER). The ﬁrst is that the empirical success of our scientiﬁc theories is explained by the hypotheses that their laws are true and that their terms refer. The second is that the fact that scientists seek to preserve earlier theoretical mechanisms, and generally succeed therein, is explained by the hypothesis that these earlier theories are approximately true and have genuinely referential terms. On the basis of these arguments, and assuming that past and present science has indeed been successful, they then claim that, if (CER) were true, it would explain the success of science, while if it were false, the success of past and present science would be a miracle (Laudan, 1981, p. 21 – 22). Laudan now claims that (CER), in this formulation “is neither supported by, nor has it made sense of, much of the available historical evidence” (1981, p. 20).

Connecting empirical success to truth and reference Laudan first picks apart the first argument, which relies, according to him, on two elements: a presumed close connection between success and reference, and a presumed close connection between success and approximate truth. He first turns to the relation between success and reference, where he defines success as follows: “a theory is successful so long as it has [. . . ] functioned in a variety of explanatory contexts, has led to confirmed predictions and has been of broad explanatory scope” (Laudan, 1981, p. 23). To explain why certain theories are successful in such a way, a realist will then take the theory’s central terms to refer as follows: “the terms in a theory may be genuinely referring even if many of the claims the theory makes about the entities to which it refers are false[,] [p]rovided that there are entities which ‘approximately fit’ a theory’s description of them” (Laudan, 1981, p. 24). Laudan then argues, however, that it is not necessarily the case that a theory whose central terms genuinely refer will be a successful theory, since there have been examples of theories that genuinely refer but were not successful (1981, p. 24 – 25).19 Nor is it necessarily the case, he continues, that if a theory is successful, we can infer that its central terms refer, since there are many examples of successful theories that we now take to be non-referring.20 This leads Laudan to the claim that contrary to what the realist presumes, there is no such strong connection between success and reference.

19 His list of examples includes, among other things, Wegener’s theory of continental drift and atomic theories in the 18th and 19th century. While the central terms of these theories referred, they had “a strikingly unsuccessful career, [and were] confronted by a long string of apparent refutations” before they became accepted (Laudan, 1981, p. 24). 20 The most famous examples that Laudan lists here are the diﬀerent ether-theories in physics and chemistry from the 18th and 19th century (Laudan, 1981, p. 26 – 27). Further on, Laudan extends this list with the following examples: the crystalline spheres of ancient and medieval astronomy; the humoral theory of medicine; the eﬄuvial theory of static electricity; ‘catastrophist’ geology, with its commitment to a universal deluge; the phlogiston theory of chemistry; the caloric theory of heat; the vibratory theory of heat; the vital force theories of physiology; the theory of circular inertia; and theories of spontaneous generation (Laudan, 1981, p. 33). For a discussion and evaluation of an updated version of this list, see Vickers (2013).

16 Experiment, Time and Theory

Laudan next turns to a discussion of the relation between success and approximate truth. The main problem is that it is unclear what it means for a theory to be approximately true, which renders it unclear how a theory’s success would lead us to the claim that it is approximately true (1981, p. 29 – 32). And even if we assume that a theory being approximately true entails it being successful, it is still unclear how a theory’s success could provide evidence for it being approximately true, since approximate truth requires reference: “a realist would never want to say that a theory was approximately true if its central theoretical terms failed to refer” (Laudan, 1981, p. 33). But this leads us again to the problem raised by the list of successful but non-referential theories (see footnote 20). Moreover, the history of science also provides examples of genuinely referring and empirically successful theories that we would nonetheless not consider to be approximately true (Laudan, 1981, p. 35).21 This leads Laudan to his ﬁrst conclusion, that as it stands, there is no ground for the realist to claim that the empirical success of science can be taken as a reliable indication of the approximate truth or genuine reference of our theories.

Connecting historical convergence to truth and reference Laudan then turns to the second argument presented by the realist, which concerns the convergence of scientific knowledge. There are several problems with it. First, it is not the case that scientists generally adopt theories because they contain earlier theories as limiting cases, or reject theories because they do not retain earlier theories (1981, p. 37 – 38).22 Moreover, in many cases of theory change there has been significant loss of important parts of earlier theories (1981, p. 39 – 42).23 Further, results established by David Miller indicate, according to Laudan, that there are specific issues with the way in which realists see theories as converging, which “show in principle that the kind of cumulation demanded by the realist is unattainable” (1981, p. 42).24 Finally, it is hard to make sense of, in a general way, what it means for a theory to

21 Here, Laudan gives the following examples: geological theories pre-1960s, which were successful and referred to continents, but which are, from our contemporary point of view, not even approximately true, since they have no conceptualization of continental drift; chemical theories of the 1920s, which were successful and referred to the atomic nucleus, but which we would now no longer take as approximately true, since they took this nucleus to be structurally homogeneous; and chemical and physical theories of the 19th century that were successful and referred to matter, but which are no longer taken to be even approximately true because they viewed this matter as neither created nor destroyed (Laudan, 1981, p. 35). 22 Examples of this include the wave theory of light, Lyell’s uniformitarian geology and Dar- win’s evolutionary theory, none of which were criticized for not retaining central aspects of their predecessors (Laudan, 1981, p. 38). 23 Laudan lists as examples the abandonment of the ether by special relativity, the dismissal of Darwinian pangenesis by modern genetics, and others, which leads him to claim “that some of the most important theoretical innovations have been due to a willingness of scientists to violate the cumulationist or retentionist constraint which realists enjoin ‘mature’ scientists to follow” (1981, p. 39). 24 According to Laudan (1981, p. 42), Miller established the following results for views that conceptualize scientiﬁc theories as a conjunction of statements and their consequences: (a) that the familiar requirement that a successor theory, T2, must both preserve as true the true consequences of its predecessor, T1, and explain T1’s anomalies is contradictory; (b) that if a new theory, T2, involves a change in the ontology or conceptual framework of a predecessor, T1, then T1 will have true and determinate consequences not possessed by T2; (c) that if two theories, T1 and T2, disagree, then each will have true and determinate consequences not exhibited by the other. Laudan does not provide any reference to an article or book where Miller established these results, and there is no real discussion of these results found in the literature on Laudan’s work either.

17 Chapter 1. Manipulation and Realism explain the success of its predecessors (1981, p. 43 – 45). This then leads Laudan to his second conclusion, that as it stands, there is no ground for the realist to claim that the history of science provides in any way an argument for the claim that our scientiﬁc theories are converging towards or approximating the truth.25

1.3.5 Scientific Realism: Anthropology, Strategy and Hy- pothesis Putnam’s elaboration of a realist position, we have seen, relied on a philosophical anthropology that conceptualized human beings as language speakers who, through successful interactions with their environment, would obtain accurate representations of that environment. This anthropology then offered Putnam a strategy for elaborating realist hypotheses with respect to the representations constructed in different domains: find the way in which humans interact with their environment in these domains, and if this interaction is successful, one can take the representations constructed about these domains to accurately correspond to the reality studied in these domains. As we have seen, there are in fact two central scientific elements on which Put- nam’s realist hypothesis depend: the correspondence between the accuracy of the constructed representations and the success of the interactions with the environment, and the increase of this accuracy over time, which Putnam called the convergence of scientific knowledge. Because of this, Putnam’s realist hypotheses essentially rely on the historical stability of the connection between representations and reality that is established through interaction with the environment. Quine and van Fraassen, we have seen, focused on the two elements tied by this connection. Quine’s concern was with the way in which scientists construct representations: given our limitations as human beings confronted with an infinite amount of possible observation statements, there are always alternative, empirically equivalent but logically incompatible theories about reality possible. Van Fraassen’s concern was with how scientists interact with the environment: given that we, as human beings, are limited to interact with that which is observable for us, there is no reason to assume that our theories are true about that which goes on beyond what is observable. These arguments by Quine and van Fraassen are clearly concerned with the anthropology underlying Putnam’s realist strategy. They argue, more specifically, that if humans are limited to observers, then we cannot expect that which they produce – representations – to go beyond that which is observable – reality. And Laudan then argues that there is no reason, historically speaking, to take the success of a theory as a criterion for its approximate truth. In this way, Quine, van Fraassen and Laudan target the realist hypothesis, by arguing that we have no evidence for a historically stable connection between representations and reality that is established through successful interaction with our

25 The above does not mean that Laudan is an anti-realist. He points out at the end of his article that it should not be read as refuting the in principle possibility of scientiﬁc realism: “[a]ll of us would like realism to be true; we would like to think that science works because it has got a grip on how things really are. But such claims have yet to be made out. Given the present state of the art, it can only be wish fulﬁlment that gives rise to the claim that realism, and realism alone, explains why science works” (1981, p. 48).

18 Experiment, Time and Theory environment. And they do this in a way that is very similar to Hacking’s claim that the realism-issue is a product of an observation-focused anthropology. In what follows, we will discuss how Cartwright and Hacking tried to overcome these issues on the basis of a diﬀerent anthropology, one that conceptualizes human beings not as observers but as manipulators. On this view, “[e]xperimental work provides the strongest evidence for scientiﬁc realism [. . . ] because entities that in principle cannot be ‘observed’ are regularly manipulated” (Hacking, 1983, p. 262).

1.4 Manipulability and the Realist Strategy

1.4.1 Ian Hacking: Manipulating the Unobservable Manipulability and observation Before we turn to how manipulability can give rise to an argument in favour of scientiﬁc realism,26 we ﬁrst need to discuss how Hacking sees observation and manipulability. Hacking does not dispute that observation can play a role in science, but it certainly is not as important as many philosophers take it to be:

Observation, as a primary source of data, has always been a part of natural science, but it is not all that important. Here I refer to the philosophers’ conception of observation: the notion that the life of the experimenter is spent in the making of observations which provide the data that test theory, or upon which theory is built. This kind of observation plays a relatively minor role in most experiments. Some great experimenters have been poor observers. Often the experimental task, and the test of ingenuity or even greatness, is less to observe and to report, than to get some bit of equipment to exhibit phenomena in a reliable way. (Hacking, 1983, p. 167)27

26 The concern here is primarily with the manipulability-idea as a proposal for a realist position, and not with whether Hacking himself is or was a realist. For while he does elaborate a proposal for a realist position, he also states that he does not see it as an issue of much importance: “Hacking (1983) took scientific realism seriously when it presented an experimental argument for realism about theoretical entities – as the best argument, not as a conclusive one. A remark on page 2 is seldom noticed: ‘Disputes about both reason and reality have long polarized philosophers of science. [. . . ] Is either kind of question important? I doubt it.’ I continue to doubt it” (Hacking, 2012, footnote 4, p. 606). We can also wonder whether Hacking took the explicit elaboration of a realist position on the basis of his manipulability-approach to be the best way to contribute to the debate. For, according to him, “[d]efinitions of ‘scientific realism’ merely point the way. It is more an attitude than a clearly stated doctrine. It is a way to think about the content of natural science. [. . . ] [W]e speak of movements rather than doctrine, of creative work sharing a family of motivations, and in part defining itself in opposition to other ways of thinking. Scientific realisms and anti-realisms are like that: they too are movements. We can enter their discussions armed with a pair of one-paragraph definitions, but once inside we shall encounter any number of competing and divergent opinions that comprise the philosophy of science in its general state” (Hacking, 1983, p. 26). 27 A similar point is made by Cartwright: “[M]any of the things that are realities for physics are not things to be seen. They are non-visual features – the spin of the electron, the stress between the gas surface, the rigidity of the rod. Observation – seeing with the naked eye – is not the test of existence here. Experiment is. Experiments are made to isolate true causes and to eliminate false starts” (Cartwright, 1983, p. 7).

19 Chapter 1. Manipulation and Realism

To understand how we are to conceptualize observation in science, according to Hacking, we need to take into account that scientists need to learn how to observe, and this learning is something that is done by doing: “you learn to see through a microscope by doing, not just by looking” (Hacking, 1983, p. 189). It is by handling and working with a sample under a microscope that we learn, according to Hacking, to be observant about what is going on, in the sense that one notices when one is correctly observing: “[t]he good observer is often the observant one who sees the instructive quirks or unexpected outcomes of this or that bit of equipment” (1983, p. 167). As such, observation is but one of many practices employed in science in order to investigate whether we are dealing with an actual object or an artifact:

Practice – and I mean in general doing, not looking – creates the ability to distinguish between visible artifacts of the preparation or the instrument, and the real structure that is seen with the microscope. This practical ability breeds conviction. (Hacking, 1983, p. 191)

In this way, Hacking displaces the epistemological focus from observation to manipulation. It is through learning how to manipulate a preparation under a particular kind of microscope that we obtain the ability to observe that we are indeed dealing with something real, i.e. independent from our experimental set-up, rather than with an artifact. This is not, however, something that one obtains merely from interventions within one particular set-up. It emerges by varying the set-ups in which we handle that which we are studying: “[i]f you can see the same fundamental features of structure using several diﬀerent physical systems, you have excellent reason for saying ‘that’s real’ rather than, ‘that’s an artifact”’ (Hacking, 1983, p. 204). In this way, observation can oﬀer a criterion for reality only insofar as it is itself a practice in which one carries out manipulations. So how are we to see such manipulability-based realism?

Manipulability and realism Hacking’s realism is often summarized in terms of the slogan “if you can spray them then they are real” (Hacking, 1983, p. 23). He makes this claim in the context of a discussion of experiments to detect quarks. While it was long thought that there was an elementary unit of charge, e, embodied by the electron, theoretical advances in particle physics suggested an entity, a quark, with a charge of 1/3e. The experiments were carried out on a ball of niobium that was rendered superconducting by cooling below the temperature of 9K, which means that “[o]nce an electric charge is set going round this very cold ball, it stays going, forever” (Hacking, 1983, p. 23).28 Because of its particular state of magnetization, this superconducting ball can then be kept afloat in a magnetic field, and its position and velocity can be changed by varying the strength of the magnetic field. The charge of the current on the ball is then changed by spraying it, i.e. by firing particles with positive or negative charge at it: positrons (positive charge) if one wants to increase the charge on the niobium ball, or electrons in order to decrease it. At a certain point, the charge will change from positive to negative (or vice versa), and

28 The early history of superconductivity will be the subject of chapter 3. In short, when certain substances are cooled below a particular temperature while a magnetic ﬁeld with a strength below a certain threshold is applied, they become superconducting, which means that a current, i.e. a stream of charged particles, will arise on the surface of the substance, and it will continue running as if it experiences no resistance.

20 Experiment, Time and Theory it is then measured whether this transition occurs precisely at zero or ±1/3e. If the latter were the case, there should be at least one loose quark on the niobium ball. These experiments provided measurements of “four fractional charges consistent with +1/3e, four with −1/3e, and 13 with zero” (Hacking, 1983, p. 23). The realism that we should infer from these kinds of experiments, according to Hacking, is not concerned with the existence of quarks. For there were theoretical and experimental worries about what was measured exactly. Rather, his claim concerns that with which the charge of the niobium ball was manipulated, i.e. the electrons and positrons that were used to influence the behaviour of the object studied. This can only be done because “[w]e understand the effects, we understand the causes, and we use these to find out something else” (Hacking, 1983, p. 24). Entities such as e.g. the electron and the positron in this case “are tools, instruments not for thinking but for doing” (Hacking, 1983, p. 262). It is with respect to these entities, i.e. those which can be manipulated as instruments in an experimental situation, that we can be realist, according to Hacking’s “if you can spray them then they are real” (Hacking, 1983, p. 23).29 On Hacking’s view, we do not have to be realists about the entities that we want to investigate: they could turn out very differently than we hypothesized. This is not the case for the entities we manipulate and use in these investigations: “[e]xperimenting on an entity does not commit you to believing that it exists. Only manipulating an entity, in order to experiment on something else, need do that” (Hacking, 1983, p. 263). And this form of realism, according to Hacking, is significantly different from the realism about theories that one normally finds in philosophy. For there is no such thing as the theory of the electron that is used when these entities are manipulated in experiments to measure, for example, the charge of a ball of superconducting niobium when it changes from negative to positive charge:

But might there not be a common core of theory, the intersection of everybody in the group [of experimenters], which is the theory of the electron to which all the experimenters are realistically committed? I would say common lore, not common core. There are a lot of theories, models, approximations, pictures, formalisms, methods and so forth involving electrons, but there is no reason to suppose that the intersection of these is a theory at all. Nor is there any reason to think that there is such a thing as ‘the most powerful non-trivial theory contained in the intersection of theories in which this or that member of a team has been trained to believe.’ Even if there are a lot of shared beliefs, there is no reason to suppose they form anything worth calling a theory. (Hacking, 1983, p. 264)

On the manipulability-approach, realism about the electron is thus not a realism about the theory of the electron. It is rather a realism about the electron as an

29 Hacking (1983, 265 – 275) also makes similar claims in a discussion of the construction of PEGGY II, a polarizing electron gun that fired a laser beam, i.e. a stream of electrons, in order to test whether weak neutral currents displayed parity conservation, which would show itself in a difference in number between electrons with left-handed and right-handed polarization. The construction of this instrument shows, according to Hacking, that we can be justified in taking the electron to exist, because we can manipulate it by means of its causal properties in order to investigate weak neutral currents, without being committed to the truth of any kind of particular theory of the electron. Hence, we have entity realism without theory realism.

21 Chapter 1. Manipulation and Realism entity, or, more specifically, a realism about the electron’s causal properties insofar as they have been established in a robust way through several different experimental manipulations. For it is not the case, Hacking claims, that we are convinced of the electron’s existence once we have been able to manipulate it as we want in one particular experiment. Rather, we try to manipulate them in all kinds of ways, in a trial-and-error fashion, until we are convinced that we can reproduce reliable behaviour, of the form ‘if we manipulate in way x, we can expect effect y’. Such statements, which Hacking calls ‘home truths’, contain causal information about how the electron’s properties interact with other aspects of nature, and it is about these that we become realists through repeated experimental manipulations of the electron:

We are completely convinced of the reality of electrons when we regularly set out to build – and often enough succeed in building – new kinds of device that use various well-understood causal properties of electrons to interfere in other more hypothetical parts of nature. (Hacking, 1983, p. 265)

As we will see soon, the manipulability-idea allows for the elaboration of a response to the central arguments raised against the standard scientiﬁc realist. As such, it can allow for a viable realist position, at least insofar as these responses are satisfactory. It is mainly through Nancy Cartwright’s (1983; 1999) work that such a position has been formulated.30

1.4.2 Nancy Cartwright: Constructing Nomological Machines How the Laws of Physics Lie Cartwright’s entity realism is very similar to Hacking’s.31 Both argue that while we have no reason to believe in the truth of theoretical laws,32 causal knowledge can provide us with independent reasons to believe in the existence of some entities postulated by those theories. However, while Hacking focuses on causal knowledge obtained through experimental manipulations, in her book How the Laws of Physics Lie (1983) Cartwright focuses on how it is obtained through the construction of explanations. In philosophy, she starts her book, a distinction is often made between phenomenological laws, which are about the observable appearances, and theoretical laws, which are concerned with the unobservable reality behind the appearances. The standard realism-issue is then about whether we can take these theoretical laws

30 Hacking’s primary concern, we have seen in footnote 26, is not to elaborate such a position. As William Seager puts it: “Hacking’s views on entity realism [. . . ] are less worked out. If Cartwright represents the main column of the army, Hacking is more of a scout or sniper, ready to aid the attack but reluctant to fully join the ranks” (2012, p. 219). This does not mean that Hacking is not completely convinced of Cartwright’s work: as he puts it in the first paragraph of the acknowledgements of his (1983) book, “there are several parallels between her book and mine”, and “we converge on similar philosophies” (1983, p. vii). 31 Cartwright explicitly acknowledges the parallels between her work and Hacking’s, when she states that her book “is a complement [. . . ] to the fine dicussions of representation, experimentation, and creation of phenomena in Ian Hacking’s Representing and Intervening” (1983, p. 30). That they explicitly acknowledge the parallels with each other’s work is thus already a first parallel to be drawn. 32 Recall Hacking’s claim, discussed on page 6, that insofar as physics is concerned with representations, there is no truth to be had.

22 Experiment, Time and Theory to be true. But Cartwright takes this distinction to be misguided, and in need of replacement, since it is purely philosophical, and not connected to the practice of physicists. Practicing physicists, she claims, distinguish phenomenological laws from fundamental laws, a distinction that comes down to the following: For the physicist, unlike the philosopher, the distinction between theoretical and phenomenological has nothing to do with what is observable and what is unobservable. Instead the terms separate laws which are fundamental and explanatory from those that merely describe. [. . . ] In modern physics, and I think in other exact sciences as well, phenomenological laws are meant to describe, and they often succeed remarkably well. But fundamental equations are meant to explain, and paradoxically enough the cost of explanatory power is descriptive adequacy. Really powerful explanatory laws of the sort found in theoretical physics do not state the truth. (Cartwright, 1983, p. 2 – 3) Since phenomenological laws stay close to what is directly observed, they can be confirmed and hence are capable of being true.33 Fundamental laws, on the other hand, are more remote from physical experience, and hence cannot be confirmed in this way. Scientific realists, Cartwright (1983, p. 4) points out, normally claim that these laws are confirmed by [IBE]. But following van Fraassen (1980), Cartwright argues that this inference should not be taken to be generally valid, since there is no pressing reason to accept that a hypothesis offering the best explanation of a phenomenon entails the truth of that hypothesis. The central problem with this [IBE]-assumption, according to Cartwright, is that underlying it is a conception of explanation that does not do justice to scientific practice, namely the covering-law model of explanation. This model conceptualizes the search for an explanation as follows: [W]e fit a phenomenon into a theory by showing how various phenomenological laws which are true of it derive from the theory’s basic laws and equations. [. . . ] The ‘covering’ of ‘covering-law model’ is a powerful metaphor. It teaches not only that phenomenological laws can be derived from fundamental laws, but also that the fundamental laws are laws that govern the phenomena. They are the laws that cover the phenomena, perhaps under a more general or abstract description, perhaps in virtue of some hidden micro-structural features; but still the fundamental laws apply to the phenomenon and describe how they occur. (Cartwright, 1983, p. 16 – 17) Where the covering-law model goes wrong, more specifically, is that it assumes that it is “just the laws of nature [that] pick out which factors we can use in explanation”

33 Cartwright follows Francis Everitt in taking Airy’s law of Faraday’s magneto-optical effect as an example of a phenomenological law. Michael Faraday discovered that magnetism had a rotational effect on the polarization of light, i.e. on the direction of the wave’s oscillation with respect to the wave’s direction of motion. Airy showed, according to Cartwright, that “it could be represented analytically in the wave theory of light by adding to the wave equations, which contain second derivatives of the displacement with respect to time, other ad hoc terms, either first or third derivatives of the displacement” (1983, p. 2). This law is phenomenological in that it gives a description of the phenomenon, but no explanation. Such an explanation was given by Lorentz’s later electron-theoretical treatment of the effect (Cartwright, 1983, p. 2).

23 Chapter 1. Manipulation and Realism

(Cartwright, 1983, p. 45). On the covering-law view, we construct an explanation of a phenomenon by deriving the phenomenological law that describes it from the fundamental laws. These fundamental laws then explain the phenomenon and are, because of this explanatory power, taken to be true. This picture, however, cannot be correct, according to Cartwright, since many scientiﬁc explanations are in terms of laws that are not true:

Many phenomena which have perfectly good scientiﬁc explanations are not covered by any laws. No true laws, that is. They are at best covered by ceteris paribus generalizations – generalizations that hold only under special conditions, usually ideal conditions. The literal translation is ‘other things being equal’; but it would be more apt to read ‘ceteris paribus’ as ‘other things being right’. (Cartwright, 1983, p. 45)

While most philosophers take laws in physics to form exceptionless generalizations, Cartwright argues that their validity is in fact conditional: it is only under well- specified conditions that the behaviour described by the laws arises.34 Specified without these conditions, our fundamental laws are strictly speaking false, and hence they cannot be explanatory. And specified with these conditions, they hold only in these very few cases where the conditions are exactly right. As such, Cartwright argues, the covering-law model has a serious issue: “For most cases, either we have a law that purports to cover, but cannot explain because it is acknowledged to be false, or we have a law that does not cover” (1983, p. 45 – 46). The covering-law adherent will respond, according to Cartwright, that while we have not yet found the true condition-less formulation of e.g. Snell’s law, there is one to be found, and it is probably close in form to the current formulation of Snell’s law. But this, Cartwright claims, is a metaphysical bet that cannot be based on actual scientific practice. What we have there are lots of separate, very specialized fields of research without much unification. This entails that “[w]e do not know whether we are in a tidy universe or an untidy one”, and hence assuming that there is to be a condition-less regularity governing the whole is a metaphysical claim that goes beyond science (1983, p. 49). This line of reasoning does not lead her to a complete anti-realism, however: it is not because our explanatorily powerful theoretical laws are very limited in the cases they cover, and false about the other ones, that there is no realist interpretation to be given of how phenomena are explained in science. When a scientific explanation is given, according to Cartwright, what we obtain is what she calls an explanation by composition of causes. What we want to explain are complex phenomena, described by our phenomenological laws. We do this by breaking the phenomenon down into more simple components, i.e. contributions to the cause of the phenomenon, which are covered by different fundamental laws. We then combine these different accounts into an explanation of the complex phenomenon. This approach to explanation entails, according to Cartwright, the

34 Cartwright speciﬁes this by means of the example of Snell’s law, which links the angle of incidence θ and the angle of refraction θt of a ray of light passing from one medium to another one by means of the following equation, where v1 and v2 are the velocities of propagation in the two media, and n1 = c/v1 and n2 = c/v2 the indices of refraction (with c the velocity of light): sinθ/sinθt = n2/n1. This law in fact only holds when the two media are optically isotropic, i.e. that their permeability and permittivity for light rays is the same in all directions (1983, p. 46 – 48).

24 Experiment, Time and Theory trade-off between truth and explanatory power that we see in scientific practice. These fundamental laws are not true, since they do not describe the complex phenomenon found in nature, but rather some idealized case, in which the causal factor it describes would occur on its own.35 They are, however, explanatory, since they allow for the construction of explanations of these complex phenomena by means of the composition of different contributing factors (Cartwright, 1983, p. 59). It is this interpretation of the explanatory power of fundamental laws in terms of composition of causes that makes that Cartwright is not fully anti-realist. She rejects the [IBE] that we can only explain the explanatory success of our fundamental theories by accepting the hypothesis that these theories are true (1983, p. 75). For inferring truth from explanatory power requires that there are no other possible explanations, and this is not the case with theoretical explanations: there is always redundancy of theory, in the sense that there are always multiple possible theoretical explanations (Cartwright, 1983, p. 76). With causes, however, this is not the case. Once we have picked out a complete cause for a particular effect, we do not expect there to be other complete causes at work as well. If an effect occurs, and we have good reason to infer that this effect was brought about by a specific cause, then we do have good reason to believe in the existence of that cause. In this way, Cartwright replaces [IBE] with what she calls inference to the most probable cause:

[C]ausal explanations have truth built into them. When I infer from an effect to a cause, I am asking what made the effect occur, what brought it about. No explanation of that sort explains at all unless it does present a cause; and in accepting such an explanation, I am accepting not only that it explains in the sense of organizing and making plain, but also that it presents me with a cause. [. . . ] An explanation of an effect by a cause has an existential component, not just an optional extra ingredient. (Cartwright, 1983, p. 91)

What these causes denote, according to Cartwright, are speciﬁc items, i.e. theoretical entities: their properties are causally responsible for the phenomena captured in our phenomenological laws, and their existence is conﬁrmed if we are capable of explaining the observed phenomenon by causally connecting it to the causal properties that we ascribe to such an entity. Moreover, if we can show that a certain entity is causally responsible for a given phenomenon, then this connection is theory-independent: we can have many incomplete and incompatible theories about the entity, but if it is established that it is causally responsible, then that holds independently of whatever theory we prefer. Discussing the spraying-technique that led Hacking to his realism- claim, Cartwright similarly claims that it does not make much sense to assume that such a successful manipulation provides an argument for the realism of any theory of the electron:

35 They are idealized because, if we make their ceteris paribus clauses explicit, we come to see that they are (almost) never to be found in nature as such. The law of gravitation holds, for example, on the condition that there are no other forces at work besides the gravitational force. But these laws do not apply to the complex phenomena we ﬁnd in nature, where there are always other factors at work besides those stated in the ceteris paribus clause. It is not the case, according to Cartwright, that we ﬁnd in nature both a gravitational force and an electromagnetic one separately, and that these are then brought together by nature in a resultant force that gives rise to the complex phenomenon. Rather, only the resultant force is to be found in nature. See (Cartwright, 1983, p. 62 – 69) for an extensive discussion of this.

25 Chapter 1. Manipulation and Realism

What I invoke in completing such an explanation are not fundamental laws of nature, but rather properties of electrons and positrons, and highly complex, highly specific claims about just what behaviour they lead to in just this situation. I infer to the best explanation, but only in a derivative way: I infer to the most probable cause, and that cause is a specific item, what we call a theoretical entity. But note that the electron is not an entity of any particular theory. In a related context van Fraassen asks if it is the Bohr electron, the Rutherford electron, the Lorentz electron or what. The answer is, it is the electron, about which we have a large number of incomplete and sometimes conflicting theories. (Cartwright, 1983, p. 92)

As such, Cartwright’s realism diﬀers from standard realism in that it does not take explanatory success to lead the truth of the laws that are used to construct the explanation. It rather gives us reason to believe in the existence of the causal properties that our laws of nature allow us to bring together into an explanation of a complex phenomenon. As such, we could say that these laws of nature are true about the entities endowed with these causal properties. But these properties, we have seen, can be found only in very idealized circumstances, and hence these laws are only true ceteris paribus. In her book The Dappled World (1999), Cartwright elaborates in more detail how we are to understand these circumstances.

The Dappled World Ceteris paribus laws, Cartwright claims, “obtain only in special circumstances: they obtain just when a nomological machine is at work” (Cartwright, 1999, p. 25). Such a machine comes down to the following:

What is a nomological machine? It is a ﬁxed (enough) arrangement of components, or factors, with stable (enough) capacities that in the right sort of stable (enough) environment will, with repeated operation, give rise to the kind of regular behaviour that we represent in our scientiﬁc laws. (Cartwright, 1999, p. 50)

This regular behaviour of correctly operating nomological machines is thus what we describe in our phenomenological laws. And these machines can be expected to bring about such regular behaviour because they consist of causes, what Cartwright calls capacities or natures, that will give rise to this regular behaviour according to our fundamental laws, when composed and shielded in the right way (1999, p. 65). Such machines thus consist of theoretical entities which are endowed with capacities for displaying a particular kind of behaviour when placed in the right circumstances.36 Important here is that the behaviour of these capacities is in itself open-ended: “[o]bjects with a given capacity can behave very differently in different circumstances” (Cartwright, 1999, p. 59). Hence, depending on how we arrange a capacity within a nomological machine, it can display different behaviour. But

36 While there are a few nomological machines to be found in nature, such as e.g. the planetary system, most of the regular behaviour described by phenomenological laws and accounted for by theoretical laws is found in nomological machines of our own making, according to Cartwright: “Sometimes the arrangement of the components and the setting are appropriate for a law to occur naturally, as in the planetary system; more often they are engineered by us, as in a laboratory experiment” (Cartwright, 1999, p. 49).

26 Experiment, Time and Theory they will only function together properly, in the sense that the machine will display a phenomenological regularity, if they are shielded: “[i]t is not enough to insist that the machine have the right parts in the right arrangement; in addition there had better be nothing else happening that inhibits the machine from operating as prescribed” (Cartwright, 1999, p. 57). In this way, our ceteris paribus laws of nature can be said to be true in exactly those cases where we have particular capacities operating together in specific circumstances without interference. The knowledge we obtain in science should therefore not primarily be characterized in terms of laws of nature belonging to particular theories, since what these laws explain exactly – the behaviour displayed by theoretical entities – depends on the circumstances in which it occurs. Rather, what we primarily learn in science, especially through experimentation, are the causal capacities that entities have, what Cartwright calls their natures: “our basic knowledge – knowledge of capacities – is typically about natures and what they produce” (Cartwright, 1999, p. 80).37 What is characteristic about this kind of knowledge is that it distinguishes what an entity can do from what that entity is: “[f]or modern science what something really is – how it is defined and identified – and what it is in its nature to do are separate things” (Cartwright, 1999, p. 81).38 She now elaborates how this knowledge is to be seen in terms of capacities operating within a particular nomological machine by means of the following three points. First, knowledge of a particular nature should not be taken to correspond with any particular kind of substance, as the example of the agitated atom shows (see footnote 38): independently of what we take to be the atom, we can have the knowledge that when it is agitated within a particular set-up, it will produce light. As such, “we assign natures not to substances but rather to collections or configurations of properties, or to structures” (Cartwright, 1999, p. 81). Second, the phenomenon observed in a particular experimental set-up should not be taken to be the result of one particular nature: “what appears on the surface is a result of the complex interaction of natures” (Cartwright, 1999, p. 81). Hence, we should not take observation itself as a guide for distinguishing different natures: “[i]t takes the highly controlled environment of an experiment to reveal them” (Cartwright, 1999, p. 81). And third, we should not see these natures as the essential behaviour of an entity: which be-

37 Cartwright often switches between talk about capacities and talk about (Aristotelian) natures, but this should not be taken as indicating any kind of significant difference: “When we ascribe to a feature (like charge) a generic capacity (like the Coulomb capacity) by mentioning some canonical behaviour that systems with that capacity would display in ideal circumstances, then I say that that behaviour is in the nature of that feature. Most of my arguments about capacities could have been put in terms of natures had I recognised soon enough how similar capacities, as I see them, are to Aristotelian natures” (Cartwright, 1999, p. 84 – 85). 38 This is a point that Cartwright already raised in her (1983), when she claimed that in science, we can obtain all kinds of causal knowledge about the behaviour of electrons without having any particular true theory about what the electron is (see the quote on page 26). Cartwright now also gives a similar example, in terms of the emission of photons by an atom: “An atom in an excited state, when agitated, emits photons and produces light. It is, I say, in the nature of an excited atom to produce light. Here the explanatory feature – an atom’s being in the excited state – is a structural feature of the atom, which is defined and experimentally identified independently of the particular nature that is attributed to it. It is in the nature of the excited atom to emit light, but that is not what it is to be an atom in excited state” (Cartwright, 1999, p. 81). Whatever we take an atom to be exactly, through experimentation and manipulation we can know, according to Cartwright, that it is in its nature to produce light when agitated. In this way, she takes modern science to have separated identity from behaviour.

27 Chapter 1. Manipulation and Realism haviour will be displayed depends not only on the entity’s nature, but equally well on the circumstances in which it is placed. If we characterize the knowledge provided by science in terms of these three points, Cartwright then claims, we can see how experimentation can provide us with causal knowledge about an entity’s capacity. We construct our experiments, more speciﬁcally, by means of a two-step procedure that is supposed to bring out the capacity under ideal circumstances:

First we try to find out by a combination of experimentation, calculation and inference how the feature under study behaves, or would behave, in a particular, highly specific situation. By controlling for or calculating away the gravitational effects, we try to find out how two charged bodies ‘would interact if their masses were zero’. But this is just a stage; in itself this information is uninteresting. The ultimate aim is to find out how the charged bodies interact not when their masses are zero, nor under any other specific set of circumstances, but rather how they interact qua charged. That is the second stage of inquiry: we infer the nature of the charge interaction from how charges behave in these specially selected ‘ideal’ circumstances. (Cartwright, 1999, p. 83 – 84, original emphasis)

What this shows, according to Cartwright, is that the process through which we can obtain knowledge of, for example, the nature of charge, i.e. what capacities for behaviour charged bodies can display, is in essence a procedure of idealization, where ‘ideal’ is to be read in two ways. First, it means that we are dealing with circumstances that mostly do not occur directly in nature, but rather only in very speciﬁc fabricated settings. And second, it means that these are the right circumstances for studying the nature in itself, i.e. without interference from other natures. It is when we recognize that this is indeed the case, i.e. that the fabricated circumstances entail that the behaviour displayed is without hindrance or impediment, that we can say that we have knowledge of a particular nature. In experimentation, we try to eliminate all kinds of external inferences that we can imagine, and if we then succeed in displaying a particular kind of behaviour that we take to be repeatable, we have good reason to assume, according to Cartwright, that we have succeeded in showcasing a particular nature. This in turn gives us reason to infer that the claim that, under these speciﬁc conditions, such behaviour will occur, is indeed a law of nature:39

We get no regularities withouth a nomological machine to generate them; and our conﬁdence that this experimental set-up constitutes a nomological machine rests on our recognition that it is just the right kind of design to elicit the nature of the interaction in a systematic way. (Cartwright, 1999, p. 89)

1.4.3 Manipulability and the Realism-Issue We have seen that, for Hacking and Cartwright, the main problem with the scientiﬁc realist position was its observation-focused epistemology. Instead of observation,

39 This can even be the case, as she argues by means of both the Stanford Gravity Probe experiment (1999, p. 85 – 95) and Newton’s prism experiment (1999, p. 102), for experiments we in fact never repeat.

28 Experiment, Time and Theory they claimed, we should focus on manipulability: it is through the repeated manipulation of particular experimental entities, under varying experimental set-ups, in order to obtain insight into the properties of postulated hypothetical entities, that we become convinced of the existence of these experimental entities. What we acquire insight into, more specifically, according to Cartwright, are the capacities these entities are endowed with, and the behaviour that is in their nature to display when they are placed within particular circumstances. It is the behaviour that these capacities display in such specific circumenstances that our fundamental laws of nature are concerned with. The realist position, we have seen, came down to the hypothesis that there is a historically stable connection between our representations and reality that is constructed through successful interaction with the environment. Putnam’s argument for this hypothesis was based on his representation-focused anthropology, according to which successful interaction gives us reasons to believe in the accuracay of the representations constructed and used in such an interaction. Quine and van Fraassen, however, provided anthropological arguments of their own, concerning the limitations of human beings as observers that construct representations, that problematized this correspondence between representation and reality. Instead of one representation corresponding to reality, they argued, the way in which scientists construct representations through their interactions with the environment makes us expect that there will always be multiple, incompatible theories that equally well account for, and are only true about, that which is observable, i.e. phenomena. And Laudan then argued that there is no reason to believe that successful interaction gives rise to a historically stable correspondence between representation and reality. Insofar as the manipulability-idea is to offer a viable realist position, it should therefore provide a response to these issues. In what follows, we will elaborate how Cartwright and Hacking see this response, and how this leads them to reconceptualize the three elements that raised issues for the realist anthropology: phenomena, theory and history.

Manipulability, Phenomena and Theory We have already seen that both Cartwright and Hacking follow van Fraassen in his claim that the empirical success of a scientific theory does not give us reason to believe that it is true about what goes on beyond observation. They do not follow him, however, into his constructive empiricist anti-realism, since it is still based on an observation-focused epistemology that does not fit well with what they take to be actual scientific practice. Scientists do often infer the existence of unobservable entities, but not by means of [IBE]. They rather do this by means of a combination of experimental manipulations and what Cartwright dubbed inference to the most probable cause. When scientists argue that a particular entity is the most probable cause of a phenomenon, then it is probable that the entity exists. If we are then able to use this causal information about the entity to manipulate it in such a way that the phenomenon arises, we have as good evidence as we can get that the entity exists. In this way, the manipulability-proposal does not fall prey to van Fraassen’s deconstruction of [IBE], since manipulation provides a theory-independent way to ascertain the existence of the entities postulated in explanations of phenomena. Van Fraassen’s deconstruction of [IBE], we have seen, was concerned with the way in which scientists interact with their environment: given that they are limited

29 Chapter 1. Manipulation and Realism to what is observable for them, we have no reason to assume that scientific theories are true about that which lies beyond the observable. Quine’s [UA], we have seen, was concerned with the other aspect of the realist’s correspondence between representations and reality, namely the way in which scientists construct theories: given that we are not capable of overseeing an infinite amount of possible observation sentences, we have to compress them in a finite formulation, which entails that there are multiple, incompatible and empirically equivalent ways to represent reality. According to Cartwright and Hacking, however, we do have a way of acquiring information about what goes on beyond the unobservable. If we can experimentally manipulate a theoretical entity, which we believe to be the cause of an observable effect because of an inference to the most probable cause, in such a way that the effect does indeed occur, then we have good evidence that the entity does indeed exist. And while this does not show us which theory about the identity of the entity manipulated is correct – as we have seen, Cartwright takes modern science to have separated identity and definition from behaviour (see page 27) – it does provide us with evidence for its existence, and knowledge about what is in its capacity to do within particular conditions. What these responses to Quine and van Fraassen show is that the manipulability- idea allows Cartwright and Hacking to reconceptualize the connection between representation and reality in the realist’s anthropology in such a way that it can with- stand the challenges raised. Instead of conceptualizing this connection in terms of a correspondence between observation sentences derived from a theory and observation sentences obtained through experimentation, we have causal knowledge of a theoretical entity, expressed in terms of home truths that tell us what to expect if we manipulate the entity in a specific way, and an experimental manipulation bringing about this effect. Successful interaction then does not mean observing what the observation sentences tell us, but rather bringing about what the home truths make us expect. And this success does not mean that a theory about the entity’s identity is true, but rather that the entity exists. This shows that the manipulability-idea brings Cartwright and Hacking to reconceptualize both theory and phenomena. Theories, on their view, are a collection of unrelated models, approximations, idealizations, etc., that can serve as instruments for the formulation of home truths.40 These home truths have to be constructed in this way because the laws provided by our theories do not apply directly to the complex phenomena that we are confronted with. Phenomena are not, as philosophers according to Hacking often assume, observable regularities out there in nature waiting to be discovered.41 Rather, they are significant or noteworthy regularities that are mostly created in the laboratory.

40 Hacking (1983, p. 209 – 219) offers a discussion of the different roles that theory and models can play. 41 Hacking characterizes this philosophical view as follows: “[p]henomena remind us, in that semiconscious repository of language, of events that can be recorded by the gifted observer who does not intervene in the world but watches the stars” (Hacking, 1983, p. 225). He contrasts it with what he takes to be the way in which scientists conceptualize phenomena, which he describes as follows: “[The term ‘phenomenon’] has a fairly definite sense in the common writings of scientists. A phenomenon is noteworthy. A phenomenon is discernible. A phenomenon is commonly an event or process of a certain type that occurs regularly under definite circumstances. The word can also denote a unique event that we single out as particularly important. When we know the regularity exhibited in a phenomenon we express it in a law-like generalization. The very fact of such a regularity is sometimes called the phenomenon” (Hacking, 1983, p. 221).

30 Experiment, Time and Theory

By this, Hacking means that for many regularities that we take to be phenomena, work is required in the sense that an apparatus needs to be devised that can bring about the regularity in a reliable and shielded way.42 Observing a phenomenon requires the elimination of interference and the puriﬁcation of materials. As such, it is manipulation that is responsible for what van Fraassen assumes that we observe directly:

To experiment is to create, produce, reﬁne and stabilize phenomena. If phenomena were plentiful in nature, summer blackberries there just for the plucking, it would be remarkable if experiments didn’t work. But phenomena are hard to produce in any stable way. That is why I spoke of creating and not merely discovering phenomena. That is a long hard task (Hacking, 1983, p. 230).

Manipulability and History As such, on Cartwright’s and Hacking’s formulation of the realist anthropology, manipulation can bring about a connection between representations, in the form of theory-independent causal knowledge expressed in home truths, and reality, in the form of experimentally created phenomena. In order to form a viable realist position, however, the manipulability-idea also has to entail that this connection is historically stable, in order to address Laudan’s [PMI]. The home truths that we obtain by means of successful manipulations are theory- independent, according to Hacking (see the quote on page 21) and Cartwright (see the quote on page 26). As such, insofar as Laudan’s [PMI] claims that theory change over time argues against the assumption that successful theories are true, it does not present an issue for Cartwright’s and Hacking’s position, since the home truths obtained by means of successful manipulation are theory-independent, and thus stable under theory-change:

[W]hen we can manipulate our theoretical entities in ﬁne and detailed ways to intervene in other processes, then we have the best evidence possible for our claims about what they can and cannot do; and theoretical entities that have been warranted by well-tested causal claims like that are seldom discarded in the progress of science. (Cartwright, 1983, p. 98)

As it did with the philosophical notions of phenomena and theory, the manipulability- idea now also brings Hacking to reconceptualize the notion of history underlying the realism-debate. When scientists in the laboratory are successful in manipulating

42 Hacking illustrates this with a discussion of the Hall effect: “the Hall effect does not exist outside of certain kinds of apparatus. Its modern equivalent has become technology, reliable and routinely produced. The effect, at least in a pure state, can only be embodied by such devices” (Hacking, 1983, p. 226). In his Treatise on Electricity and Magnetism (1873), James Clerk Maxwell suggested that when a magnetic field was applied to a conductor carrying a current, the field would act on the conductor but not on the current. E.H. Hall took this to mean that either the resistance of the conductor would be affected, or an electric potential might be produced. He did not find any evidence for the first interpretation, but when applying a magnetic field to a gold leaf carrying a current, he did obtain a potential difference across it with a direction perpendicular to the applied field and the current. Through later work, Hall showed that the effect also occurred in other materials, and hence “the buildup of a transverse voltage as an electric current passes through a metal in a magnetic field” became known as the Hall effect (Hoddeson et al., 1992, p. 112).

31 Chapter 1. Manipulation and Realism an entity, they establish, we have seen, a correspondence between representations (the home truths) and reality (a created phenomenon). The establisment of such a correspondence, Hacking argues in a later paper (1992), is in fact to be understood as a process of stabilization of a relation between three elements: ideas, items and marks.43 When searching for such a stability, each of these elements can be adapted: we can change our apparatus to bring it in line with theory, we can change our statistical methods in light of the obtained data, we can change our theories in response to the experimental results, etc. (Hacking, 1992, p. 54). This process is a historical process, in the sense that ideas, items and marks co-evolve in such a way that they become self-vindicating. They come to determine their own domain, and over time, items, ideas or marks that do not ﬁt within the co-evolved group are just taken to be outside of the domain of the stable ensemble: “[t]heories mature in conjuncture with a class of phenomena, and in the end our theory and our ways of producing, investigating, and measuring phenomena mutually deﬁne each other” (Hacking, 1992, p. 57). This entails that, within the laboratory sciences, the relation between an observation and a theoretical claim is often remarkable stable, since the experimental phenomenon and the theoretical account of it have evolved together:

[A]s a laboratory science matures, it develops a body of types of theory and types of apparatus and types of analysis that are mutually adjusted to each other. They become what Heisenberg [. . . ] notoriously said New- tonian mechanics was, ‘a closed system’ that is essentially irrefutable. They are self-vindicating in the sense that any test of theory is against apparatus that has evolved in conjunction with it – and in conjunction with modes of data analysis. Conversely, the criteria for the working of the apparatus and for the correctness of analyses is precisely the ﬁt with theory. (Hacking, 1992, p. 30)

In this way, the manipulability-idea leads to a reconceptualization of history. The history of the sciences is no longer to be conceptualized in terms of the convergence of scientiﬁc knowledge, but rather in terms of the self-vindication of a stable relation between ideas, items and marks.

1.5 Manipulability and its Relation to Theory

Manipulability and the realist strategy Cartwright’s and Hacking’s claim that the manipulability-idea can lead to a viable realist position essentially relies on their claim that the home truths concerning the causal properties of theoretical entities are theory-independent. For if they are not, then they could fall prey to the same issues as those raised against the standard scientiﬁc realist position. In what follows, I will discuss three arguments, by Margaret Morrison, Michela Massimi and

43 Under ‘ideas’, Hacking lists the following: questions, background knowledge, systematic theory, topical hypotheses, and modeling of the apparatus (1992, p. 44 – 46). The group of ‘things’ comprises the following: a target, a source of modiﬁcation or interference connected with the target, detectors, tools, and data generators (1992, p. 46 – 48). And in the group of ‘marks’, he places the following items: data, data assessment, data reduction, data analysis, and interpretation (1992, p. 48 – 50).

32 Experiment, Time and Theory

Theodore Arabatzis, that indicate that this assumption of theory-independence is problematic.44 The source of this problem, I will argue then, lies with the way in which Cartwright and Hacking characterize the information provided by these home truths. This will then lead to the research question, already stated on page 3, that is to guide and structure the rest of this dissertation.

1.5.1 Margaret Morrison: Manipulability and Theory Morrison’s primary target of her (1990) paper is Hacking’s notion of ‘home truths’, which “are supposedly robust under theory change and do not constitute anything like the kinds of complex frameworks that are normally taken to be definitive of a theory” (1990, p. 1). It is by means of this notion, according to Morrison, that Hacking tries to be a realist with respect to entities without committing himself to any full-blown theory. But this move is problematic, Morrison claims, for two reasons: first, she doubts whether “such theory-impoverished characterizations are really sufficient to describe the ways in which entities like electrons interact in con- crete situations” (1990, p. 6); and second, even if we are able to draw this distinction, it is not completely clear what should compel us to be realists about the first, but agnostic or even anti-realist about the second. Morrison elaborates the first problem by means of a discussion of instruments such as the cloud chamber, which is a detector that contains air that is supersatu- rated with water vapor. A charged particle moving through the chamber will ionize the air in the chamber, in such a way that water droplets will form around these ions, hence giving rise to a cloudy trail that can be taken as an indication of the charged particle’s trajectory. In order to determine further which kind of particle we are dealing with, magnetic fields are applied, which influence the specific trajectory of the moving particle. But this determination process, according to Morrison, now relies significantly on electromagnetic theory, mechanics, heat theory and atomic theory. As such, it seems that when we want to acquire further insight into the kind of particle we are investigating, we rely on more than just home truths, which raises the question how we are to distinguish the two (Morrison, 1990, p. 6 – 10). Even if we assume, for the sake of the argument, that we can in some cases distinguish low-level generalizations concerning the behaviour of the manipulated entity from higher level theory, Morrison’s second issue still remains. According to Hacking, because we have obtained these home truths through manipulation, we are automatically justified in being realists about them: we establish their truth through manipulation. It is this claim that Morrison disputes. For in order to understand what these home truths say about the behaviour of entities that are manipulated, she argues, we need to rely on larger theoretical frameworks, in order to make sense of the behaviour they display within a particular experimental set-up: we rely on theory when we use home truths about an electron’s charge to manipulate electrons in a cloud chamber (Morrison, 1990, p. 15 – 16). As such, it is unclear why successful manipulation would only commit us to a realism about home truths, since we always rely on both. If we want to be realists on the basis of manipulation, Morrison argues, this problem together with the previous one then leads to the following dilemma:

44 Besides the work by Morrison, Massimi and Arabatzis, there have also been some other criticisms of the entity realist position, which I do not discuss here. See Matthias Egg’s (2018) overview of the entity realist position for a more comprehensive oversight.

33 Chapter 1. Manipulation and Realism

If we acknowledge a realistic interpretation of home truths the set of such truths is often so small that no substantive characterization of the entities can be given. Home truths are not suﬃciently complex to allow for the kind of successful engineering Hacking demands. If, however, we enlarge the set of home truths to include accounts of causal interactions and processes based on higher level theory, then due to their instability we face the problems that beset theory realism. (Morrison, 1990, p. 16)

As such, Morrison raises issues with the theory-independence of the home truths used in successful manipulation, and as such, with the representation part of the historically stable connection between home truths and created phenomena that underlies Hacking’s and Cartwright’s proposal for a realist position. The problem is that manipulation is less theory-independent than Hacking (and Cartwright) assumes: “in privileging manipulation to the extent [Hacking] does and in separating entities from theories one tends to lose sight of the way that practice informs and is informed by theory” (Morrison, 1990, p. 20).

1.5.2 Michela Massimi: Manipulability and Phenomena Where Morrison questions the proclaimed theory-independence of the home truths obtained via manipulation, Michela Massimi’s (2004) article targets the direct connection, assumed by Hacking, between the manipulated cause and the phenomenological effect brought about in an experiment. The way in which experiments in particle physics convinced scientists of the existence of colored quarks as constituents of nucleons, Massimi argues, shows that even when a manipulation is taken to have been successful, “[t]here might be more than one potential causal entity at work behind the observed phenomena” (2004, p. 38). The only way to understand how scientists were convinced that the results of particular experiments showed that it were colored quarks, rather than partons, that constituted nucleons, is by taking into account a prior choice for the quark-theory over the parton-theory, since on their own, the data produced by the experimental manipulations carried out could not have provided a decision in favour of either particle. This leads her to a conclusion very similar to Morrison’s, namely that manipulability leads to evidential claims for the existence of an entity that are less theory-independent than assumed by Hacking: “sheer experimental evidence by itself does not tell us which entity is at work in the observed phenomena; for that we must commit ourselves to a full-blown scientific theory” (Massimi, 2004, p. 40). The standard model of elementary particles makes a division between leptons, which are particles with light masses (e.g. electrons, neutrinos and muons), and hadrons, which in turn divide into mesons, which are particles with medium mass (e.g. pions and kaons), and baryons, particles with heavy mass (nucleons, i.e. protons and neutrons) (Massimi, 2004, p. 41). What is specific about hadrons such as protons, in contrast with e.g. electrons, is that they are clusters of microscopic entities, and underdetermination can then arise with respect to these clusters: “there might be another cluster of rival entities equally accounting for the known properties of protons” (Massimi, 2004, p. 41).45 This was indeed the case, according to Massimi,

45 That we are dealing here with two diﬀerent clusters is important, according to Massimi, since it shows that Steve Clarke’s (2001) elaboration, from the perspective of entity realism, of

34 Experiment, Time and Theory in the case she discusses, which concerns the observed phenomena brought about in deep inelastic scattering experiments carried out in the 1970s, where a beam of leptons is fired towards a hadronic target. Through measurements of different features of the set of hadrons after the scattering, these kinds of experiments “offered for the first time experimental evidence for the existence of inner constituents of nucleons” (Massimi, 2004, p. 46). What Massimi now argues is that, with respect to what was manipulated in the experiments, the dynamical properties of both partons and quarks could equally well account for the data produced, even though these dynamical properties were radically different. On a purely experimental basis, there was thus no way to know which kind of entity was being manipulated. It was only by applying the theory of quantum chromodynamics (QCD), which is a natural habitat for the colored quarks but a strange environment for partons, to both the quark and the parton that a possible experimental result was suggested that could distinguish the two. The deep inelastic scattering experiments then produced this result, and only in this way can the experiments be seen as producing evidence in favour of quarks over partons (Massimi, 2004, p. 52 – 53). As such, Massimi can be seen as raising issues with the theory-independence of the creation of phenomena. Manipulation in itself did not tell us which phenomenon was displayed: did the data produced instantiate significant regularities regarding color quarks or regarding partons? As such, Massimi problematizes the reality-aspect of the historically stable connection between home truths and a created phenomenon that underlies Hacking’s and Cartwright’s proposal for a realist position. And this leads her to the same conclusion as Morrison, namely that Cart- wright and Hacking underestimate the importance of theory:

The main point of my argument is that whenever we have prima facie rival potential causes for the same phenomena, in order to distinguish between them and to determine what entity-with-causal-powers has actually produced the observed effects, we must in the end rely on the description of what causal powers/capacities/dispositions an entity is to have so as to produce the observed effects. This description is given by a scientific theory; and rival theories give rival descriptions. Only by choosing between different descriptions, and hence by committing ourselves to one theory rather than another, can we identify what entity is at work behind the experimental phenomena. (Massimi, 2004, p. 42 – 43) a response to an underdetermination argument such as the one presented by Massimi, is not completely sufficient. For Clarke sketches the underdetermination claim as the possibility that the phenomenological effects observed in an experimental set-up, assumed to be caused by an electron, are in fact caused by a cluster of microscopic particles that are invariably joined together. Clarke’s response to this would be the following: “[. . . ] the alleged different possible entities either turn out, on closer inspection, to be different theories about the composition, or the nature, of the same entity, or it turns out that we have not interacted with the entity that we are claiming exists, and that what has happened is a case of an experiment that, unbeknownst to us, has not been successful” (Clarke, 2001, p. 719). In the case Massimi is discussing, we are not dealing, however, with a choice between an entity we believe to exist, and the possibility of a cluster of unknown microparticles that somehow always display the same behaviour as we ascribe to the electron. Rather, we have two known possible clusters that are equal candidates for the constitution of the nucleon (Massimi, 2004, p. 41).

35 Chapter 1. Manipulation and Realism

1.5.3 Theodore Arabatzis: Manipulability and History In his (2006) book Representing Electrons, Theodore Arabatzis presents what he describes as a biography of the electron, one of the paradigmatic entities within the realism debate.46 This historical work, he argues, raises issues with Hacking’s notion of home truths, which for the electron “would include well-known causal properties of electrons, like their charge mass, and spin, which enable us to manipulate them in order to investigate other less well-known aspects of nature” (Arabatzis, 2006, p. 253). The problem is, as Morrison argued, that it is difficult to disentangle these home truths from a broader background theory. For example, the meaning of charge differed profoundly between Maxwellian electrodynamics, where it was merely an epiphenomenon of the electromagnetic field, and Lorentz’s electromagnetic theory, where it was an independent entity that could interact with the electromagnetic field. And even the causal properties ascribed to electric charge differ from theory to theory: whereas putting a charge in motion would make it radiate according to classical electrodynamics, it would not radiate according to the old quantum theory (Arabatzis, 2006, p. 253). Arabatzis then raises the question what this would mean for the entity realist with respect to the issue of theory change. Even what Hacking would consider to be home truths and causal properties are subject to theory change. If we cannot find a theory-independent stable core of properties that we can ascribe to the electron, how are we justified in claiming that we are still referring to the same entity, when our theories concerning the electron change? But we should not despair either, according to Arabatzis, since “[e]ven though [Hacking’s] ‘causal properties’ do not provide a theory-independent access to the corresponding entities, they do provide a core of meaning that has proved relatively immune to theory change” (2006, p. 257). Every future theory of the electron will at least have to incorporate these properties, or show how they can be reinterpreted. In this way, according to Arabatzis, history shows that over time, the electron has been characterized in terms of a relatively stable set of statements. These are not just causal claims about the electron’s properties, however, since we need a background theory as well to interpret them. Arabatzis therefore proposes to extend Hacking’s collection of causal properties to include any belief that is stable over theory change. Moreover, such a theoretical characterization of the electron in terms of beliefs about it that have remained stable over theory change only provides a necessary, but not a sufficient condition for realism about the electron: “[e]ven if

46 This biographical approach “amounts to considering theoretical entities as active agents whose internal dynamic transcends the beliefs, abilities, and wishes of human actors and acts as a constraint on the development of scientific knowledge. Even though they are the product of scientific construction, they have a certain independence from the intentions of their makers; that is, they have a life of their own” (Arabatzis, 2006, p. 36). Theoretical entities are, on Arabatzis view, the theoretical representations constructed by scientists of unobservable entities on the basis of particular data. They ascribe to these representations definite properties and laws, and it is because of these ascriptions that these entities can act, e.g. by being recalcitrant to attempts to make them obey to new results or theoretical hypotheses, or by raising questions that can then guide scientists in their further research. Elaborating the history of the electron from this perspective can then “illuminate the gradual transformation of the theoretical entity, showing how that transformation was hindered or facilitated by its previously acquired character” (Arabatzis, 2006, p. 42). In this way, the theoretical entity itself can become an explanatory resource for the historian, since it was, at least in part, the representations used at a certain point in time that influenced the way in which history developed further.

36 Experiment, Time and Theory a core of beliefs about electrons has not been aﬀected by theory change, one cannot exclude the possibility of an alternative, empirically adequate theory that would not include electrons in its ontology” (Arabatzis, 2006, p. 257). As such, Arabatzis raises issue with the theory-independence of the home truths, by arguing that they are not immune to theory change, not even when our characterization of the electron is extended to include all beliefs about it that have been stable until now. As such, he problematizes the historical stability of the connection between home truths and created phenomena that underlies Hacking’s and Cartwright’s proposal for a realist position.

1.6 Research Question

As we have seen in the beginning of section 1.5, the viability of the entity realist position essentially relies on the claim that the home truths obtained by means of successful experimental manipulations provide scientists with theory-independent knowledge of the causal properties of the entities manipulated. These home truths or capacity claims have to be theory-independent in order to ensure that the entity realist does not fall prey to the arguments raised against the traditional scientific realist. That this knowledge is theory-independent means, on Cartwright’s and Hacking’s account, that manipulation in itself can tell us that we are dealing with a particular entity endowed with specific causal properties responsible for the created phenomenon, and that this knowledge is established in the sense that it remains stable over time under theory change. What Morrison, Massimi and Arabatzis all three argue, however, is that it is not possible to obtain such information purely on the basis of experimental manipulations. The issue is that entity realism expects from successful experimental manipulation not solely information about the entity manipulated, but also that it shows in some sense that this information is justified. It should convince the scientist that the manipulation carried out was indeed successful, which means that the experimental manipulation should bring about the effect that we would expect on the basis of the entity’s causal properties.47 But such justification cannot be obtained solely from the effect brought about by the manipulation, as Massimi argues. How could the results of the deep inelastic scattering experiments in themselves convince the scientists that they were successfully manipulating quarks and not partons, given that their different causal properties could bring about exactly the same results? On a purely phenomenological level, there would be no difference between manipulating one entity rather than another, and it was only because of a prior commitment to one theory that this conviction could arise. As such, it is unclear how we are to understand the theory-independence of the home truths that we use in successful maniulation. And even if we were able to distinguish the home truths from the theoretical claims used by the scientists in these experiments, Morrison then asks, why should we take successful manipulation to entail realism with respect to these home truths,

47 That this is the case can be seen from the quotes by Hacking on page 20, where he states that it is through manipulation that one breeds conviction, and that learning to observe by means of manipulation allows one to see whether equipment has functioned properly. Cartwright expresses similar thoughts in the quote on page 28.

37 Chapter 1. Manipulation and Realism but not for the theoretical claims concerning the identity of the entity that was supposedly manipulated? One cannot argue that contrary to these theoretical claims, the home truths have remained stable over theory change, since, as Arabatzis has shown in his biography of the electron, these home truths are subject to theoretical change as well. As such, the home truths at play in experimental manipulations are not as theory-independent as Cartwright and Hacking assume. Scientists have to rely on theory in order to make sense of what they are manipulating exactly. This entails, as all three argue, that if one wants to remain committed to the realism of the entity realist position, one ends up as a standard scientiﬁc realist, since successful manipulation inextricably involves theory. As Massimi puts it, they are rather to be seen as two versions of the same realism, one top-down from theory to entities, and one bottom-up from manipulation to theory:

Scientific realism traditionally contends that we are justified to believe in the theoretical claims of our scientific theories, and that we must read these claims literally, i.e., we must believe that the entities postulated by the theories exist and have the properties defined by the theories. This is a typical top-down approach: from theory-realism to entity-realism, where belief in the existence of scientific entities is justified on theoretical grounds (insofar as they are postulated by the theories we believe to be true). Here I want rather to suggest the following bottom-up approach to scientific realism, starting from the experimental ground typical of experimental realism: the decisive evidence that warrants us to believe in the existence of some entities with certain properties [. . . ] is tout court the same evidence that warrants us to believe in the scientific theory concerning these entities, rather than in a rival one. (Massimi, 2004, p. 43)

Morrison’s, Arabatzis’ and Massimi’s concern is primarily with entity realism as a realist position, and hence after reaching this conclusion, they then consider what kind of argument the manipulability-idea could provide in favour of scientiﬁc realism.48 As we have seen, however, what gave rise to the issues discussed above was exactly that Cartwright and Hacking conceptualized their manipulability-idea in terms of a realist epistemology. Manipulability in itself had to provide scientists with the established theory-independent knowledge that they are manipulating a particular entity endowed with speciﬁc causal capacities. But it is not because the manipulability-idea was formulated in terms of a problematic epistemology that we have to throw out the whole idea, especially given that it seems intuitive to say that manipulability can provide us with some kind of information, even though this information is not as Cartwright and Hacking conceptualized it. Because of this, this dissertation will be concerned with the following research question, which we already encountered on page 3:

48 There are quite some different characterizations of the manipulability-idea as an argument in favour of realism to be found in the literature. Morrison (1990) has argued that we can only make sense of this claim if we take it as a transcendental argument. Richard Reiner and Robert Pierson (1995) have argued that it in fact forms an inference to the best explanation. And Boaz Miller (2016) has argued that there are in fact five different argumentative readings: a no miracles argument, an indispensability claim, a transcendental argument, what he calls a vichian argument, or not in fact an argument at all.

38 Experiment, Time and Theory

[Research Question]: How are we to characterize the information provided by experimental manipulations?

In the following two chapters, this question will be investigated by means of a discussion of two historical episodes concerning the experimental manipulation of the electron. Chapter 2 concerns the experiments carried out by Walter Kaufmann and others on the velocity-dependence of the electron’s mass, and chapter 3 covers the experiments by Heike Kamerlingh Onnes and others on the state of magnetization of superconducting materials.49 The aim of these chapters is to investigate how the scientists involved took the manipulations carried out on these entities to provide information about the electron’s properties. In line with the motivation of the research question, my concern will not be with whether these manipulations provided evidence for the existence of the electron. In both cases, all scientists involved took their existence as already established. In this way, the epistemology of manipulation can be investigated without framing it in terms of existence, and the focus can be strictly on the kind of information produced about the electron’s identity. A second characteristic of the experiments discussed, besides that they do not concern the electron’s existence, is that the information they were taken to provide changed over time. While the experiments were, for a certain time, taken to be successful in providing insight into specific properties of the electron, they were later seen either as not successful or as successful in a different way than was assumed before. Investigating which factors were responsible for this change will provide us with information about the factors at play in a scientist’s conviction that a manipulation has been successful, i.e. that it provides information about the properties of the manipulated entity. What motivated me to study these historical episodes in the first place were statements by some philosophers of science, claiming that the transformations in the information supposedly provided by the manipulations in these episodes were either theory- or experiment-driven. They claimed that it was either solely through new theoretical developments or through new experimental developments that the original interpretation of the experimental results brought about by means of manipulation was shown incorrect.50 Investigating these episodes in more detail convinced me, however, that this could not be the case, and that the establishment and transformation of the information provided was instead the result of a delicate interplay between theory and experiment. As such, the research presented in this dissertation should not be seen as merely philosophical: it was rather developed in a way that tries to integrate history and philosophy of science.

49 As we will see, the superconducting state was conceptualized in terms of the motion of the electrons constituting the superconducting currents, and hence, these experiments also concerned the manipulation of electrons. 50 As such, it was not Hacking’s or Cartwright’s entity realism that originally drove me to investigate these historical episodes. Rather, in the case of the Kaufmann experiments, it was Michel Janssen’s (2009, p. 35) claim that it were theoretical developments regarding special relativity that showed that Kaufmann’s experimental results were wrong, a claim to which I responded in my (2019a) article. In the superconductivity case, it was the debate between Cartwright, Mauricio S´uarezand Towﬁc Shomar on the on hand, and Steven French and James Ladyman on the other, about whether the development of the London & London model of superconductivity was either theory- or experiment-driven. In my (2019b) article, I argued that the development was neither purely theory-driven nor solely experiment-driven.

39 Chapter 1. Manipulation and Realism

On the basis of these discussions, I will then elaborate, in chapter 4, an alternative to Hacking’s and Cartwright’s characterization of the information provided by experimental manipulation. On the basis of Friedrich Steinle’s work on exploratory experimentation, Michela Massimi’s work on exploratory modeling, and Uljana Feest’s work on the stabilization of phenomena, I will argue that this information is rather to be characterized in terms of modal, not factual, knowledge about the properties of the entities manipulated, where this modality is shapen and constrained by how a scientist conceptualizes what she takes to be earlier successful manipulations of the entity. In this way, I will claim, we can understand how certain scientists can be convinced that experimental results provide specific information about the more hypothetical properties of the entity manipulated, while others see the experimental manipulations as providing a different kind of information. This work will also allow me to argue that it is when (later) experimentation and modeling work closely together that there can be significant transformations in the information that an earlier experiment is supposed to provide. I will call the epistemology of manipulation I will develop there an epistemology of exploration. In the final part of chapter 4, I will then return to the realism-issue and the anthropology underlying it. I will argue there that if it is indeed the case that the recognition of a manipulation as successful depends on what a scientist takes to be earlier successes, that something extra needs to be added to the anthropology, namely temporal dimensions. This will lead me to reconceptualize what it means for the connection between representation and reality that is at the heart of the realist hypothesis to be historically stable. This historical stability is not something that is to be discovered as a given, but rather something that scientists constantly remake in the light of how they conceptualize successful experimental manipulations.

40 Chapter 2

Experiment and the Electron’s Velocity-Dependence of Mass

2.1 Introduction

The first historical episode to be discussed concerns experiments on the velocity- dependence of the electron’s inertial mass.51 That an electron’s inertial mass should depend on its velocity was first suggested by J.J. Thomson (1881) as follows. When a charged body is at rest, it is surrounded by its own electrostatic field. When it is moving, Maxwell’s equations tell us that in addition, it will also give rise to a magnetic field. As such, “a charge in motion must accordingly pass through its own electromagnetic field, with a consequent decrease in velocity – just as if it had gained mass” (Staley, 2008a, p. 220). The experiments that will be discussed investigated this phenomenon by measuring and comparing the charge-to-mass ratios of electrons with different velocities, whose motion was taken to be quasi-stationary.52 The masses obtained through an analysis of their charge-to-mass ratios, could then provide information about the precise way in which these masses depended on the electron’s velocity. The main reason for carrying out these experiments was the belief that they could provide insight into, and maybe even a definitive answer regarding, the electron’s constitution, i.e. its form, charge distribution and dynamics.53 These kinds of experiments involving either Becquerel rays (later known as β- rays) or cathode rays, were first carried out by Walter Kaufmann (1901a; 1901b; 1902; 1903; 1906b), and later by Adolf Bestelmeyer (1907), Alfred Bucherer (1908) and Karl Erich Hupka (1909). Especially Kaufmann’s results were seen as significant, since they were long taken to provide strong evidence in favour of Max Abra-

51 In general, a body’s inertial mass m is deﬁned, in line with Newton’s equation F = ma, as the ratio of the force F exerted on the body and the body’s acceleration a produced by that force. For a historical-conceptual discussion of the concept of inertial mass and its relations to other conceptions of mass in physics, see Jammer (1961, 2000). 52 That an electron’s motion is described as quasi-stationary comes down to “the assumption that the instantaneous electromagnetic mass of an accelerating charge was the same as the mass of an equivalent charge in a state of uniform motion with the same velocity” (Warwick, 2003, p. 391). 53 Mechanics, i.e. the science of bodies in motion, is generally divided into two parts: kinematics, “the science that deals with the motions of bodies or particles without any regard to the causes of these motions”, and dynamics, “the science that studies the motions of bodies as the result of causative interactions” (Jammer, 2000, p. 5).

41 Chapter 2. Experiment and the Electron ham’s electromagnetic account of the electron over the relativistic electron-account proposed by Hendrik Antoon Lorentz, Henri Poincaréand Albert Einstein. Ac- cording to Poincaré,for example, Kaufmann’s (1906b) experimental results entailed that the principle of relativity could not be as universal as was often assumed: “in their newest version, Kaufmann’s experiments have confirmed Abraham’s theory. The principle of relativity hence does not seem to have the rigorous value that was assumed” (Poincaré,1906a, p. 262).54 By the end of the decade, however, this situation had changed, as one can glimpse from the following statement by Max von Laue:

Every completely static system behaves in the case of quasi-stationary acceleration as a mass point. The electron with its ﬁeld as well is a system of this kind; this result now teaches us the following: out of experiments on the quasi-stationary acceleration of electrons one cannot conclude anything about its form or charge distribution, nor about the part contributed by the electromagnetic momentum to its total momentum. (von Laue, 1911, p. 170)55

While Kaufmann’s experiments were a central point of discussion and investigation regarding the electron’s constitution until a few years earlier, as we will see in detail in what is to follow, von Laue states here that their importance is overestimated: they cannot provide any concluding insight into the electron’s constitution. It is von Laue’s view that seems to have survived over time. In Arabatzis’ biography of the electron (see footnote 46), for example, we ﬁnd the claim that Kaufmann’s experiments only reﬁned and sharpened earlier results, obtained by Thomson and others:56

54 Except for Einstein, none of the other scientists discussed have been translated, so I will provide my own translations. I have added the original text in footnote, for the sake of comparison. In the case of Einstein I have made use of the translation by Anna Beck of the Einstein Papers project (see footnote 113). The original French goes as follows: “[s]ous leur nouvelle forme, elles [i.e. Kaufmann’s experiments] ont donnéraison àla théoried’Abraham. Le Principe de Relativité n’aurait donc pas la valeur rigoureuse qu’on étaittentéde lui attribuer”. 55 The original German goes as follows: “Jedes vollständigestatische System verhältsich bei quasistationärerBeschleunigung wie ein Massenpunkt. Auch das Elektron mit seinem Feld ist ein System der genannten Art; daher lehrt dies Ergebnis: Man kann aus Versuchen über quasis- tationäreBeschleunigungen des Elektrons niemals eines Rückschluß ziehen auf seine Gestalt und Ladungsverteilung sowie über den Anteil des elektromagnetischen Impulses am Gesamtimpuls.” 56 I have chosen to end the historical episode with von Laue’s claims about the experiments, even though afterwards there were still experiments carried out on the velocity-dependence of the electron’s mass (see the references in footnote 154), for the following reasons. First, von Laue’s (1911) discussion forms the latest extensive discussion, from a relativistic point of view, of these experiments that I have found in the literature. Second, his book was, as Richard Staley describes it, “[t]he first and authoritative textbook on relativity” (2008a, p. 334). As such, we can expect that its treatment of the Kaufmann experiments has been quite influential. This indeed seems to be the case, given that most theoretical work in fundamental physics carried out in the years after seemed no longer concerned with the electron’s mass. Attention rather turned towards the development of quantum theory and what later became known as the general theory of relativity. And finally, this chapter is based on, and is a further elaboration of, an article of mine (Potters, 2019a), in which I discussed Michel Janssen’s (2009) account of the relativistic response to Kaufmann’s experiments. Since Janssen claimed there that it was especially through von Laue’s work that it became clear that the importance of these experiments was overestimated, my focus has been mainly on the historical period up until von Laue’s (1911) book.

42 Experiment, Time and Theory

In the subsequent development of the representation of the electron, the value of its charge-to-mass ratio was refined (but not altered significantly) and the experimental situations associated with it expanded in a cumulative fashion [. . . ]. Even when Kaufmann’s investigations of β-rays showed that their charge-to-mass ratio varied according to their velocity, this effect did not call into question the identification of β-rays with fast-moving electrons. (Arabatzis, 2006, p. 108)

I have no problem with the final part of Arabatzis’ claim, namely that all involved assumed that the experiments were concerned with electrons. As we will see, however, the electron’s precise charge-to-mass ratio and how to obtain it was the issue of much dispute. Because of this, these experiments and the responses they received provide an excellent opportunity to study the research question that I have outlined in the previous chapter. This chapter will therefore be concerned with the way in which the manipulations carried out by Kaufmann and others in their experiments – which were manipulations of the electron’s charge-to-mass ratio through the application of electric and magnetic fields – were taken to provide information about the electron’s dynamics by different scientists at the time, and how this changed over time, in such a way that von Laue could claim by 1911 that we should not take these experiments to provide any information about the electron’s constitution.

2.2 Kaufmann’s First Experiments and the Elec- tromagnetic Electron

In 1896, Pieter Zeeman carried out experiments that showed that if one applies a magnetic field to a sodium flame, its spectral lines will split, which indicated that magnetism has an effect on light.57 This could be explained by Lorentz’s electrodynamical theory (1895), which saw the molecules that make up the rays of light emitted by the flame as constituted by what Lorentz called ‘ions’, small particles that carry charge. To ensure that his ion-model fitted the observed spectral lines, Lorentz had to assume that this ion was negatively charged, and that its charge-to-mass ratio (/µ) was 103 times smaller than the mass of the positively charged hydrogen ion. Since Lorentz could determine that the ion’s charge had to be more or less of the same magnitude as that of the hydrogen ion, he was then brought to the conclusion that this ion’s mass had to be approximately 350 times smaller than hydrogen ion’s mass (Arabatzis, 2006, p. 85). Hence, these experiments indicated that “the ‘ions’ did not refer to the well-known ions of electrolysis, but corresponded instead to extremely minute subatomic particles” (Arabatzis, 2006, p. 83).58

57 Spectral lines are discontinuities in the wave spectrum of emitted radiation, i.e. dark or bright lines in an otherwise continuous and uniform spectrum. See Klaus Hentschel’s entry on Spectroscopy in the Compendium of Quantum Physics (2009, p. 721 – 725) for a short historical oversight of the study of spectra. For a historical discussion of Zeeman’s work, see (Arabatzis, 2001) and (Arabatzis, 2006, p. 74 – 86). 58 Electrolysis is a phenomenon that occurs in certain substances called electrolytes: applying a current to these substances will decompose them in charged ions and non-charged molecules (Darrigol, 2002, p. 83). The hydrogen ion was at that time the particle with the smallest known mass-to-charge ratio (opposite of charge-to-mass) (Smith, 2001, p. 43).

43 Chapter 2. Experiment and the Electron

Zeeman was not the only one to obtain such charge-to-mass ratios that suggested the existence of charged bodies that were much smaller than hydrogen ions. Exper- iments by, among others, Kaufmann, Thomson and Emil Wiechert provided similar results for the particles assumed to constitute cathode rays between 1897 and 1899 (Smith, 2001, p. 21 – 22).59 These results taken together, and the fact that they could be accounted for by different theories, led many scientists to believe in the existence of these subatomic charged particles (Arabatzis, 2006, p. 104 – 105). It also prompted many investigations into their properties and the role they play in different phenomena. In his (1901a) lecture to the Naturforscherversammlung (the annual meeting of German natural scientists), Kaufmann gave a summary of the most recent findings. They had shown, he claimed, that this particle was to be characterized in terms of a mass and a charge, which could be either positive (in which case the particle would be bound to a molecule) or negative (in which case the particle could move freely). It contributed to all sorts of radiation – cathode rays, Röntgen rays, Becquerel rays, black-body radiation – and it was responsible for electrolysis, the conduction of currents through metals and gases, as well as many optical phenomena (Kaufmann, 1901a, p. 10 – 14). Regarding the many different theoretical investigations that were around at the time, Kaufmann (1901a, p. 14) picked out one, which concerned an idea first suggested by Theodor des Coudres (1898), namely that the electron’s total mass µ consisted of an unchangeable, mechanical part m (often called the ‘real mass’ at the time) and a velocity-dependent, electromagnetic part µe (often called its ‘apparent mass’). This distinction had recently led Wilhelm Wien (1901) to the suggestion that the electron’s mass could be completely electromagnetic in nature, which meant that its inertial mass could be accounted for completely in terms of the electromagnetic forces exercised on the electron by electric and magnetic fields. If, moreover, electrons could be taken to be the fundamental building blocks not only of electromagnetic phenomena but of all matter, Wien then argued, this could lead to the elaboration of an electromagnetic world view, according to which the laws of electrodynamics would replace those of mechanics as the foundation for the whole of physics. Kaufmann presented Wien’s hypothesis as follows:60

If, purely because of its electrodynamical properties, an electron were to behave exactly the same as an inertial mass-particle, would it then not be possible that all mass were merely apparent? Should we not, instead of all these unfruitful attempts to account for the electric phenomena in a mechanical way, inquire into the opposite, namely to reduce mechanics to electric phenomena? [. . . ] If all material atoms consist of a collection of electrons, their inertial mass can be obtained immediately. (Kaufmann, 1901a, p. 14)61

59 These different experiments have given rise to a whole philosophical debate about whether we can ascribe the discovery of the electron to any one of them in particular, and what it means to speak about a discovery in this case. See Arabatzis (2006) and the papers in Buchwald and Warwick (2001) for an overview of the debate. 60 Ever since Russel McCormmach’s first papers on the topic (1970a; 1970b), there has been a debate within the history of science on how to identify the electromagnetic program and its influence exactly. For the most recent version of this debate, and a good overview of the existing literature, see the papers by Suman Seth (2004; 2005), Shaul Katzir (2005) and Richard Staley (2008b). 61 The original German goes as follows: “Wenn ein elektrisches Atom bloss vermögeseiner

44 Experiment, Time and Theory

As Wien (1901, p. 513) had already pointed out, however, this was merely a theoretical suggestion, which could only be elaborated further by means of experiment. Given that such experiments were not available yet, Kaufmann proposed to investigate the issue through a study of the way in which applied electric and magnetic ﬁelds would inﬂuence the mass of the electrons constituting Becquerel rays.62

Kaufmann’s First Experimental Run Recent experimental investigations on Becquerel rays had shown, according to Kauf- mann, that these were qualitatively similar to cathode rays – they are both de- flectable by electric and magnetic fields and their charge-to-mass ratios are of the same order of magnitude – even though there were quantitative differences: the deflection of Becquerel rays by magnetic fields, for example, seemed to be much larger, and they could attain a velocity v much closer to the velocity of light (up to 0.9c) than cathode rays (around 0.3c) (Kaufmann, 1901b, p. 143 – 144). Wien (1901, p. 509) had already pointed out that, in order to be able to best observe the velocity- dependence of the electron’s mass, one would have to work with very high velocities, since at lower velocities the effect would be too small to notice. Given, however, that the existing experiments on Becquerel rays were somewhat crude, Kaufmann set out both to improve on them and, by doing this, to obtain information about the electron’s velocity-dependent mass:

The goal of the experiments that will be presented in what is to follow is to determine the velocity and the ratio /µ for Becquerel rays as exactly as possible, and at the same time to obtain, out of the degree of dependency between /µ and v, information about the ratio of “real” and “apparent” mass. (Kaufmann, 1901b, p. 144)63

Kaufmann’s experimental set-up at the time looked more or less as on figure 2.1.64 As the source of his electrons, Kaufmann used a piece of radioactive radium bromide, which he placed at point O on one side of a lead barrier with a diaphragm D. The elektrodynamischen Eigenschaften sich genau so verhält,wie ein träges Massenteilchen, ist es dann nicht möglich, überhaupt alle Massen als nur scheinbare zu betrachten? Könnenwir nicht statt all der unfruchtbar gebliebenen Versuche, die elektrischen Erscheinungen mechanisch zu erklären, nun umgekehrt versuchen, die Mechanik auf elektrische Vorgängezurückzuführen? [. . . ] Wenn alle materiellen Atome aus einem Konglomerat von Elektronen bestehen, dann ergiebt sich ihre Trägheitganz von selbst.” 62 Recent investigations by Henri Becquerel and Pierre and Marie Curie on radium had shown that this material would emit radiation, Becquerel rays more specifically, out of its own, i.e. without any external interference. They had also shown that these rays could be deflected by applying electric and magnetic fields, which allowed for the measurement of their charge-to-mass ratio, which was of the same order of magnitude as that of cathode rays, and of their velocity, which could be almost as high as the velocity of light. Because of these properties, Kaufmann suggested, these rays offered a good way to investigate experimentally into the precise contribution of the electron’s velocity-dependent (apparent, electromagnetic) mass to its total mass (1901a, p. 14). 63 The original German goes as follows: “Zweck der im Folgenden mitgeteilten experimentellen Untersuchung ist es, die Geschwindigkeit sowie das Verhältniß /µ fürBequerelstrahlen möglichst genau zu bestimmen und gleichzeitig aus dem Grade der Abhängigkeit zwischen /µ und v Auf- schluß über das Verhältnißvon ‘wirklicher’ und ‘scheinbarer’ masse zu erhalten.” 64 In fact, this figure represents an improved version of the experiment, carried out a few years later, which was, however, very similar to the experimental set-up of Kaufmann’s (1901b) experiments.

45 Chapter 2. Experiment and the Electron

rays where then guided through two capacitor plates P1 and P2, which, if turned on, gave rise to a constant electric field E. The enclosure was evacuated of air as much as possible, in order to prevent the radiation from ionizing any remaining air, since this would influence the applied electric field. The whole set up was surrounded by two electromagnets (not depicted on figure 2.1) that gave rise to a magnetic field B. The direction of both fields was perpendicular to the electrons’ direction of motion. The electrons emitted would then end up leaving a mark on a photographic plate (see figure 2.3 for an example of a plate from a later run), which was situated at a specific distance from the source that could be adjusted by means of screws in the colums S1,S2 and S3.

Figure 2.1: Frontal and top view of Kaufmann’s experimental set-up from a later run of experiments. This ﬁgure is larger than the set-up was in reality: for his (1901b, p. 145) run of experiments, the set-up measured more or less 3 cm in length (from O to B), 2 cm in width and 4, 5 cm in height. Figure source: (Kaufmann, 1906b, p. 496).

One particular characteristic of Becquerel rays is that their velocity spectrum is inhomogeneous, i.e. there is a great variation in the precise velocity of the diﬀerent emitted particles that make up the radiation. By making use of August Kundt’s method of crossed spectra, Kaufmann was able to disentangle the electrons moving at diﬀerent velocities. The method goes more or less as follows:65 when no electric

65 See (Cushing, 1981), (Miller, 1981, p. 48 – 50), (Staley, 2008a, p. 225) for a more elaborate

46 Experiment, Time and Theory or magnetic fields are applied, all electrons, regardless of their velocity, end up at the same place on the plate, opposite the diaphragm, and form a dot, depicted as the point B(0, 0, 0) on figure 2.2. Applying solely an electric field leads to a deflection in the z-direction, with the higher-velocity electrons being deflected more, in such a way that they will form the image of a straight vertical (x−z)-line on the plate. The further a dot is removed from the point B, the higher thus its velocity. Applying both a magnetic and an electric field then leads to a curved line in the y − z-plane, where the higher-velocity electrons are on the upper end of the curve (see figure 2.2 for a graphical representation of the deflection of the electron, and figure 2.3 for an example of such a photographic plate).

Figure 2.2: Geometrical representation of the deﬂection in the y − z-plane resulting from the application of both an electric and a magnetic ﬁeld. Figure source: (Hon, 1995, p. 181).

Kaufmann let his experimental set-up run for about three to four days, in order to obtain a sufficient number of dots on the plate. After two days he would reverse the direction of the applied electric field, thus mirroring the curve around the z- axis (see figure 2.3), in order to check the homogeneity of the field. If its strength had changed, this would be visible because the two curves would not be symmetric around the z-axis (Staley, 2008a, p. 227). Kaufmann would then measure, for each of the dots captured on the plate, its precise distance (O, y0, z0) from the point of origin (O,O,O).66 These different points would then be fitted together in a curve with a particular curvature ρ. Combining these measurements with information about the invariant quantities of his set-up, such as the distance set by the screws and the strength of the applied electric and magnetic field, then allowed him to determine the electron’s charge-to-mass ratio and mass.67 The curvature ρ of the obtained curve in the y − z-plane is linked to the electron’s charge-to-mass ratio e/µ explanation of this method. 66 These were precision measurements: the photographic plates of his first run allowed him to measure distances as small as 1/200 cm (Kaufmann, 1901b, p. 148). 67 The discussion that follows is mainly based on Kaufmann’s original (1901b) paper, Cushing (1981) and (Miller, 1981, p. 47 – 54).

47 Chapter 2. Experiment and the Electron

Figure 2.3: Kaufmann’s famous plate 19 from his (1903) experiments, which he described as ”oﬀering by far the most clear and problem-free image” (Staley, 2008a, p. 232). Its actual size is tiny: more or less 2 × 2 cm. Figure source: (Miller, 1981, p. 65).

(where e = /c) and its velocity by means of the following equation: 1 e = B (2.1) ρ µvc

The y0-deﬂection brought about by the electric ﬁeld E is described by the following equation, where s1 denotes the point of maximum curvature, and s2 the projection on the x − y-plane of the β-ray’s linear trajectory (Kaufmann, 1901b, p. 151): e y = Es s (2.2) 0 µv2 1 2 Equations (2.1) and (2.2) then give the following equation for β (= v/c):

β = Es1s2/y0ρB (2.3) They also provided Kaufmann with an equation for the electron’s charge-to-mass ratio /µ (1901b, p. 151): v = (2.4) µ ρB Applying these equations to his photographic plate68 then showed him that there was indeed a velocity-dependence of the electron’s mass µ:

/µ varies very strongly in the observed interval; with increasing v, /µ decreases very strongly, which entails a not insigniﬁcant part of ‘apparent mass’, and this part has to increase when the velocity of light is approximated. (Kaufmann, 1901b, p. 153)69

The central question, however, was not primarily whether there was such a dependence, but rather how much it was precisely. To determine this, Kaufmann

68 In his first run of experiments, Kaufmann obtained two photographic plates. Only one of those was really usable, however, since the other one was obtained without a constant electric field (Kaufmann, 1901b, p. 152). 69 He could conclude this from the measurements of the electron’s charge-to-mass ratio, since it was generally assumed at the time that the electron’s charge remained stable with changing velocity (Cushing, 1981, p. 1138). As such, a changing charge-to-mass ratio was taken to indicate a change in the electron’s mass. The original German goes as follows: “/µ variirt in dem beobachteten Intervall sehr stark; mit wachsendem v nimmt /µ stark ab, woraus ein nicht unbeträchtlicher Anteil von ‘scheinbarer Masse’ folgen würde,welch letztere ja bei Annäherungan die Lichtgeschwindigkeit zunehmen muß [. . . ].”

48 Experiment, Time and Theory proceeded as follows. The total mass µ of the electron, we have seen, was assumed to consist of a constant part m, its real or mechanical mass, and a variable part µe, its apparent or electromagnetic mass:70

µ = m + µe (2.5) To calculate the electron’s apparent mass µe, Kaufmann used an equation provided by G.F.C. Searle (1897) for the energy of a moving sphere, with the electron’s e 4 2 2 apparent mass in the case of no applied ﬁelds µ0 = 3 (e /2Rc ), and R the electron’s radius:

1 dEe 3 µe 1 1 + β 2 µe = = 0 − ln + (2.6) v dv 4 β2 β 1 − β 1 − β2 By means of this equation, Kaufmann could then re-express the electron’s charge- to-mass ratio of equation (2.4) so as to isolate the velocity-dependent part of the electron’s mass η (η = µ/m):

e /µ = /(m + µ0η) (2.7) During this first series of experiments, Kaufmann could carry out five deflection- measurements on the photographic plate obtained (1901b, p. 154). Taking these as input for equation (2.7) then provided him with a charge-to-mass ratio /µ for 71 high-velocity-electrons and a charge-to-mass ratio /µ0 for low-velocity electrons. The value obtained for this second one was close to one obtained earlier by S. Simon (1899) for cathode rays. Applying these equations to the results derived from his plate then led him to the result that for low-velocity electrons one third of their mass was apparent or electromagnetic in nature, and that for high-velocity electrons we could expect the electromagnetic part of their mass to be larger:72

For velocities that are low with respect to the velocity of light, the ratio of apparent to real mass is [. . . ] approximately 1/3. Even though this last number is still characterized by considerable uncertainty (an error of 10% in the constants determining the magnetic deﬂection would make the real mass vanishingly small), one can still claim, on the basis of the results obtained above, that the apparent mass is of the same order of magnitude as the real mass and that, in the cases of the fastest Becquerel rays, it even overpasses the latter one. (Kaufmann, 1901b, p. 155)73

70 The e-superscript indicates that this mass is induced by electromagnetic fields. 71 Since low-velocity electrons were less prone to deflection, their values were very close to that of the non-deflected electrons. Hence, these are also indicated with the 0-subscript. 72 Kaufmann does not specify why he does not give a number for the dependence for high- velocity electrons, but I assume that it is because there were still many uncertainties involved in the experimental set-up, and because it would require more data. 73 The original German goes as follows: “Das Verhältnißvon scheinbarer zu wirklicher Masse beträgtalso fürGeschwindigkeiten die klein sind gegen die Lichtgeschwindigkeit [. . . ] angenähert 1/3. Wenn auch die letztere Zahl noch mit erheblicher Unsicherheit behaftet ist (ein Fehler von 10% in den fürdie magnetische Ablenkung maßgebenden Konstanten würde die wirkliche Masse verschwindend klein machen) so kann man doch auf Grund obiger resultate schon soviel behaupten, daß die scheinbare Masse von derselben Größenordnung ist wie die wirkliche und bei den schnellsten Becquerelstrahlen die letztere sogar bedeutend übertrifft.”

49 Chapter 2. Experiment and the Electron

In this way, Kaufmann’s ﬁrst series of experiments provided evidence that the electron’s mass indeed depended on its velocity, and that this dependence seemed to get bigger for faster electrons. At the same time, however, Kaufmann (1901a, p. 155) himself pointed out that the speciﬁcs of the results depend on the electron model used, namely Searle’s spherical charge model. It is this assumption that Max Abraham discussed in his interpretation of Kaufmann’s experiments.

Abraham’s Electromagnetic Momentum

The main issue with Searle’s model, according to Abraham (1902, p. 21), was that it could not provide what Kaufmann is in fact after. In Kaufmann’s experimental set- up, the electron’s acceleration was almost completely transversal, i.e. perpendicular to its direction of motion, because of its magnetic deflection in the y-direction. Such acceleration does not involve a change in energy, and hence it could not be computed from Searle’s equation (2.6) (see page 49). Given that two different accelerations were involved, a model was required that provided two different inertial masses: the electron’s longitudinal mass mk, i.e. its inertia opposing its acceleration in the direction of its motion, and its transverse mass m⊥, i.e. its inertia opposing its acceleration perpendicular to its motion (Staley, 2008a, p. 229). Searle’s model could only provide the electron’s longitudinal mass, but not what Kaufmann was in fact after, namely its transverse mass. To overcome this, Abraham set out to construct an alternative model of the electron (1902, p. 21).74 Abraham constructed his model of the electron on the basis of the following constraints. First, it could not be conceived as a point particle, since this would entail that its energy would be infinite (Abraham, 1902, p. 22). Second, he assumed that its motion was quasi-stationary, which meant that its velocity could only change slowly, i.e. not instantaneously, which allowed for the computation of its electromagnetic field purely on the basis of its momentaneous velocity (see footnote 41 for a general description of quasi-stationary acceleration). This was an important assumption, since it allowed Abraham to equate the electron’s mass times acceleration (ma in Newton’s equation) to its rate of change of momentum (Miller, 1981, p. 59), which provided him with a way to compute the electron’s mass that did not rely on its energy, as in the case of Searle’s model: Abraham could conceptualize it in terms of its momentum. He borrowed, more specifically, the notion of electromagnetic momentum G from Poincaré,which was formulated in terms of the Poynting vector S (the directional energy transfer per unit area per unit time of the electromagnetic field, S = 1/(4πc)(E × B)): G = (1/c2) · RRR dV S, where V denotes the electron’s volume (Abraham, 1902, p. 25). This assumption of quasi-stationary acceleration now entailed that both the electron’s electromagnetic energy and its electromagnetic momentum depend only on the electron’s velocity, since it is this velocity that completely determines its field (Abraham, 1902, p. 26). As such, by means of the quasi-stationary assumption, Abraham could formulate the following expressions for the electron’s electrodynamic longitudinal and transverse mass in terms of the electron’s electromagnetic energy

74 This discussion is mainly based Abraham’s original (1902) paper and (Miller, 1981, p. 55 – 61). Abraham (1903) oﬀers a very extensive elaboration of the electromagnetic foundations of the points raised here. For a good historical discussion of Abraham’s work, see e.g. Goldberg (1970).

50 Experiment, Time and Theory and momentum:75

dG µe = ; (2.8) k dv

G µe = (2.9) ⊥ v To apply these equations, assumptions needed to be introduced about the electron’s constitution, since G depended on its volume, and hence on its shape. In order to obtain these, Abraham reasoned as follows. A general requirement was that force- free motion – i.e. “inertial motion that could be maintained without any external forces balancing the electron’s [self-induced] forces” (Miller, 1981, p. 57 – 58) – had to be possible in all directions. This required that the electron’s momentum was collinear with its velocity, which could only be obtained, Abraham showed, if its shape is symmetrical about axes perpendicular to its direction of motion. (1902, p. 31). This left two possible shapes for the electron, an ellipsoidal one and a spherical one. For both shapes, Abraham showed, it does not make any real difference whether we distribute its charge over its volume or only over its surface (1902, p. 36; 38). Applying his spherical electron-model to Kaufmann’s (1901b) observations then led Abraham to the claim that if one conceives of the electrons that constitute cathode rays and low-velocity Becquerel rays as spherical charges, their mass could be accounted for in completely electromagnetic terms: their µ⊥ was close enough to e Abraham’s µ⊥. For high-velocity Becquerel rays, the results were less clear, since it was more difficult to measure their deflection precisely. In order to overcome this, more experiments were needed, but this discrepancy between measurement and theory could not be overcome, according to Abraham, by introducing a mechanical mass besides their electromagnetic mass. As such, he concluded that the experiments provided good evidence for the electromagnetic nature of the electron’s mass:

The introduction of a constant ‘material’ mass will not cancel out the deviation between theory and experiment, but rather enlarge it; for the theoretical mass will, when a constant element is added to it, increase even slower with rising velocity [relative to the theoretical mass without a constant element]. If there really is such a deviation when the velocity of light is approximated, then unknown inﬂuences have to be at play. If it is merely because of experimental errors, then we will be able to conclude: the inertial mass of the electron is completely brought about by its electromagnetic ﬁeld. (Abraham, 1902, p. 40)76

75 To obtain these, Abraham reasoned as follows. The total force experienced by the electron e consisted of two parts: the force Fext due to external ﬁelds, and the force F due to the self-induced e ﬁelds. In terms of the Newtonian force law, this then gave the following: F + Fext = m0a. Here, m0 denoted the mechanical mass, which was, given Abraham’s adherence to the electromagnetic e world view, equal to zero (m0 = 0), which hence provided F + Fext = 0. Now, according to Newtonian mechanics a force exercised on a body is equal to the rate of change of the body’s momentum. With regards to the electron’s electromagnetic momentum, this then entailed that e F = −dG/dt and Fext = dG/dt, which in turn allowed for the calculation of the electron’s longitudinal and transverse mass (Miller, 1981, p. 59 – 60). 76 With theoretical mass, Abraham means here the mass predicted by his electron model, which he contrasts with the observed mass of Kaufmann’s experiments. The addition of a constant element he is referring to would be the introduction of a mechanical mass m besides the electron’s

51 Chapter 2. Experiment and the Electron

Kaufmann’s Conﬁrmation Kaufmann (1902) immediately accepted Abraham’s corrections of his original experimental analysis. Applying Abraham’s notions of electromagnetic momentum and transverse mass to his original calculations then showed him that the equations (2.1) and (2.2), discussed on page 48 had to be replaced. According to Abraham’s theory, the electron’s transverse mass was given by the following equation:

3 m = µeψ(β) (2.10) ⊥ 4 0 where, with β an electron’s velocity relative to the velocity of light, i.e. β = v/c:

1 1 + β2 1 + β ψ(β) = ln − 1 (2.11) β2 2β 1 − β

Kaufmann now applied equation (2.10) to his experimental set-up as follows. From his photographic plates, we have seen, he obtained a curvature ρ and, for each electron, a deﬂection y0 caused by the magnetic ﬁeld B. This allowed him to calculate values for s1, the point of maximum curvature, and s2, the projection on the x − y- plane of the Becquerel rays’ linear trajectory. Filling in these values in equation (2.3) provided him with a value for β for each dot on the plate. This could in turn be used, by means of equation (2.11), to obtain a value for ψ(β) for that particular point. In terms of the values obtained by means of Kaufmann’s experimental set-up, equation (2.10) could then be expressed as follows:

s1s2 4 B 2 ψ = e 2 (2.12) y0ρ 3 µ0 E Applying this to his original measurements then showed, he claimed, that Abra- ham’s electromagnetic hypothesis was indeed correct: “The mass of electrons is completely electromagnetic in nature” (Kaufmann, 1902, p. 295).77 One issue that arose, however, concerned the value of the velocity of light he calculated by means of his equation (2.11) for ψ(β), on the basis of the charge-to-mass ratio of lower-velocity electrons: this was 7.2% lower than it should be, which, according to Kaufmann, was probably due to observational errors and the applied electric field being not completely constant over time.78 Correcting for these then led him to a value for e /µ0 that was even closer than his (1901b) estimate to the value obtained by Simon (1899) for /µ0, which Kaufmann took as an indication that there had been errors in his original (1901b) experimental procedures. electromagnetic mass µe. The original German goes as follows: “Die Einführungeiner constan- ten ‘materiellen’ Masse würdedie Abweichung zwischen Theorie und Experiment nicht aufheben, sondern vergrößern;denn die theoretische Masse würde,bei Hinzufügung eines constantes Gliedes, relativ noch langsamer mit wachsender Geschwindigkeit ansteigen. Tritt jene Abweichung wirklich bei Annäherungan die Lichtgeschwindigkeit ein, so müssenunbekannte Einflüsseins Spiel kommen. Ist sie nur durch Versuchsfehler bedingt, so wird man behaupten können: Die Trägheitdes Electrons ist ausschließlich durch sein electromagnetisches Feld verursacht.” 77 The original German goes as follows: “Die Masse der Elektronen ist rein elektromagnetischer Natur”. 78 This was an essential requirement, since in order to obtain sufficiently accurate photographic plates, Kaufmann had to keep his experiment running for 48 hours. Inconstancies in the electric field over this period entailed a larger error margin in his measurements (Miller, 1981, p. 53).

52 Experiment, Time and Theory

In order to overcome these, Kaufmann then decided to carry out new, improved experiments by using a stronger source of electrons and a better battery for keeping the electric field constant over time (1903, p. 90 – 91).79 This allowed him to obtain a finer curve and a bigger deflection, hence improving the accuracy of his measurements. The experimental set-up itself remained the same. Kaufmann also changed his way of analysing the photographic plates: instead of calculating the curvature ρ directly from the points (y0, z0) on the plate, Kaufmann used what he called ‘reduced electric and magnetic deflections’ y0 and z0, which were values extrapolated from y0 and z0 by multiplying them with infinitely small deflections, i.e. the ratio of the apparatus’s dimensions to the infinite limit of s1s2. This allowed him to obtain points for the calculation of the curvature that would render the curve more proportional to the actual deflection.80 Combining the equations for these reduced constants with equation (2.12) then allowed him to re-express the charge-to-mass ratio of low-velocity Becquerel rays as e /µ0 = k1k2N1, where “k1, k2 and N1 where constants that depended on the apparatus’ dimensions, the velocity of light and the electric and magnetic field strengths” (Miller, 1981, p. 63). This offered him a more theory-independent way of comparing e the value for /µ0 obtained from theory with that determined through experimentation. He then compared his results with Abraham’s electron-model, with respect e to both ρ and /µ0, which led him to the claim that the agreement for both values was satisfactory (Kaufmann, 1903, p. 100). To ensure that his experiments were in agreement with earlier measurements, he also compared the value he obtained e for /µ0 with the one obtained by Simon (1899), as he had done for his earlier experiments. While there was a 6% difference,81 this was probably due to observation errors, according to Kaufmann. This led him to the conclusion that the results corroborated Abraham’s hypothesis that the electron’s mass is completely electromagnetic in nature:

The result of this investigation can be summarized as saying that not only Becquerel rays but also cathode rays consist of electrons whose mass is completely electromagnetic in nature (Kaufmann, 1903, p. 103)82

Abraham’s Rigid Electron With Kaufmann’s (1902) claim – “[d]ie Masse des Elektrons ist rein elektromagnetischer Natur” (see footnote 77) – as his starting point, Abraham (1903, p. 107) turned towards the elaboration of a completely electromagnetic dynamics of the

79 It is from this run of experiments that Kaufmann obtained the photographic plate depicted here as figure 2.3. 80 These reduced deflections are “proportional to the actual experimental deflections [y0 and z0] and differ very little from them” (Cushing, 1981, p. 1141). The main reason why Kaufmann introduced them was because it simplified the calculation: “[t]o facilitate the calculations required, Kaufmann considered only deflections that were infinitely small relative to the dimensions of his apparatus and reduced his actual observations appropriately” (Staley, 2008a, p. 240). 81 In the original publication, Kaufmann (1903, p. 102) actually claimed that his measurements differed from Simon’s with only 4%. However, as he pointed out in the errata to this article (1903, p. 148), this value was based on an incorrect calculation. 82 The original German goes as follows: “Wir könnendas Resultat der Untersuchung wohl dahin zusammenfassen, daß nicht nur die Becquerelstrahlen sondern auch die Kathodenstrahlen aus Elektronen bestehen, deren Masse rein elektromagnetischer Natur ist.”

53 Chapter 2. Experiment and the Electron electron.83 This required the electron to form a rigid, i.e. undeformable, body, since otherwise non-electromagnetic internal forces would be required to keep such a deformable electron from collapsing (Abraham, 1903, p. 108 – 109). Of importance here are the conditions that Abraham established for force-free inertial motion, i.e. “inertial motion that could be maintained without any external forces balancing the electron’s self-forces” (Miller, 1981, p. 57), to be possible. A first condition was that its velocity could not be higher than the velocity of light (Abraham, 1903, p. 141). A second condition was that its velocity and momentum had to be collinear, which meant, as we have already seen on page 51, that its shape had to be symmetrical around axes perpendicular to its direction of motion (Abraham, 1903, p. 141). These conditions entailed that for a spherical electron, force-free inertial motion was possible in all directions, since it is, of course, completely symmetric with respect to such axes (Abraham, 1903, p. 142 – 143). After showing that his dynamics could also be formulated in terms of Lagrangian mechanics,84 Abraham turned to the topic of quasi-stationary acceleration. As we have seen on page 50, he assumed the electron’s motion to be quasi-stationary to make its electromagnetic energy and momentum completely velocity-dependent. In his (1903) article, his concern was more specifically with the demarcation of what counted as quasi-stationary acceleration, which he defined as follows: “We take a motion of the electron to be quasi-stationary if the change in velocity is so slow that one can calculate the momentum for any velocity in the same way as for stationary motion” (Abraham, 1903, p. 149).85 The reason for introducing this requirement, as we have seen on page 50, was that it offered a way to determine the electron’s mass, conceptualized in terms of its electromagnetic momentum G, by means of its acceleration and the force exerted on it (Miller, 1981, p. 59). Abraham (1903, p. 159) showed that Becquerel rays with very high velocity, which Kaufmann had used in his experiments, obeyed this condition of quasi-stationary acceleration. This entailed that his dynamics of the electron could indeed be applied to Kaufmann’s observations. In the final section of his (1903), Abraham investigated whether the electron

83 Dynamics, as we have seen in footnote 53, is the study concerned with the causes responsible for the behaviour of material bodies in motion. Abraham’s goal was hence to offer an account of the behaviour of the electron that would only appeal to electromagnetic causes, in line with his commitment to the electromagnetic world view (Abraham, 1903, p. 106). 84 Lagrangian mechanics is a reformulation of Newtonian mechanics, first proposed by Joseph- Louis Lagrange. It characterizes a system in terms of a Lagrangian function L, which is a function of the system’s location in space and its velocity. L is most often expressed in terms of the system’s kinetic energy T = (1/2)mv2 and its potential energy V (where the precise expression for a system’s potential energy depends on the kind of force acting on the system): L = T −V . Its evolution over time between a particular beginning state a and an end state b, which is called an action S, can R t=b then be expressed in terms of the following equation: S = t=a Ldt. When the system obeys the principle of least action, which states that the variation of the system’s action is zero (δS = 0), we can obtain the system’s equations of motion out of its Lagrangian L. See Coopersmith (2017) and Lemons (1997) for extensive historical and philosophical discussions of the principle of least action, and chapter 6 of Coopersmith (2017) for an exposition of Lagrangian mechanics. 85 As Miller points out, this means that “the electron’s acceleration occurred during a time interval t that was much greater than the time taken for light to traverse the electron’s radius R” (1981, p. 58 – 59). Stationary motion means that there is no change in velocity. The original German goes as follows: “Wir bezeichnen eine Bewegung des Elektrons als quasistationär, wenn die Geschwindigkeitsänderungso langsam erfolg, daß man den Impuls aus der jeweiligen Geschwindigkeit, wie bei stationärerBewegung, berechnen kann”.

54 Experiment, Time and Theory could also display an ellipsoidal shape. Unlike for a spherical electron, he showed, force-free inertial motion is not possible in all directions for an ellipsoidal electron. The only stable motion that is possible for such an electron is motion parallel to its big axis (1903, p. 179).86

Manipulability and the early Kaufmann Experiments (1) The goal of this chapter is to investigate how we can characterize the way in which diﬀerent scientists took the experiments discussed to provide information about the electron’s velocity-dependent mass and its dynamics. I will therefore regularly interrupt the historical narrative to discuss how the experiments were carried out and analysed. I will argue that the experiments are to be analysed on two levels. One level I will call the experimental inference. It concerns the way in which the entity is manipulated by means of an experimental set-up, and how this produces an eﬀect that scientists can take to be informative. In the case of Kaufmann’s early experiments, we can express the manipulations carried out in terms of the following experimental inference:

[Kaufmann’s Experimental Inference]: c i e µ + (E&B) −→ y0&ρ −→ µ0η

Let us go through this experimental inference step by step in order to clarify what it expresses.87 Completely on the left, we have the entity manipulated, the electron. It is represented in terms of what were taken to be its two relevant established properties, namely its charge and its mass (see Kaufmann’s characterization of the electron in his Naturforscherversammlung lecture, discussed on page 44). The aim of the experiments is to manipulate the ratio of these two properties, i.e. its charge- to-mass ratio. This manipulation is carried out by applying an electric field E and a magnetic field B to it. These are the supposedly stable properties of the experimental set-up. I distinguish entity from set-up by means of brackets (), and I express that they are made to interact by means of the +-sign. The &-sign denotes that the electric and magnetic field do not primarily act on each other. This interaction between set-up and entity brings about an effect, which I express by means of a causal arrow −→c . The effect in this case is that the electrons are deflected in such a way that they produce marks on Kaufmann’s photographic plates, which have a specific magnetic deflection y0 and form a curve with a curvature ρ. These are Kaufmann’s data. From these data, Kaufmann could then infer (which I express in terms of an i e inferential arrow −→) that the electron’s electromagnetic mass µ0 was influenced by a velocity-dependent factor η. As such, the experimental inference tells us that if the properties of the electron and the set-up are indeed as Kaufmann assumed, and if the manipulation was carried out properly, that Kaufmann’s data indeed display a velocity-dependence of mass.

86 For Abraham, a particular motion is stable when the internal rotational force that arises because of a change of direction ensures that the x-axis attached to the charge is adjusted to this new direction (1903, p. 175). As such, if an ellipsoidal electron were to move in any direction other than parallel to its big axis, it would not be stable on Abraham’s account, unless other forces were to counterbalance the electron’s internal rotational forces. 87 In appendix A, I give an overview of the diﬀerent inferences and their interpretations that are discussed in the two historical chapters, and a small summary of how they are to be read.

55 Chapter 2. Experiment and the Electron

This was not the information that Kaufmann was primarily after, however. His goal was rather to determine precisely how the electron’s mass depended on its velocity. As such, we could say that he was looking for knowledge of the causal properties of the electron: how did the application of electric and magnetic fields to the electron manipulate it precisely? For this, we have seen, Kaufmann had to rely on a theoretical model. It is here that we arrive at the second level of our analysis of the experiments, namely the interpretation. An electron-model such as Abraham’s or Searle’s offers an interpretation of the experimental inference in the sense that it gives an account of how the manipulation, according to the model, influences the entity, and how this influence is to be conceptualized. This conceptualization can then be applied to the data obtained, which then allows the scientist to obtain information out of the experiment. Let us turn to the electromagnetic interpretation of Kaufmann’s experimental inference, offered by Abraham’s electron-model, to clarify what this comes down to:

[The Electromagnetic Interpretation]: c i e −dG i e i µ + (E&B) −→ quasi-stat. −→ F = dt −→ µ⊥ −−→ m+µe η y0,ρ 0⊥

This interpretation says that the application of electric and magnetic fields to the electron deflects it in such a way that it is endowed with quasi-stationary acceleration. This is the influence exercised by the electric and magnetic fields on the entity, and hence it is denoted by a causal arrow. If the electron’s motion can indeed be characterized in this way, we then can infer, as we have seen on page 50, that the force Fe exercised by the electron’s self-induced fields on the electron can be expressed in terms of its electromagnetic momentum G. This in turn provides us e with an expression for the electron’s electromagnetic transverse mass µ⊥ (see Abra- ham’s equation 2.9 on page 51). Applying this conceptualization of the electron’s mass to the data produced by Kaufmann, which I denote by means of an inferential i arrow with the data y0 and ρ as subscript (−−→), then provides us with information y0,ρ about how the electron’s mass µ can be divided into a mechanical mass m and a e velocity-dependent electromagnetic component µ0⊥η. On Abraham’s interpretation, it showed, more specifically, that the electron’s mass was completely electromagnetic in nature. As such, in order to obtain information about the electron’s causal properties out of the manipulations carried out by Kaufmann, a model of the electron was required. This indicates that experimental manipulations are different, epistemologically speaking, from how Cartwright and Hacking conceptualize them. In what follows I will continue to analyze the way in which scientists interpreted the experimental manipulations carried out by Kaufmann, and very similar ones by others.88 Reflections on what this suggestion, that experimental manipulations have to be analysed on two levels, means for the epistemology of manipulation will be presented in chapter 4.

88 Since these manipulations are very similar to those carried out by Kaufmann, I will characterize them in terms of the same experimental inference. The way in which they differed, and what the significance of these differences was, will be discussed further on.

56 Experiment, Time and Theory

2.3 Lorentz’s Deformable Electron and the Prin- ciple of Relativity

Lorentz’s Electromagnetic Electron Abraham was not the only one who proposed an electron-model according to which its mass was velocity-dependent. Already in his (1899), Lorentz had obtained equations for the velocity-dependence of the mass of his ‘ions’. This (1899) paper started with a new, simplified, formulation of the transformation equations for coordinates and electric and magnetic fields he had derived in his (1895) electrodynamics. These transformations relate a laboratory frame (x0, y0, z0, t0) with the unprimed ether rest 0 frame (x0, y0, z0, t0), where t denotes the local time (which Lorentz took to be merely a fiction for the sake of calculation), γ = 1/p1 − v2/c2, v is the velocity of the primed frame with respect to the ether, and l is an undetermined coefficient that differs from unity by a factor of second order (v2/c2): v x0 = lγ(x − vt ); y0 = ly ; z0 = lz ; t0 = lγ t − x (2.13) 0 0 0 0 0 c2 0 In his (1895) book, Lorentz had proposed these in response to the Michelson & Morley experiment, which attempted to measure the influence of the earth’s velocity on the electromagnetic ether.89 The issue was that the experimental results, while being very accurate, did not indicate any influence, which at the time was taken to form quite a problem for most theories of the ether. In order to overcome this, Lorentz introduced his transformation equations, as the mathematical expression of the hypothesis that a body’s motion through the ether influences its dimensions in the same way as the electric and magnetic field values are influenced by such motion. These equations thus tell us how to transform dimensions and field values in such a way that the Michelson-Morley result, i.e. that no influence of the earth’s motion with respect to the ether could be detected, could be accommodated (Janssen and Mecklenburg, 2006, p. 79; Janssen, 2009, p. 32). In the second part of the (1899) paper, which is what concerns us here, Lorentz elaborated some of the physical consequences of these transformation equations by considering their implications for a particular system, an oscillating ion. These considerations led him to claim that the accelerations of such an electron in the laboratory frame S = (x0, y0, z0, t0) are, in the x0, y0 and z0 directions respectively, 1 1 1 γ3l , γ2l and γ2l times what they are in the ether rest frame S0 = (x0, y0, z0, t0). On the basis of this result, the Newtonian force-law then led him to the suggestion of velocity-dependent masses:90

If therefore the required agreement is to exist with regard to the vibrations parallel to [x], the ratio of the masses of the ions in S and S0 γ3 γ should be [ l ]; on the contrary we ﬁnd for this ratio [ l ], if we consider

89 See (Staley, 2008a, p. 21 – 131) for a very extensive discussion of Michelson’s work and its historical context. 90 I have replaced some of Lorentz’s original symbols by those between square brackets in order to ensure consistency with notation elsewhere. Lorentz obtained the ratios for the masses expressed in the quote as follows. According to Newton’s force-law, an acceleration is equal to the ratio of force to mass. Given the ratios for the accelerations and those for the forces exercised by the electromagnetic ﬁelds he had obtained from his transformation equations, Lorentz could then obtain the ratios for the masses in the diﬀerent frames (Janssen, 2009, p. 33).

57 Chapter 2. Experiment and the Electron

in the same way the forces and accelerations in the directions of [y] and [z]. Since [l] is diﬀerent from unity, these values cannot both be 1; consequently, states of motion, related to each other in the way we have indicated, will only be possible, if in the transformation of S0 into S the masses of the ions change; even, this must take place in such a way that the same ion will have diﬀerent masses for vibrations parallel and perpendicular to the velocity of translation. (Lorentz, 1899, p. 442)

In his (1904), Lorentz then elaborated how he saw the dynamical constitution of such an ion, which he now called an electron. His central assumption, in line with his physical interpretation of his transformation equations, was the following:

[T]he electrons, which I take to be spheres of radius R in the state of rest, have their dimensions changed by the eﬀect of a translation, the dimensions in the direction of motion becoming [γl] times smaller and those in perpendicular directions [l] times smaller. (Lorentz, 1904, p. 21)

An electron with a spherical shape in its frame of rest will thus have an ellipsoidal shape in frames in which it is in motion. The second assumption he introduced was that, whatever the natures of the forces holding together the particles that make up a material body, they will transform in the same way as the electrodynamical forces he had discussed in his earlier work (Lorentz, 1904, p. 22). These two assumptions allowed him to calculate the electron’s electromagnetic momentum. By applying Newton’s force law to this electromagnetic momentum, Lorentz obtained the following equations for the electron’s longitudinal and transverse mass, which showed that, on his account as well, “there is no other, no ‘true’ or ‘material’ mass” (1904, p. 24):

2 d(γlv) µe = (2.14) k 6πc2R dv 2 µe = γl (2.15) ⊥ 6πc2R As such, at this moment in time Lorentz’s model as well gave a completely electromagnetic account for the velocity-dependence of the electron’s mass in the case of quasi-stationary acceleration, just as Abraham’s. However, Lorentz pointed out, the equations he obtained were different from the ones proposed by Abraham and confirmed by Kaufmann’s (1903) experiments, since they offered different models of the electron’s constitution: “[t]he ground for this difference is to be sought solely in the circumstance that, in [Abraham’s] theory, the electrons are treated as spheres of invariable dimensions” (Lorentz, 1904, p. 31). Lorentz was able to show, however, that his formulae showed an agreement with Kaufmann’s (1902; 1903) results that was equally good as Abraham’s (1904, p. 31 – 34).

The Stability of Lorentz’s Electron Abraham’s Foundations of the Theory of the Electron In his (1904) paper, Abraham compared his own electron theory with the one proposed by Lorentz (1904) by means of a discussion of the principles that he took to underly both theories. Before listing the diﬀerences, however, he presented the following four principles

58 Experiment, Time and Theory which, he claimed, any electron theory would have to incorporate (Abraham, 1904, p. 576):

1. Empty space, devoid of any matter and electricity, can be described in terms of the Maxwell-Hertz equations;91

2. Electricity consists of discrete, positively or negatively charged particles, called ‘electrons’;92

3. Every electric current is a convection current of moving electrons;93.

4. The electromagnetic force is composed in an additive way out of the force exercised by the electric ﬁeld on electricity at rest and the force exercised by the magnetic ﬁeld on moving electricity.94

After that, Abraham listed the three principles that, together with principles (1) – (4), characterize his theory of the electron which, he pointed out, he introduced in order to provide a completely electromagnetic account of the results of Kaufmann’s experiments (Abraham, 1904, p. 576 – 577):

5. The electromagnetic forces exercised on the electron by external ﬁelds and by the ﬁeld induced by the electron itself hold each other in equilibrium, in the sense of the mechanics of rigid bodies;95

6. The electron’s form cannot change at all;96

7. The electron forms a sphere with equally distributed volume- or surface-charge. 97

Abraham then turned to Lorentz’s electron theory, which, he pointed out, was not formulated in response to Kaufmann’s experiments, but rather in response to the Michelson & Morley experiment. This led Lorentz to build his theory on the following principles, together with principles (1) – (4) and Abraham’s principle (5) (Abraham, 1904, p. 577 – 578):

91 In the 1880s and 1890s, Heinrich Hertz thoroughly reformulated and extended Maxwell’s electrodynamics, turning, for example, Maxwell’s original twenty equations into the four equations we know now, by means of vector notation. See (Miller, 1981, p. 11 – 14) for a short overview of Hertz’s electrodynamical work, and Buchwald (1994) and (Darrigol, 2002, p. 234 – 262) for extensive historical discussions of Hertz’s work. The original German goes as follows: “In dem von Materie und Elektrizitätleeren Raume gelten die Maxwell-Hertzschen Gleichungen”. 92 “Die Elektrizitätbesteht aus diskreten positiven und negativen Teilchen, die ‘Elektronen’ genannt werden”. 93 “Jeder elektrische Strom ist ein Konvektionsstrom bewegter Elektronen”. 94 This principle expresses the Lorentz force equation F = e(E + v × B). The original German goes as follows: “Die elektromagnetische Kraft setzt sich additiv zusammen aus den Kräften,die im elektrischen Felde auf die ruhende, und im magnetischen Felde auf die bewegte Elektrizität wirken”. 95 In classical mechanics, a rigid body is defined as a body for which, when forces were exercised upon it, “the distance [. . . ] between any two points remained the same” (Miller, 1981, p. 244). “Die elektromagnetische Kräftedes äusseren und des vom Elektron selbst erregten Feldes halten sich an dem Elektron im Sinne der Mechanik starrer Körper das Gleichgewicht”. 96 “Das Elektron ist einer Formänderungüberhaupt nicht fähig”. 97 “Es ist eine Kugel mit gleichförmigerVolum- oder Flächen-ladung”.

59 Chapter 2. Experiment and the Electron

8. As a consequence of the motion of the earth, bodies undergo a deﬁnite contraction parallel to the earth’s direction of motion;98

9. The quasi-elastic forces, which ensure the electron’s state of equilibrium, undergo as a consequence of the motion of the earth the same changes as electric and molecular forces.99

10. The electron, which in its state of rest is endowed with an equally distributed volume- or surface-charge, will ﬂatten when it is put in motion, in such a way that its diameter parallel to the direction of motion will be shortened with a ratio of p1 − v2/c2/1;100

11. The mass of molecules is completely electromagnetic in nature.101

Abraham then argued that Lorentz’s principles led to a problematic conceptualization of the electron in motion. Such an electron, on Lorentz’s view, would not only give rise to self-induced electromagnetic fields that exercise a force on it, which means that the electron performs a certain amount of work. It would also, in line with principle 10, deform, which means that the electron will carry out extra work.102 Calculating the amount of work the electron could carry out in terms of its electromagnetic momentum showed the following, according to Abraham. The electromag- e R netic momentum obtained from its electromagnetic field [GEM = (1/4πc) E×BdV ] e e differed from the one obtained from its Lagrangian [GL = ∂L /dV] by one third e (where E0 is the electron’s electromagnetic energy in its rest frame): 4 Ee v Ee v Ge = 0 ; Ge = 0 (2.16) EM 3 p1 − v2/c2 c2 L p1 − v2/c2 c2 Given that the electron’s velocity-dependence of mass was conceptualized in terms of its electromagnetic momentum, this entailed that one could obtain two different dependencies, which also differed with a factor 1/3. According to Abraham, it was not clear how this factor could be compensated in purely electromagnetic terms, in line with Lorentz’s commitment to a completely electromagnetic electron (principle 11). What Lorentz’s electron rather required, according to Abraham, were non- electromagnetic elastic forces that, in line with principles 5 and 10, kept the electron in equilibrium when it deformed as a consequence of its motion. Moreover, Abraham continued, even when such forces could be introduced successfully, the electron’s shape would still be ellipsoidal when it was deformed, which entailed that it could not carry out force-free inertial motion in just any direction, except if these newly

98 “Infolge der Erdbewegung erfahren die Körper eine gewisse Kontraktion parallel der Bewe- gungsrichtung”. 99 “Die quasielastischen Kräfte,welche die Elektronen an ihre Gleichgewichtslagen binden, erfahren infolge der Erdbewegung die gleiche änderung,wie die elektrischen bezw. die molekularen Kräfte”. 100 “Das im Ruhestand mit gleichförmigerVolum- oder Flächen-Ladung erfüllteElektron plattet sich bei der Bewegung ab, indem sein der Bewegungsrichtung paralleler Durchmesser im Verhältnis [p1 − v2/c2/1] verkürztwird”. 101 “Die Massen der Molekülesind elektromagnetischer Natur”. 102 When a force is exerted on a body in such a way that the body is displaced or transformed, the force is said to have done work on the body. That a body is deformable then means that it can be deformed because of the work done on it, but also that the body needs to carry out work itself in order to keep a particular shape.

60 Experiment, Time and Theory introduced forces would somehow ensure this. But it was unclear, according to Abraham, how they could do this:

A consequent reading of hypothesis (10) forces one to accept other, non- electromagnetic inner forces besides the inner electromagnetic forces, which together determine the electron’s shape. These will then provide in the case of contraction the required work, which together with the work of the external forces is equivalent to the increase in the electron’s electromagnetic energy. As long as one does not specify according to which law these forces will work, the hypothesis-system (1), (2), (3), (4), (5), (10) is incomplete. This incompleteness now entails that the stability of an electron obeying this system is not sure. The motion of a ﬂattened rotation-ellipsoid with a non-deformable shape parallel to its axis of rotation is, as has been shown above, unstable.103 The proof that those non-electromagnetic forces will stabilize the motion of a deformable ellipsoid is missing. (Abraham, 1904, p. 578)104

Poincar´eintroduces ether stresses It was Poincar´e(1905; 1906b) who suggested how Lorentz’s electron could be saved from this instability. He summarized his proposal as follows:

If one wants to uphold Lorentz’s theory and avoid intolerable contradictions, one has to presuppose a special force that explains at the same time the contraction and the constancy of the two axes.105 Investigating how this force can be determined, I have found that it can be identiﬁed with a constant external pressure, exercised on the deformable and com-

103 Abraham’s claim about the unstability of a non-deformable ellipsoidal electron follows from his (1903) argument, discussed in section 2.2, that force-free inertial motion for a rigid ellipsoidal electron is only possible in the direction of its big axis. Abraham had derived this instability- consequence earlier in the paper: “I have extended the investigation to ellipsoidal electrons of undeformable shape; this showed, that for such an electron, translational motion is stable only in the direction of its big axis. A flattened rotation-ellipsoid can not move parallel to its axis of rotation; the smallest push would make it fall over” (Abraham, 1904, p. 577).(“Ich habe die Untersuchung auch auf ellipsoidische Elektronen von unveränderlicher Gestalt ausgedehnt; es ergab sich, dass die Translationsbewegung eines solchen Elektrons nur in Richtung der grossen Achse stabil ist. Ein abgeplattetes Rotationsellipsoid kann sich nicht parallel der Rotationsachse bewegen; der kleinste Anstoss würdees zum Umschlagen bringen”). Translational motion is a movement that changes the position of an object. 104 The original German goes as follows: “Die konsequente Verfolgung der Hypothese (10) zwingt also dazu, neben der inneren elektromagnetischen Kräftennoch andere, nicht elektromagnetische, innere Kräfteanzunehmen, welche im Verein mit jenen die Form des Elektrons bestimmen. Diese würdendann bei der Kontraktion die erforderliche Arbeit leisten, die zusammen mit der Arbeit der äusserenKräfteder Steigerung der elektromagnetischen Energie des Elektrons äquivalent ist. Solange man nicht angiebt, nach welchem Gesetz diese Kräftewirken sollen, ist das Hypothesensys- tem (1), (2), (3), (4), (5), (10) unvollständig.Die Unvollständigkeit des Hypothesensystem bedingt es, dass man der Stabilitäteines diesen gehorchenden Elektrons nicht sicher ist. Die Bewegung eines abgeplatteten Rotationsellipsoids von unveränderlicher Form parallel seiner Rotationsachse ist, wie oben erwähnt, instabil. Es fehlt der Nachweis, dass jene nicht elektromagnetischen Zusatzkräfte die Bewegung des deformierbaren Ellipsoids stabil machen.” 105 These are the two axes that, on Lorentz’s view, remain constant when an electron’s shape contracts in the direction of the third axe.

61 Chapter 2. Experiment and the Electron

pressible electron, and of which the work performed is proportional to variations of the volume of such an electron. (Poincar´e,1906b, p. 130)106

The problem with Lorentz’s electron, as we have seen on page 60, was that it could be characterized in terms of two different conceptualizations of its momentum: one deriving from its self-induced fields, and one from its Lagrangian. This was a consequence of the fact that a moving electron, on Lorentz’s view, not only had to carry out work against these self-induced fields, but also against its deformation. This meant, according to the energy principle,107 that if such an electron was to be stable, an extra source of energy besides its electromagnetic one was required. The e electron’s total electromagnetic energy ET , Abraham had argued, should be of the following form: 4 Ee Ee = 0 (2.17) T 3 p1 − v2/c2

The total energy ET obtained from Lorentz’s electron, however, was of the following form:

e ep 2 2 4 E0 ET = E 1 − v /c + (2.18) 0 3 p1 − v2/c2

ep 2 2 which meant that there had to be another source of energy −E0 1 − v /c , provided by the elastic forces responsible for the electron’s shape under deformation, such that its total energy was to be equal to equation (2.17). To address this issue, Poincar´e made use of the principle of least action, which he expressed in the following terms (1906b, p. 136):108 Z S = [Le + Lc] dt (2.19)

e ep 2 2 Here, L = lL0 1 − v /c is the Lagrangian concerning the electron’s self-electromagnetic fields (in which l is the same undetermined coefficient as Lorentz’s, see page 57). c cp 2 2 c e L = −E0 1 − v /c (with E = E0/3) is an additional Lagrangian, which Poincaré introduced to ensure that l = 1, in order to make sure that Lorentz’s transformation equations formed a group (Poincaré,1906b, p. 146).109 And the Lorentz transfor-

106 The original French goes as follows: “[S]i l’on veut la conserver [i.e. Lorentz’s theory] et éviter d’intolérablescontradictions, il faut supposer une force spécialequi explique àla fois la contraction et la constance de deux des axes. J’ai cherchéàdéterminercette force, j’ai trouvéqu’elle peut être assimiléeàune pression extérieureconstante, agissant sur l’électrondéformableet compressible, et dont le travail est proportionnel aux variations du volume de cet électron.” 107 This principle states that the increase of a body’s total energy per unit of time is equal to the work performed by the external forces exercised on it (Abraham, 1902, p. 25). 108 See footnote 84 for the principle of least action. 109 As Andrew M. Steane puts it in his handbook on relativity, “a mathematical group is a set of entities that can be combined in pairs, such that the combination rule is associative (i.e., (ab)c = a(bc)), the set is closed under the combination rule, there is an identity element and every element set has an inverse. Closure here means that for every pair of elements in the set, their combination is also in the set” (2012, p. 135). That the Lorentz transformations (discussed on page 57, here with l = 1) form a group now means that combinations of these transformations are also Lorentz transformations: if we have a combination of three transformations (ab)c that is a Lorentz transformation, the associative combination a(bc) also forms a Lorentz transformation; that the identity transformation, which transforms a Lorentz transformation into itself, is also a Lorentz

62 Experiment, Time and Theory mations had to form a group, according to Poincaré,since it was the only way to ensure that no absolute motion could be detected (Poincaré,1906b, p. 163). This additional Lagrangian Lc described the energy resulting from an internal stress acting upon the electron, which later became known as the Poincaréstress. It prevented the deformable electron from collapsing in its rest system, since it e increased its total energy ET in such a way that, instead of ending up with equation (2.18), one ended up with equation (2.17), as required by Abraham (Miller, 1981, p. 83 – 84). In this way, Poincaréclaimed, Lorentz’s electron could remain stable in motion while safeguarding the principle of relativity, and he even suggested that Lorentz’s electron could remain completely electromagnetic in nature:110

If the inertia of electrons is of a purely electromagnetic nature, if they are subject solely to electromagnetic forces or to forces that bring about the ether stress, no experiment can provide evidence for absolute motion. Which are then these forces that bring about this stress? They can of course be assimilated with a pression in the electron’s interior; everything would occur as if each electron would form a hollow capacity subject to a constant internal pressure (independent of its volume); the work of such a pressure would of course be proportional to variations of the volume. (Poincar´e,1906b, p. 165)111

Einstein’s Relativistic Derivation Albert Einstein as well derived, in his (1905c) article on the principle of relativity, equations for the electron’s longitudinal and transverse mass. These equations were, as was first pointed out by Kaufmann (1906b, p. 530 – 531), equivalent to Lorentz’s (2.14) and (2.15) with l = 1 (see page 57).112 What was special, however, was the way in which Einstein obtained these equations. For, while Lorentz and Abraham derived their equations from their respective electron models, Einstein transformation; and that the inverse of a Lorentz transformation is also a Lorentz transformation. See (Steane, 2012, p. 134 – 139) for a more technical elaboration. 110 I use the term ‘suggested’ here because Poincarédoes not really specify how this could be accomplished, and he points out afterwards that not all forces can be of electromagnetic origin: gravity, for example, is non-electromagnetic. This then leads him to interpret Lorentz’s claim about the electron’s mass being completely electromagnetic in nature as meaning that all forces behave as if they are electromagnetic in nature: because the electromagnetic field is distinct from the gravitational field, “Lorentz has been forced to add to his hypothesis the supposition that forces of whatever origin, and in particular gravition, are affected by a translation (or, if one likes it better, by the Lorentz transformation) in the same way as the electromagnetic forces” (Poincaré, 1906b, p. 166). (“Lorentz a donc étéobligéde compléterson hypothéseen supposant que les forces de toute origine, et en particulier la gravitation, sont affectéespar une translation (ou, si l’on aime mieux, par la transformation de Lorentz) de la mêmemanièreque les forces électromagnétiques”). 111 The original French goes as follows: “Si l’inertie des électronsest exclusivement d’origine électromagnétique,s’ils ne sont soumis qu’ àdes forces d’origine électromagnétique,ou aux forces qui engendrent le potentiel supplémentaire (F) [i.e. the Poincaréstress], aucune expériencene pourra mettre en évidence le mouvement absolu. Quelles sont alors ces forces qui engendrent le potentiel (F)? Elles peuvent évidement êtreassimiléesàune pression qui régnerait àl’intérieurde l’électron;tout se passe comme si chaque électronétaitune capacitécreuse soumise àune pression interne constante (indépendante du volume); le travail d’une pareille pression serait évidemment proportionnel aux variations du volume”. 112 This was only pointed out later since, as we will see in section 2.5, Einstein himself presented equations that differed from Lorentz’s because he used a non-relativistic force equation.

63 Chapter 2. Experiment and the Electron did not employ such a model. Einstein’s starting point, rather, were the following two principles, which functioned as postulates of his theory of relativity:

1. The laws governing the changes of the state of any physical system do not depend on which one of two coordinate systems in uniform translational motion relative to each other these changes of the state are referred to.

2. Each ray of light moves in the coordinate system ‘at rest’ with the deﬁnite velocity V independent of whether this ray of light is emitted by a body at rest or a body in motion. (Einstein 1905c, p. 895; Beck 1989, p. 143)113

Reflections on the measurement of lengths and times by means of rigid rods, clocks and light signals constrained by these principles then led Einstein to the same transformation equations (2.13) for coordinates as Lorentz had obtained earlier, with an unspecified coefficient l.114 By means of symmetry considerations, Einstein was then led to put l = 1, thus obtaining the same transformations as Poincaré(1906b).115 In the second, electromagnetic part of the paper, Einstein used these transformation equations to obtain the transformation equations for the electric and magnetic fields that figure in the Maxwell equations. In the last section of this part, Einstein then applied all these transformation equations to the case of a moving electron, which he characterized as a point particle endowed with an electric charge . Pro- ceeding in this way provided him with the relativistic formulation of the electron’s equations of motion. Applying Newton’s force law, i.e. F = ma, to these equations then led him to equations for the electron’s longitudinal and transverse mass, which, however, later turned out to be incorrect.116 As such, Einstein obtained equations for the electron’s longitudinal and transverse mass that were equal to Lorentz’s, with l = 1, without relying on any specific model of the electron. In fact, Einstein himself pointed out, these equations are not

113 As stated in footnote 54, Einstein’s papers from this period have been translated to English by Anna Beck. These translations, as well the original papers, can be found on the webpage of the Einstein Papers Project, https://einsteinpapers.press.princeton.edu. To allow for comparison with the original papers, I will refer to both the page numbers of the original papers and those of the translation. 114 See Giovanelli (2014) for an extensive discussion of the way in which Einstein conceptualized these rods and clocks in the development of the theory of relativity. 115 Einstein obtained this result as follows. The transformation equations relate two coordinate frames in relative motion, K and k, which moves with a velocity v with respect to K. These equations, however, contain an expression φ (i.e. the coefficient l, not used here to prevent confusion with the length l), a function of the velocity v that is at that point in the derivation unknown. To clarify the meaning of this unknown term, Einstein then introduces a third reference frame moving with velocity −v with respect to the frame k. This shows him that φ(v)φ(−v) = 1. Reflecting on the length of a rod, at rest in k and thus in motion with respect to K, then shows him that the length of the rod in K is l/φ(v). Reasons of symmetry, he then claims, show us that the length of the rod does not change when v is replaced by −v: after all, just reversing a rod’s direction with the same velocity does not normally change its length. This then leads him to φ(v) = φ(−v), which entails that φ(v) = 1 (Einstein, 1905c, p. 901 – 902). 116 Ironically, Einstein himself seemed to be aware of the importance of applying the correct conceptualization of force, since he pointed out immediately afterwards that a different conceptualization would entail a different result: “Of course, with a different definition of force and acceleration we would obtain different numerical values for the masses; this shows that we must proceed with great caution when comparing different theories of the electron” (Einstein, 1905c, p. 919; Beck, 1989, p. 169.)

64 Experiment, Time and Theory even particular to the electron. On the relativistic view, they obtained for any material body, since Einstein deﬁned the electron as a point particle with an arbitrarily small charge:

It should be noted that these results concerning mass are also valid for ponderable material points, since a ponderable material point can be made into an electron (in our sense) by adding to it an arbitrarily small electric charge. (Einstein, 1905c, p. 919; Beck, 1989, p. 170)

Manipulability and the Early Kaufmann Experiments (2) Kaufmann’s experimental manipulations, we have seen on page 55, can be characterized in terms of an experimental inference that links an interaction between the relevant properties of the electron and the set-up – the electron’s charge-to-mass ratio, the applied electric and magnetic fields – to the production of an effect that is supposed to provide information about the property under investigation, i.e. the electron’s velocity-dependent mass. In order to obtain information from the data produced about this property of investigation, however, Kaufmann’s experimental inference had to be interpreted. Such an interpretation is offered by a model of the electron, and it provides an account of how the manipulation influences the entity manipulated, and how this influence is to be conceptualized. Applying this conceptualization to the data produced then allows the scientist to obtain information out of the experiment. In short, such an interpretation tells us how we are to understand the functioning of the experiment. Abraham’s interpretation of Kaufmann’s experimental inference, we have seen, provided such an account in terms of the forces exercised on the electron by electromagnetic fields. Elaborating this account further provided him with information about the electron’s dynamical constitution, i.e. concerning its form, charge distribution and rigidity. Lorentz’s work soon suggested, however, that a different interpretation of the functioning of the experiments was also possible. He offered an interpretation that equally well accounted for the results produced by Kaufmann’s manipulations in terms of the electromagnetic forces exercised on the electron. This electron was not rigid as Abraham’s, but deformable, in line with Lorentz’s aim to have his electron-model account as well for the workings of the Michelson-Morley experiment. This electron-model could equally well account for the functioning of Kaufmann’s experiments, according to Lorentz, since it was equally well in line with the results obtained. This means that it offered an alternative account of how the manipulations carried out, influenced the electron in such a way that the velocity- dependence of its mass could be conceptualized in terms of the equations Lorentz had derived, and that the data obtained by Kaufmann fitted these equations. Abraham argued, however, that it was not very plausible that this interpretation could offer an account of the functioning of the experimental manipulations. Because it was unclear whether the motion of Lorentz’s electron could be stabilized in such a way that it could perform force-free inertial motion in all directions, it was doubtful that Lorentz’s electron could actually exist in its electromagnetic form. This led Poincaréto introduce his ether stresses, which could overcome this issue at the cost of the electron’s electromagnetic constitution. On Poincaré’sview, the application of electric and magnetic fields to the electron endows it with motion that can be characterized in relativistic terms. This allowed him to argue that the total force

65 Chapter 2. Experiment and the Electron

F exercised on the electron, which also included the stresses required to stabilize it, could be expressed in terms of the electron’s electromagnetic momentum G. This provided him with an expression for the velocity-dependence of the electron’s relativistic transverse mass µ⊥, which, if applied to Kaufmann’s data y0 and ρ, could also provide information about the precise dependency of this mass on velocity. The interpretation oﬀered by Poincar´eof the functioning of Kaufmann’s experiments can thus be expressed as follows:

[Poincar´e’sRelativistic Interpretation]: c i −dG i i µ + (E&B) −→ relativistic motion −→ F = dt −→ µ⊥ −−→ m+µ η y0,ρ 0⊥

As such, at this point in the discussion, we have two different interpretations of the functioning of Kaufmann’s experiments, i.e. two different accounts of how the influence of the experimental manipulations on the electron is to be conceptualized, and how this influence would manifest itself in the data: as a regularity expressible in terms of Abraham’s equations for the velocity-dependence of the electromagnetic e mass µ⊥ or in terms of the Lorentz-Poincaréequations (equations 2.14 and 2.15, discussed on page 58, with l = 1) for the velocity-dependence of the relativistic mass µ⊥. Because of this situation, Kaufmann decided to carry out further experiments, in order to decide between the different theories and hence to acquire more insight into the electron’s dynamics.117

2.4 Kaufmann’s Final Run of Experiments

Besides Abraham’s rigid electromagnetic electron and Lorentz’s deformable relativistic electron, Kaufmann included two other accounts of the velocity-dependence of the electron’s mass in his comparison: a deformable electromagnetic one, proposed by Alfred Bucherer (1904) and Paul Langevin (1905), which was able to combine both these aspects, since in contrast to Lorentz’s electron, its volume remained constant over deformation (Janssen and Mecklenburg, 2006, p. 86); and the derivation of the electron’s longitudinal and transverse mass provided by Einstein, who did not, however, employ a particular electron model.118 While Kaufmann saw that Einstein’s approach to the issue diﬀered quite profoundly from Lorentz’s, he still grouped them together, given that their equations for the electron’s longitudinal and transverse mass were formally equivalent (1906b, p. 491 – 493).119

117 Because Einstein’s account entailed the same equations for the velocity-dependence of mass as the Lorentz-Poincaréaccount (or at least, should lead to the same equations, see footnote 112), and because Einstein himself identified his results with Lorentz’s (see footnote 119), I group his interpretation of the experiments together with the relativistic one offered by Poincaré. 118 In his (1906a) addendum to his experimental results, Kaufmann added Emil Cohn’s electrodynamics (1902; 1904) as a fifth account to the comparison. Kaufmann listed him with Einstein and Lorentz, given that Cohn’s account also entailed the impossibility of detecting any absolute motion, and because his equations for the velocity-dependence of mass were the same as (2.14) and (2.15), with l = 1. 119 This was the first discussion in print of Einstein’s (1905c) relativity paper. Kaufmann was not the only one who drew this equivalence between Einstein’s and Lorentz’s theory. Einstein himself also grouped together his results on the electron’s mass with Lorentz’s in his (1906b) proposal for alternative experiments to establish the correct formulae for the velocity-dependence of mass, and in his (1907c) review article on relativity theory. See chapter 8 of (Staley, 2008a) for

66 Experiment, Time and Theory

In general, the experimental set-up employed by Kaufmann was similar to the ones he had used before. The only material changes concerned improved accuracy. He had the surface containing the diaphragm polished by optical means in such a way that it was as optically flat as possible, in order to ensure that the rays continued travelling in as straight a direction as possible (Kaufmann, 1906b, p. 496). He used different optical instruments to measure the precise distances between source, diaphragm and photographic plate, instead of just measuring them by hand as he had done earlier (Staley, 2008a, p. 237). And instead of using an electromagnet to bring about the applied magnetic field, he used two permanent magnets, which entailed that he did not need to ensure a constant current to maintain a constant field throughout the whole experimental run (Kaufmann, 1906b, p. 499). The most important improvement concerned the reduced deflections y0 and z0 (see page 52). Earlier, Kaufmann had introduced these deflections to make his calculations easier. He now reconceptualized them, however, in terms of what he called ‘curve constants’ R1 and R2, which were constants that could be obtained from the ‘apparatus constants’ (i.e. the electric (E) and magnetic (B) field strengths, the low-velocity charge-to mass ratio /µ0, and the dimensions of his set-up): 1 B E = e ; R2 = e (2.20) R1 µ0 c µ0 c Kaufmann (1906b, p. 529 – 530) characterized each theory in terms of a specific ψ(β) function, as he had done earlier for Abraham’s theory (see equation 2.11 on page 52). Combining these with the curve constants then led him to the following theory-dependent predictions for the reduced deflections:

0 1 1 0 1 z = ; y = R2 2 (2.21) R1 βψ(β) β ψ(β) These expressions offered Kaufmann three different ways of comparing the different theories amongst each other and with experiment. The first comparison was between the apparatus constants and those curve constants that formed the best fit with these apparatus constants for a particular theory. A second involved comparing the low- velocity charge-to-mass ratio /µ0 obtained experimentally, which was very close to that obtained by Simon (1899), with what the different theories predicted for it. The third, finally, compared a value for the reduced electric deflection, calculated for each theory out of the apparatus constants, Simon’s /µ0 and some values of the reduced magnetic deflection, with the electric deflection that was measured (Miller, 1981, p. 230; Hon, 1995, p. 190 – 194; Staley, 2008a, p. 240 – 241). The results of these analyses were presented by Kaufmann on the curves shown in figure 2.4 (see page 68). All three of the analyses, Kaufmann claimed, clearly favoured the electromagnetic models of Abraham and Bucherer-Langevin over the relativistic Einstein- Lorentz model. A decision between Bucherer-Langevin and Abraham would require increasing the precision even more, which was not possible at the time (Kaufmann, 1906b, p. 535). In any case, he concluded, the experiments not only provided a decision in favour of the equations provided by Abraham and Bucherer-Langevin, but also in favour of the electromagnetic world view over the relativistic approach, a historical discussion of the ways in which participants at the time identified and distinguished different formulations of the theory of relativity.

67 Chapter 2. Experiment and the Electron -plane, compares the results of the different theories with 0 z − 0 y observation for the reducedsource: electromagnetic Kaufmann deflections. (1906b). The In other the curve digital (fig. source 10), I concerns have the used, measured no values page that number were is used given in for the this third image. comparison. Figure Figure 2.4: Two curves presented by Kaufmann in his (1906b) article. One curve (fig. 11), on the

68 Experiment, Time and Theory since both Abraham’s and the Bucherer-Langevin electron model were completely electromagnetic in nature, whereas it was not very probable that Lorentz’s electron could be made completely electromagnetic, given the issues raised by Abraham (see section 2.3). This entailed, according to Kaufmann, that we could consider the attempt to base the whole of physics on the principle of relativity as failed:

The presented results clearly decide against the validity of the Lorentzian and hence also of the Einsteinian theory; insofar as one takes this as a refutation of these theories, one should also take the attempt, to base the whole of physics including electrodynamics and optics on the principle of relativity, as failed. Reﬂections on Einstein’s theory show that achieving correspondence with my results, while holding on to this principle, will require modiﬁcations of the Maxwell equations for bodies at rest, a step that almost no one will be willing to take. For the moment, we will rather remain with the assumption that the physical phenomena depend on motion relative to a completely determined reference system, which we denote as the absolutely resting ether. (Kaufmann, 1906b, p. 534 – 535)120

Manipulability and Kaufmann’s Final experiments According to both the relativistic and the electromagnetic electron-accounts available, Kaufmann’s earlier experiments had worked successfully, since the results he obtained in his measurements at that time were in line with their respective equations for the velocity-dependence of mass. Moreover, Kaufmann had good reasons to believe that his experiments had worked reliably, since the /µ0 value he obtained was in line with Simon’s (1899) value. As such, there was no reason to believe that improving the accuracy of the experiments would not provide a decision between the different electron-models. The experimental inference characterizing the manipulations carried out by Kaufmann in his latest run of experiments is therefore more or less the same as on page 55, except that Kaufmann now expressed his deflections in terms of the curve constants R1 and R2. In order to claim that Kaufmann’s experimental manipulations provided information about the electron’s velocity-dependence of mass, we have seen, the experimental inference characterizing them had to be interpreted. And there were two main interpretations possible: a relativistic one and an electromagnetic one. The primary difference between these interpretations concerned the motion brought about by the application of electric and magnetic fields to the electron. Whereas Abraham, Bucherer and Langevin characterized it in terms of quasi-stationary acceleration,

120 The original German goes as follows: “Die vorstehende Ergebnisse sprechen entschieden gegen die Richtigkeit der Lorentzschen und somit auch der Einsteinschen Theorie; betrachtet man diese aber als widerlegt, so wäredamit auch der Versuch, die ganze Physik einschließlich der Elektrodynamik und der Optik auf das Prinzip der Relativbewegung zu gründen,einstweilen als mißglückt zu bezeichnen. Eine Betrachtung der Einsteinschen Theorie zeigt, daß man, um bei Beihaltung dieses Prinzipes dennoch Ubereinstimmung¨ mit meinen Resultaten zu erhalten, bereits die Maxwellschen Gleichungen für ruhende Körper modifizieren müßte,ein Schritt, zu dem sich wohl einstweilen schwer jemand wird entschließen wollen. Wir werden vielmehr einstweilen bei der Annahme verbleiben müssen,daß die physikalischen Erscheinungen von der Bewegung relativ zu einem ganz bestimmten Koordinatensystem abhängen,das wir als den absolut ruhenden Ather¨ bezeichnen.”

69 Chapter 2. Experiment and the Electron

Lorentz, Einstein and Poincarétook it to be relativistic motion. Because of this, they obtained different accounts of the dynamics responsible for the electron’s mass: Abraham, Bucherer and Langevin accounted for it solely in terms of electromagnetic fields, while Einstein, Poincaréand Lorentz had to invoke non-electromagnetic forces in order to ensure the electron’s stability. These different accounts of how the experiments functioned led them to different predictions for the information that could be obtained from the data, expressed in their respective equations for the electron’s transverse mass. Both interpretations took Kaufmann’s experimental manipulations to provide information about the electron’s velocity-dependent mass in terms of its electromagnetic momentum G. Both conceptualized, we have seen, the force exercised on the electrons in terms of the rate of change of this momentum, and it was this notion that provided an expression for the electron’s mass, from which the velocity- dependent part could then be derived. Because of this, it was in terms of the electron’s electromagnetic momentum that its dynamical constitution was investigated. Abraham’s electron, for example, formed a spherical rigid body, because only in this way could he obtain an electron with a momentum that was completely electromagnetic in nature that could perform force-free inertial motion in all directions. Lorentz’s electron-model was very implausible, Abraham argued, because it entailed an expression for the electron’s electromagnetic momentum that was not in line with Kaufmann’s results; and it was only through the introduction of hypothetical non-electromagnetic stresses that Poincarécould render the electromagnetic momentum of Lorentz’s electron compatible with the electromagnetic interpretation of Kaufmann’s obtained data. As such, we see how it was because both sides of the debate interpreted Kaufmann’s experimental inference in terms of the electron’s electromagnetic momentum that the experimental results could be seen as providing information about what was possible and what was not for the electron’s dynamics. This shows that the kind of information provided by an experimental manipulation depends on how the functioning of the experiment is interpreted, and that, at the same time, which interpretation is to be preferred with respect to whether the experiments functioned properly is determined both by the results of the experiment in question and earlier experiments. At this time, Kaufmann’s experiments had to be conceived in terms of the electromagnetic interpretation of Kaufmann’s experimental inference, since this interpretation provided an expression for the electron’s velocity-dependent mass that was most in line with the experimental results. And because there was an interpretation that showed that Kaufmann’s experimental set- up had functioned reliably and in line with earlier results, nobody disputed that it provided robust results. Other interpretations of the experiments therefore had to conform to this one. Because of this, the experimental decision in favour of the electromagnetic accounts of the electron entailed that the relativistic approach had to provide an answer to it on two levels. First, on the level of the experimental results, since its formulae were not in correspondence with the data obtained. And second, on the theoretical level, since it was unclear how the electron-model put forward by the relativistic interpretation could be given a momentum that, in line with how the electromagnetic accounts conceptualized it, would ensure the stability of the electron. It is to the way in which the adherents of the relativistic approach tried to respond to these two issues that we now turn.

70 Experiment, Time and Theory

2.5 Early Relativistic Responses to Kaufmann’s Experiments

Most adherents of the principle of relativity saw it necessary to respond to the results of Kaufmann’s (1906b) experiments, and the way in which they responded shows that they took these results to form a pressing issue. Lorentz, for example, stated in his 1906 lectures at Columbia university, that Kaufmann’s experiments showed the following: “This proves that at all events the electromagnetic mass has an appreciable influence. It must even greatly predominate. Indeed, Kaufmann’s numbers show no trace of an influence of the material mass” (1909, p. 42). About this result, which he called “certainly one of the most important results of modern physics” (Lorentz, 1909, p. 43), he then wrote the following in a letter to Poincaré dated 8 March 1906:

Unfortunately my hypothesis of the flattening of electrons is in contradiction with Kaufmann’s new results, and I must abandon it. I am, therefore, at the end of my Latin. It seems to me impossible to establish a theory that demands the complete absence of an influence of translation on the phenomena of electricity and optics. I would be very happy if you would succeed in clarifying the difficulties which arise. (Miller, 1981, p. 334)121

Poincarévoiced similar concerns in different places. In his (1906a) paper, for example, he stated that Kaufmann’s (1906b) experiments definitely seemed to favour Abraham’s theory, which entailed that the principle of relativity probably did not have the universal validity that was often ascribed to it (see the quote on page 42). And in his (1906b) paper in which he introduced his stresses, he admitted that these results, preliminary as they were, were already threatened by Kaufmann’s new results: “Neither have I hesitated to publish these preliminary results, even though at this very moment the whole theory may seem to be threatened by the discovery of magneto-cathodic rays” (Poincaré,1906b, p. 132).122 Both Lorentz and Poincaré, to be clear, did not see the experiments as a definitive refutation of the relativistic approach, but they saw them as something to which a response was needed, either by means of further theory development or by means of new experiments. The same also holds for Einstein. The way in which he discussed Kaufmann’s experiments in his (1907c) review article on the principle of relativity (see further on, page 81), and the fact that he proposed alternative experiments on cathode rays (1906b) (see footnote 137), indicate that he as well took Kaufmann’s results to form an issue to which the theory of relativity had to respond. And as we will see on page 73, where we will focus on a discussion between Paul Ehrenfest and Einstein on the relativistic treatment of the electron, Einstein admitted that the theory of relativity

121 Lorentz originally wrote this letter in French. I am using Miller’s translation here. A direct copy of the parts of the letter than contain this passage can be found in (Miller, 1981, p. 336 – 337). 122 While Poincaré’s wording in terms of magneto-cathodic rays might seem strange, most historians interpret it as a reference to Kaufmann’s results: see e.g. (Darrigol, 1995, p. 40) and (Hon, 2016, p. 37 – 39). The original French goes as follows: “Aussi n’ai je pas hésitéàpublier ces quelques résultats partiels, bien qu’en ce moment mêmela théorieentièrepuisse sembler mise en danger par la découverte des rayons magnéthocathodiques”.

71 Chapter 2. Experiment and the Electron at the time could not provide a complete response to the stability issue raised by Abraham. Finally, as we will now see, Max Planck’s early work on the theory of relativity (1906a) showed the same conviction that the Kaufmann experiments posed a pressing issue for the theory of relativity, and that some kind of response was required.

Planck’s Relativistic Mechanics Planck ﬁrst referred to Kaufmann’s experiments in his (1906a) article on the principle of relativity and the laws of mechanics. He pointed out there that they seem to have provided a negative answer to the question regarding the general admissibility of the principle of relativity. Planck did not dispute Kaufmann’s measurements, but he believed that, through further elaboration, the theory of relativity could probably be made compatible with observation (1906a, p. 136). Thus for Planck as well, the experimental results raised an issue that needed to be addressed from the relativistic point of view. The issues raised by Abraham concerning the electron’s stability and form, on the other hand, should be put aside, according to Planck:

I do not give the consideration, that according to the relativity principle a moving electron would be subject to a special form of work because of its deformation, much significance, since in general this work can be calculated by means of the electron’s kinetic energy. Consequently the question concerning an electrodynamic account of the electron’s inertia remains open; this, on the other hand, offers the advantage, that it does not matter whether one ascribes to the electron a spherical form or in fact any specific form at all, to arrive at a determination of the velocity- dependence of mass. (Planck, 1906a, p. 137)123

Even when the principle of relativity would turn out false, Planck continued, developing the theory would still be worth the eﬀort, since the best way to acquire such insight is by elaborating the theory ad absurdum. For these reasons, Planck turned to the elaboration of the relativistic form of the equations of mechanics, in order to replace the Newtonian equations. These needed to be replaced, according to Planck, not because they led to problems or errors, but because if they were combined with the principle of relativity, the application of mechanical concepts such as kinetic and potential energy would become rather complex (1906a, p. 137 – 138). Bringing the equations of mechanics in better agreement with the principle of relativity requires, Planck argued, that Newton’s force law is not expressed in terms of mass and acceleration (F = ma), but rather in terms of the rate of change of momentum: F = dp/dt. And the notion of momentum, Planck argued by means of the example of the force exercised by an electromagnetic ﬁeld on a mass point endowed with charge, should no longer be conceptualized in Newtonian terms as

123 The original German goes as follows: “Auch dem bedenken, daß nach dem Relativitätsprinzip ein bewegtes Elektron einer besonderen Deformationsarbeit unterliegen würde,möchte ich kein entscheidendes Gewicht beimessen, weil man ja diese Arbeit allgemein mit zur kinetischen Energie des Elektrons rechnen kann. Allerdings bleibt damit die Frage nach einer elektrodynamischen Erklärungder Trägheiteine offene; aber dafürerwächst andererseits der Vorteil, daß man dem Elektron weder Kugelgestalt noch überhaupt irgend eine bestimmte Forme zuzuschreiben braucht, um zu einer bestimmten Abhängigkeit der Trägheitvon der Geschwindigkeit zu gelangen”.

72 Experiment, Time and Theory

mass times velocity (p = mv), but in relativistic terms as follows, where m0 is the electron’s mass in its rest frame:

m0v p = γm0v = (2.22) p1 − v2/c2 As such, Planck transformed the Newtonian force-law into the following relativistic one: " # dp d m v F = = 0 (2.23) dt dt p1 − v2/c2 In this way, Planck obtained the relativistic equations of motion for the electron, and hence the Lorentzian equations, with l = 1, for its longitudinal (equation 2.14) and transverse mass (equation 2.15). Planck then showed how the relativistic generalization of the equations of mechanics, based on equation (2.23), could also be expressed in terms of Lagrangian mechanics (see footnote 84). A system’s Lagrangian L (which Planck called its kinetic potential H) is connected to its relativistic momentum by means of the following equation: p = ∂H/∂v, which entails the following force-law: dp d ∂H F = = (2.24) dt dt ∂v As we will see in section 2.6, these equations will become central to Planck’s further work on the issues raised by the Kaufmann experiments and Abraham’s analysis of the foundations of electron theory. Before we turn to this, however, we will ﬁrst discuss a debate between Ehrenfest and Einstein on the relativistic electron.

Ehrenfest and Einstein Ehrenfest’s Challenge As we have seen in section 2.3, there was a possible stability-issue with Lorentz’s deformable electron. Abraham had shown, more specifically, that inertial force-free motion in any direction was only guaranteed if the electron’s momentum and velocity were collinear, which required that its shape was symmetric around axes perpendicular to its direction of motion. Because of its spherical form, this was no issue for Abraham’s rigid electron. For an ellipsoidal rigid electron, this entailed that such motion was only possible in the direction of its big axis, and not parallel to its axis of rotation (see footnote 103). For a deformable electron such as Lorentz’s, ﬁnally, it was therefore not clear whether, and if so, by means of which stabilizing forces, such inertial force-free motion was possible in all directions. Ehrenfest (1907) now argued that this same question also formed a pressing issue for what he called Einstein’s reformulation of ‘Lorentz’s relativistic electrodynamics’ (1907, p. 204).124 Einstein’s theory formed, according to Ehrenfest, a closed system, which means that we should be able to obtain from it, in a purely deductive way, an

124 We should not see this description of the theory as an electrodynamical one as a case of bad interpretation, since Einstein himself often characterized his work on the principle of relativity in these terms. He described e.g. his (1905a) derivation of the energy-mass equivalence E = mc2 as a very interesting consequence of what he called his (1905c) electrodynamical investigations (1905a, p. 639). Moreover, Einstein would again use this formulation in his (1907e) article (see the quote on page 76). As such, Ehrenfest had good reasons to conceptualize Einstein’s (1905a; 1905c) work on the relativity principle as oﬀering an electrodynamical theory.

73 Chapter 2. Experiment and the Electron answer to Abraham’s issue for the deformable electron, which Ehrenfest formulated as follows:

Let us assume that there exists a deformable electron which, when it is at rest, has a shape that is neither spherical nor ellipsoidal. In the case of uniform translational motion, such an electron will undergo, according to Mr. Einstein, the well-known Lorentz-contraction. Is now, for such an electron, force-free uniform translational motion possible in any direction or not? (Ehrenfest, 1907, p. 204-205)125

Two responses were possible, and both were equally problematic from a relativistic perspective, according to Ehrenfest. If the theory would tell us that such motion is not possible in all directions, then a new hypothesis should be added to the theory that explicitly excludes the existence of such electrons, for otherwise it would be possible to detect absolute motion, which goes against the principle of relativity.126 If, on the other hand, it is possible, then it should be shown how this follows from the theory without introducing a completely new axiom (Ehrenfest, 1907, p. 205). As Staley points out, “Ehrenfest’s question shows him taking the demands of relativity serious, holding the theory to its own standards” (2008a, p. 264). That Ehrenfest asked, more specifically, how the theory could answer this question without introducing new axioms shows that he recognized the importance of the two principles on which Einstein based his theory. He also saw that the theory’s most important point was the exclusion of the detection of absolute rest. And the fact that he specified that the issue arises independently of the electron’s precise form, shows that he saw what was peculiar about Einstein’s and Planck’s relativistic approach to the electron, which did not involve a specific electron model (see the quotes by Einstein on page 65 and by Planck on page 72).127

Einstein and Ehrenfest’s Closed System Einstein responded to the question raised by Ehrenfest in two publications, in which he addressed Ehrenfest’s characterization of the theory of relativity as a closed system (1907a) and Ehrenfest’s question concerning the electron (1907e) respectively. In the ﬁrst, he started by pointing out that, contrary to what Ehrenfest claimed, the principle of relativity and the principle of the constancy of the velocity of light should not be seen as forming a closed system, but rather as heuristic principles. These principles in themselves only made claims about rigid rods, clocks and light signals, i.e. the physical entities whose behaviour Einstein studied theoretically in order to obtain his

125 The original German goes as follows: “Angenommen, es existiere ein deformierbares Elek- tron, das in der Ruhe irgend eine nicht-kügelformigeund nicht-ellipsoidische Gestalt besitzt. Bei gleichförmigerTranslation erfährtdieses Elektron nach Hrn. Einstein die bekannte Lorentz- Kontraktion. Ist nun fürdieses Elektron gleich-förmigeTranslation nach jeder Richtung hin kräftefrei möglichoder nicht?”. 126 When an electron is set in motion, its shape will deform with respect to its shape in its rest frame. If this deformed shape would not be spherical, Abraham’s argument regarding the collinearity of velocity and momentum would apply (see page 51), and hence, in this motion-frame, force-free inertial motion would not be possible in all directions. As such, it would be possible, on the basis of the motion that was possible for the electron, to draw an absolute distinction between its rest frame and the other frames. 127 In fact, in his statement of his question, Ehrenfest refered explicitly to the claim by Planck, that the theory of relativity can be developed without needing to address the issue of the electron’s constitution (discussed on page 72).

74 Experiment, Time and Theory relativistic frame transformations. It is only by applying these principles to already existing laws that we can obtain further claims, according to Einstein. Moreover, these claims should only be taken as concerning relations between these laws. Thus, on Einstein’s view, we should not expect the theory of relativity to already contain, in any kind of deductive way, answers to questions concerning the dynamics of the electron, as Ehrenfest assumed, but only regarding the way in which the different laws governing the electron’s behaviour, whatever its constitution may be, relate to each other. Einstein then sketched how this works by showing how the principles could be used as heuristic instruments to formulate a relativistic theory of the electron’s motion, as he had done earlier in his (1905c) paper to obtain equations for the electron’s longitudinal and transverse mass (see page 63). This account remained silent, however, on the electron’s constitution since, as we have seen, Einstein proceeded without any particular model of the electron, and his results concerned not only electrons but all material bodies in general. In the final part of his first reply to Ehrenfest’s question concerning the electron’s dynamics, Einstein then provided a sketch of what would be required to formulate an answer. He started by pointing out that it is often assumed that the electron’s charge is distributed over a rigid body, and that this assumption comes down to the postulated introduction of forces that balance the electron’s electrodynamical forces.128 This meant that a truly deductive answer to Ehrenfest’s question would only be possible if one already had a dynamics of these balancing forces, something that, according to Einstein, could not be provided by electrodynamics in itself. Neither, however, could the theory of relativity provide this at that time:

If the theory of relativity is correct, we are still far from the latter goal [i.e. a dynamics of the rigid body]. For the time being, we only have the kinematics of parallel translation and an expression for the kinetic energy of a body in parallel translation, provided the latter does not interact with other bodies; for the rest, both the dynamics and kinematics of a rigid body have at present to be considered as unknown for the case under consideration. (Einstein, 1907a, p. 207 – 208; Beck, 1989, p. 237)

What Einstein was hinting at here is that the stability of the electron was not so much an issue solely for the theory of relativity, but equally well for e.g. Abraham’s electron theory. For Abraham could not oﬀer a dynamics of the balancing forces of the rigid body either: he just stipulated that, if we follow the electromagnetic world view, the electron had to be a rigid body. This does not inform us about the actual constitution of the electron. This does not mean, however, that Einstein saw the issue raised by Ehrenfest as a non-issue. Instead, as we will see later (page 107), the constitution of the electron would become a central topic of investigation in Einstein’s work on radiation phenomena. And in his (1907e) article, which appeared a month after his reply to Ehrenfest, Einstein investigated in how far the principle of relativity could address the issue raised by Ehrenfest. It is to this article that we will now turn.

128 See, for example, principle 5 of Abraham’s foundations of the theory of the electron, according to which the electron’s constitution is to be conceptualized in terms of an equilibrium between internal and external electromagnetic forces, in line with the mechanics of the rigid body (discussed on page 59).

75 Chapter 2. Experiment and the Electron

Einstein and the Dynamics of the Electron In his second response to Ehren- fest (1907), Einstein approached the issue within a broader study of one particular consequence of the theory of relativity, namely the equivalence it entails between mass and energy, often expressed in terms of the formula E = mc2.129 This was a claim, according to Einstein, with “extraordinary generality” (Einstein, 1907e, p. 371; Beck, 1989, p. 238). At the same time, it had only been argued for on the basis of a few specific cases.130 The fact that this equivalence rested on such specific cases raised the question whether a more general investigation of its precise scope and justification was possible. At that time, Einstein immediately pointed out, this was not the case, since a world view in conformity with the principle of relativity was still lacking:

The general answer to the question posed is not yet possible because we do not yet have a complete world view that would correspond to the principle of relativity. Rather, we must limit ourselves to the special cases that we can handle at present without arbitrariness from the standpoint of relativistic electrodynamics. (Einstein, 1907e, p. 372; Beck, 1989, p. 238)

While employing cases from relativistic electrodynamics ensures that we are on stable ground, it also entails limitations, according to Einstein: as he had shown in his recent research on radiation, speciﬁc heats and the light quantum, the Maxwell equations could not account for these phenomena, and they therefore had only limited validity.131 Given that the cases he was going to consider in this article did not concern these topics, however, this did not pose a problem (Einstein, 1907e, p. 372). After these remarks about the scope of his work on the relativity principle, Einstein then turned to a discussion of the way in which the kinetic energy of a rigid body in uniform translation subject to external forces is handled in terms of the relativistic approach. Applying the insights obtained to electrically charged rigid bodies then led Einstein to an equation for their kinetic energy which diﬀers, he pointed out, from the equation obtained earlier for the kinetic energy of a non- charged rigid body. This entails that an electrostatically charged body possesses an inertial mass that surpasses that of a non-charged body, and as such this special case provided evidence for the inertia of energy and the energy-mass equivalence (Einstein, 1907e, p. 379). In the third section, Einstein turned his attention towards a relativistic treatment of the dynamics of the rigid body, the attainment of which, he claimed, could seem to

129 During this period, Einstein provides different formulations of this equivalence. In this paper, he states it as the claim that the inertial mass of a body increases or decreases in a completely determinate way if its energy increases or decreases, i.e. “to an increase in the body’s energy ∆E there must always correspond an increase in the mass ∆E/V 2, where V denotes the velocity of light” (Einstein, 1907e, p. 371; Beck, 1989, p. 238). For an extensive discussion of the different ways in which Einstein formulated and conceptualized this equation over the years, see Ohanian (2009). 130 Einstein had obtained it in the relativistic study of the motion of a body emitting radiation energy simultaneously in two directions. Since then, he had also achieved the same results by means of the study of a different case, concerning the constancy of motion of a body’s center of gravity (Einstein, 1906a). 131 Einstein refers here to his (1905b; 1906c; 1907b) articles. For a short overview of the content of these articles, see footnote 191.

76 Experiment, Time and Theory be near at hand on the basis of the results obtained earlier. He warned, however, that the claims concerning the kinetic energy of a non-charged rigid body only hold for situations where the forces involved are constant over time. If this is not the case, he showed by means of a simple example, we would be led to results that contradict the work-energy principle (Einstein, 1907e, p. 379).132 After showing that this problem could not be resolved, in relativistic terms, by appealing to the instantaneous spread of force, since that would go against the principle of the constancy of the velocity of light, he was brought to restate his answer to Ehrenfest’s question (see page 75): “[I]f relativistic electrodynamics is correct, we are still far from having a dynamics of the parallel translation of the rigid body” (Einstein, 1907e, p. 381; Beck, 1989, p. 247).

Manipulability and the Early Relativistic Response We have seen, on page 70, that Kaufmann’s (1906b) experimental results raised two challenges for the relativistic approach: an experimental one, concerning the correspondence of the theory’s formulae with observation, and a theoretical one, regarding the viability of the theory’s account of the electron’s dynamics. Planck (1906a) attempted to drive a wedge between these two challenges, by arguing that the experimental challenge could be addressed through further elaboration of the theory, and that the theoretical challenge was not a real challenge at all (see the quote on page 72). In this way, it would be possible to put aside the experimental challenge for the moment, in order to elaborate further the theory of relativity. The question raised by Ehrenfest shows, however, that Planck’s attempt was not successful. The same question regarding the electron’s stability in motion could be raised even if we did not ascribe any speciﬁc form to it (see footnote 127). A strategy diﬀerent from Planck’s was employed by Einstein, who argued that the electron’s stability was not solely an issue for the relativistic approach, but equally well for the electromagnetic world view. Abraham postulated that the electron formed a rigid body in order to ensure its stability, but this did not provide any insight in which forces ensure this stability. And given that this question could not be answered by the Maxwell equations, according to Einstein (see page 75), the electromagnetic world view would neither be able to address this question. This response did not convince Ehrenfest, as is clear from a letter to Walther Ritz:133

“In Minkowski’s work,” Ehrenfest wrote, “I ﬁnd just the same incom- prehensibility as in Einstein: when I advanced my question, Einstein answered: I have never maintained that my postulate of relativity leads to a full determination . . . but Minkowski now maintains that his theorems lead to a full determination – to me his concept of ‘force’ is completely ununderstandable (just as with Einstein).” (Staley, 2008a, p. 269)

What Ehrenfest’s responses indicate is how Kaufmann’s experiments were taken at the time to be concerned primarily not only with the electron’s charge-to-mass ratio

132 This principle states that the change in kinetic energy of an object is equal to the net work done by all forces on the object. 133 This quote from an undated letter (probably written somewhere in 1908) was translated by Richard Staley. Minkowski’s (1908; 1909; 1915) work during this period was concerned with the elaboration of a geometrical framework for the theory of relativity. See footnote 212 for a short outline of this work.

77 Chapter 2. Experiment and the Electron or with the velocity-dependence of its mass, but rather directly with its dynamics. They were taken to provide information concerning the electron’s constitution, and hence to provide a way to demarcate those electron-models that were acceptable (Abraham, Bucherer-Langevin) from those that were problematic (Lorentz- Poincar´e-Einstein). This entailed that the experimental results came to function as constraints on how theories of the electron were interpreted and formulated, as can be seen from another of Ehrenfest’s papers (1906). Kaufmann’s experiments, he started his paper, have excluded Lorentz’s deformable electron. Hence the question was how to decide between the remaining models, a question which he then addressed in terms of the stability of Abraham’s rigid electron and the deformable Bucherer-Langevin electron. This led him to claim that only Abraham’s model was really acceptable, since the Bucherer-Langevin model equally well fell prey to the stability-issue originally raised by Abraham (Ehrenfest, 1906, p. 302). As such, Ehrenfest took Kaufmann’s experiments to provide a direct insight into the electron’s electromagnetic momentum, and it was on the basis of this result that the further viability of those electron-models that were in line with it could then be evaluated. That Kaufmann’s experiments were taken to provide such direct insight into the electron’s electromagnetic momentum and hence its dynamics, was a consequence of the fact that both the electromagnetic interpretation (see page 56) and the relativistic interpretation (see page 66) of Kaufmann’s experimental inference oﬀered an account of how the manipulations gave rise to data that would provide information about how the electron’s electromagnetic momentum was connected to its velocity-dependent mass. As long as this direct connection between manipulation and momentum was taken to be reliable and robust, there was no real possibility for the development of a relativistic dynamics of the electron that could account for the results obtained in Kaufmann’s experiments. By this I mean that it was always possible for adherents of the electromagnetic approach to point out that the electromagnetic momentum obtained out of Kaufmann’s measurements led to a stability-issue, and that as such, it would be very implausible that a relativistic deformable electron could bring about what Kaufmann’s manipulations were taken to provide information about, i.e. the electron’s electromagnetic momentum. In the following sections, we will see that said connection was problematized, however, both from the experimental and from the theoretical side, in such a way that von Laue could claim that the theory of relativity showed that Kaufmann’s experiments could not provide any information about the electron’s dynamics. To start, we will go back a little in time, to Planck’s (1906b) discussion of Kaufmann’s experiments at the Naturforscherversammlung.

2.6 Discussing Kaufmann’s Experimental Set-Up

Planck discussing Kaufmann’s Experiments Planck (1906b, p. 753 – 754) opened his discussion of Kaufmann’s (1906b) experiments by praising Kaufmann’s precision and clarity, since it allowed him to thoroughly evaluate the claims made on the basis of the experiments. Immediately afterwards, Planck outlined the main diﬀerence between Kaufmann’s original analysis and his own re-analysis. While Kaufmann reduced the measured deﬂections,

78 Experiment, Time and Theory which Planck denoted as (¯y, z¯), to infinitely small deflections (y0, z0), and then compared these with the (y0, z0) predicted by the different theories, Planck would not carry out such a reduction. He compared the measured deflections directly with the deflections provided by the equations of motion of the different theories. These equations he expressed in terms of the Lagrangian functions he obtained in his (1906a) article (see page 73), which provided equations of motion in terms of the kinetic potential H. After rewriting Kaufmann’s equations for the electric deflection and the magnetic deflection in these terms, Planck then stated what he took to be the central experimental issue on which what he calls Abraham’s ‘Kugel-theorie’ (sphere theory) and the Einstein-Lorentz ‘Relativtheorie’ differed:134

The connection between the electric deflectiony ¯ and the magnetic deflec- tionz ¯ is provided by the dependence of the momentum p on the velocity [v], and this is provided by the formula expressing the kinetic potential H as a function of [v], which is different for the different theories. (Planck, 1906b, p. 756)135

Planck then applied these alternative expressions to the data obtained in Kauf- mann’s latest run of experiments, in order to calculate the theory-independent deflections. This allowed him to compare his approach with Kaufmann’s equations (2.20) and (2.21), which showed that his approach performed equally well. And on Planck’s approach as well, Abraham’s theory was closer to observation than the Einstein-Lorentz theory. In contrast to Kaufmann, however, Planck did not conclude from this that it confirms Abraham’s theory and refutes the Einstein-Lorentz theory. That would require, according to Planck, that the difference between the values provided by Abraham’s theory and the measured values would be small in comparison with the Einstein-Lorentz theory, which was not the case. The theoretical values were in fact closer to each other than any of them was to the observed values (1906b, p. 757). Planck then suggested that this failure to come to a correspondence between theory and observation was due to Kaufmann’s use of Simon’s /µ0 value, and that improving it would lead to a satisfactory decision:

One could now perhaps expect, that the lack of correspondence is caused by the value used for the ratio /µ0, and that through a ﬁtting change of this value a satisfactory correspondence with one of both theories could be attained. (Planck, 1906b, p. 757)136

The issue, according to Planck, was that if one started from the values observed in Kaufmann’s experiments, one would obtain values for /µ0 and β = v/c that

134 Planck only discussed what he took to be the most elaborate theories (Planck, 1906b, p. 756): he did not mention the equations formulated by Bucherer-Langevin and Cohn. 135 I have changed the notation of this quote to bring it in line with the rest of the chapter. The original German goes as follows: “Der Zusammenhang zwischen der elektrischen Ablenkung y¯ und der magnetischen Ablenkungz ¯ wird bedingt durch die Abhängigkeit der Impulsgröße p von der geschwindigkeit q, und diese ist gegeben durch den Ausdruck der kinetischen Potentials H als Funktion von q, welcher fürdie einzeln Theorien verschieden lautet”. 136 The original German goes as follows: “Man könnte nun vielleicht vermuten, daß der Mangel an Ubereinstimmung¨ durch den benutzten Wert [. . . ] fürdas Verhältnis /µ0 hervorgerufen ist, und daß durch eine passende Abänderungdieses Wertes eine genügende Ubereinstimmung¨ mit einer der beiden Theorien erzielt werden könnte”.

79 Chapter 2. Experiment and the Electron were not acceptable according to any of the theories. He claimed that for some of the values obtained, one would end up with velocities that surpass the velocity of light, which would go against both Abraham’s theory (see page 53) and the Lorentz- Einstein theory. This indicated that something had gone wrong with the theoretical interpretation of the measured values. This error had to be found and corrected first, before these measurements could be used to decide between the two theories (1906b, p. 757 – 758). In his final section, Planck then provided an outline of how such future research should look like. Kaufmann assumed, we have seen, that he was measuring the velocity-dependence of mass for electrons with as high a velocity as possible. But this was not what he in fact did, according to Planck: he rather investigated how much an electron would be deflected by an applied magnetic field with a specific field strength. As such, what Kaufmann was in fact measuring was the deflection for a specific momentum, determined by the applied field. But, Planck pointed out, for the same momentum, the two theories at play ascribed different velocities to the electron. For the same applied field strength, the theory of relativity would ascribe to the electrons a lower velocity than Abraham’s electromagnetic theory. Planck then argued that it would be better to carry out experiments that would compare the different theories with respect to the electric deflection of electrons with velocities neither too low nor too high. Such measurements would provide a clearer decision, because the predictions offered by the two theories for such a deflection were further removed from each other. As such, Planck argued, it would be better to perform measurements on lower-velocity cathode rays. A second advantage of using such rays, he claimed, would be that they offer a third measurable characteristic besides their magnetic and electric deflectability, which was, in contrast to Kaufmann’s velocities, theory-independent: their discharge potential P , which is equal to the ratio of the ray’s energy E and the charge : P = E/108, and which is best measured when the velocity of the rays is neither too low, nor too high. The two theories now differed, according to Planck, on how much an electron with a specific discharge potential would be deflected by an applied magnetic field. This entails a difference in the way in which the electron’s mass depends on its velocity. As a result, Planck argued, experimental investigations of this property could offer a better way to further the debate (1906b, p. 759).137 The discussion that followed Planck’s presentation again clearly shows how central the issue raised by Kaufmann’s experiments was in the German physics community at the time, for many adherents of the electromagnetic view (Abraham, Kauf- mann, Arnold Sommerfeld), immediately disputed Planck’s claims, and argued that there were good reasons to favour Abraham’s theory over the Lorentz-Einstein theory.138 Kaufmann circulated some of his photographic plates, which clearly showed,

137 As we will see on page 88, Planck’s suggestion for experiments on cathode rays was carried out by one of his doctoral students, Karl Erich Hupka. In his (1906b) article, Einstein also proposed an alternative way to determine the velocity-dependency of the electron’s mass, by means of the discharge potential of cathode rays. According to Miller, these experiments were not carried out by anyone during this period. In his (1907c, p. 437) review article, Einstein again repeats this proposal to perform experiments on cathode rays. Discussions of these experiments can be found in (Miller, 1981, p. 341 – 343) and (Illy, 2012, p. 17 – 19). 138 Presentations at the Naturforscherversammlung were published, together with the discussion sessions that followed them, in the Physikalische Zeitschrift. Hence the comments presented here can be found in Planck’s (1906b) publication.

80 Experiment, Time and Theory he claimed, that the difference between Lorentz’s theory and observation was consistently worse than that between Abraham’s theory and observation, and significantly so. Lorentz’s differed between 10% and 12%, whereas Abraham’s only differed with 3% to 5% (Planck, 1906b, p. 759 – 760). Abraham remarked that since the difference between theory and observation was more than double for Lorentz’s theory than it was for his own, his theory could be seen as providing a representation of the deflection of the electrons that was twice as good as Lorentz’s. He also argued that one of the advantages of his theory was that it provided a completely electromagnetic account of the electron’s constitution, whereas it was unclear, on the relativistic view, what was exactly responsible for the electron’s dynamics (Planck, 1906b, p. 761). To this, Planck responded that at that time, the choice for one of the two theories was a subjective preference. Only more experimental work could, in the end, decide the issue: Planck: Abraham is right, when he states that the essential goal of the spherical theory would be to provide a purely electrical theory. If this would be accomplished, then that would be very nice, but for the moment this is no more than a postulate. The Einstein-Lorentz theory is also based on a postulate, namely, that no absolute translational motion is detectable. Both postulates are, it seems, not compatible, and now the question is which of the two one prefers. For me, the Lorentzian postulate is in fact preferable. The most we could hope for now is that both approaches are elaborated further and that experiments will finally provide a decision. (Planck, 1906b, p. 761)139 In his (1907c) review article on the theory of relativity, Einstein responded in a similar way to the results of Kaufmann’s experiments. In the section on electron experiments, he there proposed that experiments on cathode rays could help illuminate the issues regarding the electron’s velocity-dependent mass (Einstein, 1907c, p. 436) (see footnote 137). He then turned to a discussion of Kaufmann’s experiments and concluded from the fact that Planck’s (1906b) re-analysis led to the same results as Kaufmann’s, that Kaufmann’s calculations were without error (Einstein, 1907c, p. 439). Following Planck, however, Einstein did not take the fact that Kaufmann had shown that the theory of relativity differed from observation to mean that the principle of relativity had to be abandoned. Only further experiments could provide a decision regarding this question. And, as for Planck, Einstein’s choice for the principle of relativity was a subjective preference. He found the assumptions about the electron underlying the electromagnetic interpretation problematic because he saw them as ad hoc:

139 To this, Sommerfeld responded that it was an expression of a rather pessimistic approach, one that could be expected from people over 40 years old, but not from those who were younger, with whom he sided (Planck, 1906b, p. 761). Sommerfeld was, at that time, almost 40, and the foremost adherents of Lorentz’s theory at the time, Poincaréand Lorentz, were already over 40 years old (Miller, 1981, p. 234). The original German goes as follows: “Planck: Abraham hat recht, wenn er sagt, der wesentliche Vorzug der Kugeltheorie würdesein, daß es eine rein elektrische Theorie wäre.Wenn dies durchführbarwäre,wäredas wohl sehr schön,vorläufigist es nur ein Postulat. Der Lorentz-Einsteinschen Theorie liegt auch ein Postulat zugrunde, nämlich, daß keine absolute Translation nachzuweisen ist. Beide Postulate lassen sich, wie es scheint, nicht vereinigen, und nun kommt es darauf an, welchem Postulat man den Vorzug gibt. Mir ist das Lorentzsche eigentlich sympathischer. Am besten wird es wohl so sein, wenn auf beiden Gebieten weiter gearbeitet wird und die Experimente schließlich die Entscheidung geben”.

81 Chapter 2. Experiment and the Electron

Only after a more diverse body of observations becomes available will it be possible to decide with conﬁdence whether the systematic deviations [of the theory of relativity from observation] are due to a not yet recognized source of errors or to the circumstance that the foundations of the theory of relativity do not correspond to the facts. It should also be mentioned that Abraham’s and Bucherer’s theories of the motion of the electron yield curves that are signiﬁcantly closer to the observed curve than the curve obtained from the theory of relativity. However, the probability that their theories are correct is rather small, in my opinion, because their basic assumptions concerning the dimensions of the moving electron are not suggested by theoretical systems that encompass larger complexes of phenomena. (Einstein, 1907c, p. 439; Beck, 1989, p. 283 – 284)

In short, by this time there was no relativistic response yet to Kaufmann’s experimental results, nor to Abraham’s stability issue. The only response possible was that more work needed to be done, and that as it stood, the main reasons to prefer the principle of relativity over the electromagnetic world view were subjective preferences. What the discussion also shows, however, is that both Einstein and Planck attempted to defuse the challenge by arguing that the issues raised against the theory of relativity were equally well issues for Abraham’s theory. Einstein did this with respect to the dynamical constitution of the electron as a rigid body. Planck did this, first, by means of his argument that Kaufmann’s use of Simon’s /µ0 led to conflicts with Abraham’s claim that the velocity of the electron could not be higher than that of light; and second, in terms of his claim that measurements of the magnetic and electric deflection of electrons were not theory-independent, and that it was better to measure the discharge potential. While these attempts in themselves were not yet sufficient to defuse the challenge, they did lead to new experimental and theoretical investigations into the electron in such a way that a relativistic response could be developed.

Bestelmeyer and the charge-to-mass ratio While Planck’s (1906b) re-analysis did not enable the theory of relativity to overcome the challenges raised by Kaufmann’s experiments, one eﬀect that it did have was that it was accompanied by a whole series of investigations and discussions about Kaufmann’s experimental set-up. Adolf Bestelmeyer, for example, turned to a study of the low-velocity charge-to-mass ratio /µ0 of cathode rays (1907). At that time, measurements by August Becker (1905) were generally taken to have established 7 140 that, for cathode rays, /µ0 = 1.8 ... · 10 , according to Bestelmeyer. A more precise determination of the charge-to-mass ratio of low velocity electrons could further the debate, according to Bestelmeyer, and hence he set out to determine it. The experimental apparatus he employed was very similar to Kaufmann’s. Within a set-up from which the air had been evacuated, cathode rays would be sent through

7 140 For comparison, Simon had obtained a value /µ0 = 1.865 · 10 (Kaufmann, 1903, p. 102). 7 In his latest experiments, Kaufmann had obtained a value /µ0 = 1.878 · 10 . Abraham’s theory 7 predicted a value /µ0 = 1.823 · 10 , which diﬀered by 2.9% from Kaufmann’s obtained value. 7 The Lorentz-Einstein equations led to a value /µ0 = 1.660 · 10 , which diﬀered by 11.6% from Kaufmann’s value (Kaufmann, 1906b, p. 533).

82 Experiment, Time and Theory a diaphragm; the electron’s constituting these rays would travel between two capacitor plates that provided the electric field; these electrons would then be captured on a photographic plate, from which their velocity and charge-to-mass ratio could be measured. There were, however, a few important differences. One was that whereas Kaufmann used electromagnets as the source of the applied magnetic field (Staley, 2008a, p. 240), Bestelmeyer employed a solenoid, “which ensured a higher degree of homogeneity than Kaufmann’s electromagnets” (Miller, 1981, p. 335). A second difference was that while Kaufmann used parallel electric and magnetic fields (Miller, 1981, p. 50), Bestelmeyer opted for crossed fields, which allowed him to filter out electrons outside a specific velocity range (Miller, 1981, p. 335). It also entailed that the electron’s velocity and charge-to-mass ratio could be determined using only the apparatus constants, whereas Kaufmann also relied, as we have seen, on Simon’s /µ0. A third difference with Kaufmann’s set-up was that the gap between the capacitor plates was reduced: whereas Kaufmann’s was 0.1243cm, Bestelmeyer’s was 0.058cm, which entailed higher accuracy in keeping the electric field uniform. Fi- nally, by making use of an improved vacuum system, Bestelmeyer’s set-up was less prone to sparking, i.e. the radiation ionizing the remaining air, which, as we will see on page 84, was a possible problem with Kaufmann’s experiments (Miller, 1981, p. 339). Bestelmeyer’s experiments then resulted in a /µ0 value that was significantly smaller than the one used by Kaufmann:

The obtained /µ value is, as one can see, signiﬁcantly smaller compared with those obtained in earlier measurements. Extrapolating from the velocity 0 one obtains, depending on the theory used, values between 1.71 and 1.73 · 107. This value is between 8% and 9% smaller than the one calculated by Kaufmann on the basis of Simon’s value (1.88 · 107). As has been pointed out, the apparatus used was built with suﬃcient care, but not with especially great accuracy. Nevertheless, we can say, on the basis of measurements of the solenoid employed and of the distance between the capacitor plates, that the error margin of the obtained value is between 1% and 2%; an error of 8% or 9% is, however, outside the bounds of the established error margins.(Bestelmeyer, 1907, p. 441)141

Bestelmeyer then used his newly obtained charge-to-mass ratio to re-analyse the results of Kaufmann’s latest experiments. Assuming that his measurements were correct, they no longer clearly favoured the electromagnetic interpretation: they would rather be in between the predictions of Abraham’s and Lorentz’s theory (Bestelmeyer, 1907, p. 442). As Bestelmeyer himself admitted, however, his experiments could not offer a definite decision between the different theories involved, since his measurements only concerned low-velocity cathode rays. Further experimentation was therefore required (Bestelmeyer, 1907, p. 444).

141 The original German goes as follows: “Wie man sieht, ergibt sich /µ im Vergleich zu den bisher bekannten Messungen auffallend klein. Auf die Geschwindigkeit 0 extrapoliert erhältman, je nach der zugrunde gelegten Theorie etwas verschieden, 1.71 bis 1.73·107. Dieser Wert ist 8 bis 9 Proz. kleiner als der von Hrn. Kaufmann aus der S. Simonschen Zahl berechnete (1.88·107). Nun ist der verwendete Apparat, wie gesagt, zwar sorgfältig,aber nicht mit besonders großer Genauigkeit gebaut. Trotzdem ergibt die Betrachtung der bei Ausmessung der Spule sowie bei Bestimmung des Abstandes der Kondensatorplatten erhaltenen Zahlen, daß der erhaltene Wert wohl auf 1 bis 2 Proz. unsicher sein kann; ein Fehler von 8 bis 9 Proz. aber liegt weit außerhalb der übersehbaren Fehlergrenzen”.

83 Chapter 2. Experiment and the Electron

Planck, Kaufmann and Stark on the Electric Field Strength Planck used Bestelmeyer’s results in a (1907) addendum to his (1906b) re-analysis of Kaufmann’s experiments, in which he specified why, according to him, Kaufmann’s experiments should not be seen as providing a decision between the different theories. As we have seen on page 79, Planck had argued that Kaufmann’s results would entail velocities higher than the velocity of light. The source of this problem was the way in which Kaufmann determined his apparatus constant for the electric field E (Planck, 1907, p. 302). Kaufmann assumed that the electric field remained constant over an experimental run, and he then obtained one value for the field strength by measuring the potential difference between the capacitor plates and dividing this by the distance between the plates. According to Planck, however, there remained the possibility that, even though as much air as possible was evacuated from the set-up before running the experiment, the remaining air could be ionized by the Becquerel rays, which would disturb the assumed linear course of the potential between the plates. This raised the question whether the measured deflections would be in better correspondence with one of the two theories if another value for the potential, closer to the one present in the different experimental runs, was used. To estimate the influence of this possible disturbing factor on Kaufmann’s measurements, Planck proceeded as follows: instead of using the value for the field strength Kaufmann had calculated, he used the equation for the electric field strength he had obtained in his 7 (1906b), together with Bestelmeyer’s /µ0 (between 1.71 and 1.73 · 10 ), in order to determine the value for the electric field for each separate experimental run carried out by Kaufmann. In this way, he obtained nine independent values, which then allowed him to determine whether, according to each of the theories, the separate runs displayed the correct electric field strength. On these results, Planck claimed, the ‘Kugeltheorie’ differed from observation with 5%, whereas the ‘Relativtheorie’ differed only by 2%. If the assumptions on which this estimation was based were correct, the chances of the Einstein-Lorentz theory would thus increase. The only real conclusion to be drawn, however, was that more investigations were needed, especially regarding the potential difference and air ionization:

These results are in favour of the theory of relativity, without, of course, being decisive. In any case, one can conclude from this investigation that, if the deviations between observation and theory obtained earlier are to be accounted for by the value for the electric ﬁeld strength used then, and if Bestelmeyer’s value for /µ0 is to be prefered, the chances of the relativity theory increase reasonably. I hope that this will inspire a closer investigation of the questions, how the decrease in potential of the applied part of the electric ﬁeld is to be determined in order to arrive at an even better connection between both theories and the observations, and whether such decrease in potential can actually be understood in terms of an ionization of the remaining gas. Renewed measurements in the same set-up would of course be even more promising. (Planck, 1907, p. 304 – 305)142

142 The original German goes as follows: “Dieser Umstand fälltzugunsten der Relativtheorie ins Gewicht, ohne natürlich entscheidend zu sein. Immerhin wird man als Ergebnis dieser Unter- suchung aussprechen können,daß, falls die frühergefundenen Differenzen zwischen Beobachtung

84 Experiment, Time and Theory

In his (1907) response, Kaufmann disputed Planck’s claim that the deviation of the Einstein-Lorentz theory from his results was to be explained by inconstancies in the electric field strength caused by an ionization of the remaining air. Such an explanation, Kaufmann pointed out, would require that over an experimental run, the electric field strength would diminish with 10%. This was impossible given the small number of ions that could arise from the radium used in the experimental set- up (1907, p. 667). He showed, more specifically, that the fluctuations in the electric field strength were of the size of 10−8, whereas they had to be of the size 10−1 to explain the deviation of the Einstein-Lorentz theory from observation (Kaufmann, 1907, p. 672). Johannes Stark (1908, p. 14) argued, however, that Kaufmann’s response to Planck relied on unacceptable assumptions, and that it therefore could not be seen as a refutation of Planck’s objection to the experimental measurements. For Kaufmann relied in his calculations of the ionization of the remaining air on the validity of Ohm’s law, according to which the velocity of the ions is proportional to the electric field strength. However, when the pressure of the gas emitted by the piece of radium is small, as in the case of Kaufmann’s experimental set-up, this law does not hold, according to Stark (1908, p. 14 – 15). Moreover, Kaufmann also assumed that the ionization of the remaining air in his experimental set-up by α-rays emanating from the piece of radium employed was proportional to the pressure of the gas. Stark pointed out, however, that besides such an ionization process, Kaufmann should also take into account ionization by α- and β-rays that was independent of the gas pressure. Finally, the ions that were produced through these processes could, in turn, give rise to more ions, thus further problematizing Kaufmann’s (1907) calculation of the ionization of the gas. As such, Stark concluded, more experiments on ionization were required:

What has been discussed suggests that Mr. Kaufmann has not disproved the objection by Mr. Planck and that this can be decided only by means of a speciﬁc experimental investigation of the real decrease in potential in Kaufmann’s measurements. (Stark, 1908, p. 16)143

In his reply, Kaufmann (1908, p. 91) pointed out that the issues raised by Stark were indeed correct, but that they could not provide the order of magnitude of potential decrease required by Planck’s argument. There were probably still sources of error to be found in his experiments, Kaufmann admitted, but as long these were not pointed out, his conclusion, that the theory of relativity deviated more from observation than the known error sources could account for, still stood. New und Theorie auf den damals fürdie elektrische Feldstärke angenommenen Wert geschoben werden dürfen,und falls die Bestelmeyersche Zahl für /µ0 vorzuziehen ist, die Chancen der Relativtheo- rie einigermaßen wachsen. Eine nähereUntersuchung der Frage, wie man den Potentialverlauf in dem wirksamen Teile des elektrischen Feldes annehmen müßte,um einen noch besseren Anschluß einer jeden der Theorien an die Beobachtungen zu erzielen, und ob ein solcher Potentialverlauf auch wirklich durch die Annahme einer Ionisation der Gasreste plausibel gemacht werden kann, ist von mir angeregt worden. Noch aussichtvoller wärenfreilich erneute Messungen in demselben Gebiete.” 143 The original German goes as follows: “Aus dem Vorstehenden dürftehervorgehen, daß Herr Kaufmann den Einwand des Herrn Planck keineswegs entkräftethat und daß nur durch eine spezielle experimentelle Untersuchung über den wirklichen Potentialverlauf in den Kaufmannschen Beobachtungen sicherer Aufschluß gewonnen werden kann.”

85 Chapter 2. Experiment and the Electron experiments that were carried out at the time by diﬀerent investigators would, he hoped, be able to shed more light on the issue:

For the moment, the result obtained in my earlier experiments, that the theory of relativity deviates more from my measurements than the error margin of the known error sources can allow for, still stands. This of course does not exclude the existence of still unknown error sources, that can provide an explanation of the obtained deviations. As long as these have not been made explicit, however, the claim against the theory of relativity remains. (Kaufmann, 1908, p. 95)144

Bucherer’s Measurements It was Bucherer (1908; 1909) who responded to Kaufmann’s call by carrying out new measurements on the deflection of Becquerel-rays. The main difference with Kaufmann’s set-up concerned the way in which the applied electric and magnetic fields were used to deflect the electrons constituting these rays. In Kaufmann’s set-up, the directions of these fields were parallel to each other, whereas they were perpendicular to each other in Bucherer’s apparatus, just as Bestelmeyer had done (see page 83). Bucherer made use, moreover, of a cylindrical set-up, in which he placed two capacitor plates, which acted as the source of an electric field with a direction along the x-axis, with in between them a piece of radium (see figure 2.5 for a top-down sketch of Bucherer’s set-up). The whole set-up was surrounded by a solenoid that acted as the source of the applied magnetic field, which had a direction along the y-axis. The cylinder’s inner wall was covered with a photographic film. When no field was applied, electrons of all velocities would travel in a straight line in all directions, forming a horizontal line on the photographic plate. The application of both an electric and a magnetic field created a velocity-filter: it allowed Bucherer to have only electrons of a specific velocity to travel beyond the capacitor plates, while the rest would be deflected in such a way that they would end up on the plates. Once these electrons with a specific velocity had crossed the capacitor plates, they would be deflected by the applied magnetic field and end up on the photographic plate at a certain distance in the z-direction below the horizontal line that resulted when no fields where applied. Electrons traveling in a straight line that formed a specific angle α with the direction of the magnetic field (in the x−y-plane, see figure 2.5 for a top-down sketch), would, however, not be deflected in the z-direction: these would end up on the horizontal line formed when no fields were applied. For each velocity, there would now be such a particular angle α for which the electrons’ trajectory would remain straight, and the way in which this angle would depend on velocity differed across the available theories.145 One particular advantage of Bucherer’s experimental set-up was that, because he could filter the velocities, he could calculate the charge-to-mass ratio /µ0 for different velocities, and compare

144 The original German goes as follows: “Es bleibt also wohl das Resultat bestehen, daß die Abweichungen meiner Messungen von der Relativtheorie größersind, als die von bekannten Fehlerquellen herrührendenwahrscheinlichen Fehler. Damit ist natürlich nicht ausgeschlossen, daß noch unbekannte Fehlerquellen existieren, die einmal zur Erklärungder Abweichungen dienen können.Solange diese aber nicht aufgefunden sind, bleibt der Widerspruch gegen die Relativtheorie bestehen”. 145 See (Miller, 1981, p. 345 – 350) and (Staley, 2008a, p. 250 – 254) for more extensive discussions and better visualizations of Bucherer’s experimental set-up.

86 Experiment, Time and Theory

Figure 2.5: Top-down geometrical sketch of Bucherer’s experimental set-up. The x-axis is depicted by the arrow to the right, the y-axis by the downward arrow. The inner circle depicts the capacitor plates. Figure source: (Bucherer, 1908, p. 757). the different theories with respect to how well they accounted for the stability of this ratio over different velocities, rather than compare them with respect to a single calculated /µ0-value, as Kaufmann had done (Miller, 1981, p. 347). The theories he compared were the following: Abraham’s electromagnetic theory, the Einstein- Lorentz relativity theory, and his own formulation of the theory of relativity.146 His results, he claimed, clearly favoured the Einstein-Lorentz theory: “This experiment is the confirmation of the relativity principle” (1908, p. 760), a claim he repeats in his (1909, p. 525).147 The discussion following Bucherer’s presentation shows that some scientists, such as Minkowski, took these results as the end of the challenge raised by Kaufmann’s experiments and as the final confirmation of the relativity principle.148 Others,

146 As we have seen, Kaufmann’s (1906b) results favoured Bucherer’s (1904) electromagnetic electron model, together with Abraham’s, over the Einstein-Lorentz theory. In contrast to Abra- ham and Kaufmann, however, Bucherer did not want to give up the principle of relativity, and he had therefore attempted to incorporate it within his own theory. 147 Bucherer’s experiments immediately ruled out his own theory (Bucherer, 1908, p. 759; Bucherer, 1909, p. 519). The original German goes as follows: “Diese Ergebnis ist die Bestätigung des Relativitätsprinzip”. 148 Minkowski expressed his joy that Bucherer’s experiments had finally shown the rigid electron to be a monstrosity that had no place in physics as follows: “I want to express how happy I am to see an experimental confirmation of Lorentz’s theory over the rigid electron. That such a day would come, was not to be doubted from a theoretical point of view. I see the rigid electron as a monster in the company of the Maxwell equations, whose most inner harmony is the principle of relativity. Approaching the Maxwell equations with the idea of a rigid electron is similar, it seems to me, to going to a concert with one’s ears stuffed with cotton balls. One has to have the utmost admiration for the courage and the strength of the school of the rigid electron, who have jumped, in a most fabulous way, over the widest mathematical hurdles with the hope of landing somewhere on experimental physical ground. But the rigid electron is not a working hypothesis, it is a working obstacle” (Bucherer, 1909, p. 762) (“Ich will meiner Freude darüber Ausdruck geben, die experimentellen Ergebnisse zugunsten der Lorentzschen Theorie gegenüber der des starren Elektrons sprechen zu sehen. Daß dem eines Tages so sein würde,konnte vom theoretischen Standpunkte

87 Chapter 2. Experiment and the Electron however, were more sceptical. Bestelmeyer, for example, pointed towards a possible source of error: since Bucherer did not provide the original velocity distribution of the radiation, it could not be excluded, on the basis of the dimensions of the set-up, that electrons with other velocities than those controlled for by the electric and magnetic field possibly displaced the curve (Bucherer, 1908, p. 760). In his response, Bucherer claimed that he was sure that this was not the case, without really specifying why he thought so. This clearly did not convince Bestelmeyer, since he again raised his concern in response to Bucherer’s reply, and even elaborated it into a published criticism (1909) of Bucherer’s experiments, which came down to Bestelmeyer “tutoring Bucherer in the rigors of precision experimentation” (Staley, 2008a, p. 254). One problem with Bucherer’s (1908; 1909) publications, according to Bestelmeyer’s published criticism (1909, p. 167), was that they did not provide enough information about what was measured and how this was carried out, which entailed that too little was known about possible sources of error. Moreover, Bucherer’s conclusion that his experiments favoured the Einstein-Lorentz theory rested almost entirely on one particular run of experiments, while his other published results – which were, in any case, far too few according to Bestelmeyer – did not provide a clear decision between the two theories (Bestelmeyer, 1909, p. 167 – 168). In a follow up paper, Bucherer (1909, p. 526 – 531), replied to the issue raised by Bestelmeyer during the discussion following his (1908) presentation, regarding a possible displacement of the curve by electrons that were not controlled by the applied fields. Bestelmeyer (1909, p. 169 – 173) did not see, however, how it was adequate. As such, Bestelmeyer concluded, Bucherer’s experiments should not be seen as a confirmation of any kind of the Einstein-Lorentz theory (Bestelmeyer, 1909, p. 174).

Hupka’s Measurements and Heil’s Remarks A final series of experiments on the velocity-dependence of the electron’s mass to be discussed were carried out by a doctoral student of Planck’s, Karl Erich Hupka (1909). Earlier experiments had all been carried out, according to Hupka, by means of Becquerel rays: Kaufmann’s experiments, which had indeed shown that there was indeed a dependency of the electron’s mass on its velocity, but which provided results that fitted neither of the theories sufficiently well; and Bucherer’s results, which argued in favour of the relativity principle (Hupka, 1909, p. 169 – 170). This raised the question how the different theories fared with regards to lower velocities (around 0.5c), which could be provided, Hupka argued, by cathode rays. These rays, when emitted, would then be accelerated by means of an electric field, in such a way that the electrons constituting these rays would acquire a particular discharge potential P . As we have seen on page 80, it was Planck who first suggested experiments on the aus gar nicht zweifelhaft sein. Das starre Elektron ist meiner Ansicht nach ein Monstrum, in Gesellschaft der Maxwellschen Gleichungen, deren innerste Harmonie das Relativitätsprinzipist. Wenn man mit der Idee des starren Elektrons an die Maxwellschen Gleichungen herangeht, so kommt mir das geradeso vor, wie wenn man in ein Konzert hineingeht und man hat sich die Ohren mit Wattepropfen verstopft. Man muß auf das höchste den Mut und die Kraft der Schule des starren Elektrons bewundern, die mit fabelhaftem Ansatz über die breitesten mathematischen Hürdenhinwegspringt in der Hoffnung, drüben auf experimentellem physikalischem Boden zu Fall zu kommen. Aber das starre Elektron ist keine Arbeitshypothese, sondern ein Arbeitshindernis”).

88 Experiment, Time and Theory discharge potential of cathode rays, since this procedure was less prone to particular theoretical preferences. According to both Abraham’s theory and relativity theory, the application of an electric field E to an electron with a charge would give the electron a discharge potential P , and hence a particular momentum p, velocity v and kinetic potential H, in line with the following equation: E = P · 108 = vp − H. Applying a magnetic field would then influence the momentum p of these electrons in such a way that they would be deflected, which influenced their kinetic potential H, since p = ∂H/∂v. Abraham’s theory now entailed the following velocity-dependency of the electron’s kinetic potential H (i.e. its Lagrangian L):

3 c2 − v2 c + v H = − µ c2 ln − 1 (2.25) 4 0 2vc c − v The Lorentz-Einstein theory, on the other hand, offered the following equation: r ! v2 H = −µ c2 1 − − 1 (2.26) 0 c2 Hupka therefore proposed to measure the precise deflection of cathode rays by an applied electric field, in order to obtain both a more precise value for the charge-to- mass ratio and a decision between the two theories (Hupka, 1909, p. 171 – 172).

Figure 2.6: Sketch of Hupka’s experimental set-up, with the cathode rays passing from R to H. Figure source: (Hupka, 1909, p. 176).

The set-up employed by Hupka (see ﬁgure 2.6) was, in general, more or less the

89 Chapter 2. Experiment and the Electron same as the one used by Kaufmann. Light emanating from a lamp L gave rise to cathode rays at point K. These rays were then guided through the discharge tube R, which was evacuated from air as much as possible. Application of an electric field at the end of the discharge tube would then accelerate the electrons, after which they passed through a diaphragm. Applying a magnetic field by means of two solenoids (N and S) would then deflect their trajectory, which entailed that they would leave a mark at a different spot on the photographic plate P than they would have left if no field was applied. The main difference with Kaufmann’s experimental set-up, however, was that Hupka not only introduced specific pieces of machinery, such as the battery B with electrostatic generator J to keep the applied electric field as constant as possible, but also a regulating device E which ensured that if the constancy were to change, this would be accommodated. Proceeding in this way entailed, Hupka claims, that the values required for further calculations could be read off allmost directly from his measurement set-up 7 (1909, p. 186 – 187). He made use of the value /µ0 = 1.80 · 10 , i.e. a value in 7 between the ones used by Kaufmann (/µ0 = 1.878 · 10 ), Bestelmeyer (between 1.71 · 107 and 1.73 · 107) and Bucherer (1.77 · 107) (Hupka, 1909, p. 187), in order to calculate the precise velocity-dependency of the kinetic potential H. This made him conclude that “[t]he results speak, as one can see, in favour of the relativity theory” (Hupka, 1909, p. 194).149 Even then, however, Hupka concluded that his experiments should not be seen as a definite argument in favour of relativity theory over Abraham’s theory, since that would require even more precision. The only real conclusion that could be drawn was that more measurents were required (1909, p. 204). This conclusion was not unjustified, as can be seen from the response to Hupka’s experiments by another doctoral student of Planck’s, Wilhelm Heil (1910). Heil pointed out, more specifically, that there were inaccuracies in Hupka’s calculations of the error margins of his measurements, and that if the right error margins were used, his results could not provide a decision at all between the two theories. Both could be brough in agreement, more specifically, with the obtained measurement 7 7 results, and using /µ0 = 1.77 · 10 or even Bestelmeyer’s /µ0 = 1.72 · 10 instead 7 of /µ0 = 1.8 · 10 , as Hupka had done, did not provide any better differentiation between the two theories (Heil, 1910, p. 523 – 530).150

This led Heil to claim that a smaller /µ0-value favours the Lorentz-Einstein view, whereas a higher one fits better with Abraham’s theory. If we were to rely on what he described as the most precise measurement available at that time (Becker’s (1905) measurements, which Bestelmeyer (1907) already had presented as the most accurate available, see page 82), then we would arrive at a decision in favour of Abraham’s theory (Heil, 1910, p. 546). But this conclusion, again, depended on the assumption that there were no problems with Becker’s measurements, which we could no longer exclude, given how previous measurements had fared. The primary conclusion to be drawn, Heil suggested in his final paragraph, was that it is very difficult to obtain a final decision in favour of one particular theory, since every

149 Original German: “Die Versuche sprechen, wie man sieht, zugunsten der Relativtheorie”. 150 The predictions of both theories, on Heil’s reanalysis of Hupka’s experiments, differed more or less with 10% to 11% from the measured results (Heil, 1910, p. 531). This claim was repeated and confirmed by Jakob Laub in his overview of all the different experimental investigations into the principle of relativity (1910, p. 459).

90 Experiment, Time and Theory measurement and calculation could always be criticized:

Measurements and calculations, that turn such a signiﬁcant decision as that between theories of the dynamics of the electron into the subject of investigation, will be open to cricitism in all their aspects. (Heil, 1910, p. 546)151

Manipulability and Kaufmann’s Experimental Set-Up Kaufmann’s experimental results raised two related challenges for the relativistic approach: an experimental one, which concerned the correspondence of the relativistic formulae for the velocity-dependence of the electron’s mass with the experimental results; and a theoretical one, regarding the stability of the theory’s dynamical account of the electron. These challenges were closely connected, as we have seen from Ehrenfest’s discussion of the early relativistic responses to them. This close connection was a consequence of the fact that both the electromagnetic and the relativistic interpretation of Kaufmann’s experimental manipulations, characterized in terms of his experimental inference (see pages 55), saw the experiments as providing information about the electron’s electromagnetic momentum. Hence, it was the G-value obtained in these experiments that set the boundaries for the electron-models that could be subject of debate. Given that the relativistic electron did not conform to this value, it was taken to be problematic. Earlier relativistic strategies to address these two challenges, we have seen in section 2.5, failed: Planck’s (1906a) attempt, to put aside the experimental challenge while arguing that the theoretical challenge was not a problem, was unsucessful because it gave rise to Ehrenfest’s (1907) issue; and Einstein’s (1907a) argument that the stability-issue equally well plagued the electromagnetic world view did not convince Ehrenfest either. In his (1906b) re-analysis of the experiments, Planck attempted a different strategy to address the experimental issue, which consisted of three elements. First, he offered a reconceptualization of what was at stake in the experiments, which was more in line with the relativistic approach: the experiments were not primarily concerned with how manipulating the electron’s electromagnetic momentum G influenced its mass, but rather with how manipulating its momentum p influenced its kinetic potential H (see the quote on page 79).152 Planck then re-analyzed the data obtained by Kaufmann in terms of this characterization of the experimental manipulations carried out. This indicated, according to Planck, that the results produced by these manipulations, insofar as they could be taken to be reliable, should not be taken to argue in favour of Abraham’s theory, but rather as an argument for more experiments, since both theories deviated more from the results than from each other.

151 The original German goes as follows: “Messungen und Berechnungen, welche eine so wichtige Entscheidung wie die zwischen den Theorien der Dynamik des Elektrons zum Gegenstand der Untersuchung machen, sollten in allen Teilen der Kritik zug¨anglich sein”. 152 This reformulation is more in line with the relativistic approach, since Planck (1906a) originally introduced his reconceptualization of Newtonian mechanics, in terms of the relativistic momentum p and the kinetic potential H, to make the application of the principle of relativity to the motion of mechanical systems less complex. At this point, Plancks’ proposal can still seem like a mere reformulation, but as we will see on page 113, this will become an essential factor in the formulation of a relativistic response.

91 Chapter 2. Experiment and the Electron

Second, Planck turned to a discussion of the reliability of Kaufmann’s data. This led him to raise questions about one of the apparatus constants employed by Kaufmann in his measurements, namely the low-velocity charge-to-mass ratio /µ0 in line with Simon’s (1899) value. This value could not be correct, he argued, as it led to β-values for the electron that were not acceptable, since they surpassed the velocity of light. In order for the experimental results to be acceptable, Planck claimed, a different, lower /µ0 value was required, and this would bring the relativistic approach in line again with the experimental results. A third way in which Planck attempted to address the experimental challenge raised by Kaufmann’s experiments was by arguing that Kaufmann’s experiments did not provide the best way to measure the velocity-dependence of the electron’s momentum. Kaufmann carried out measurements with high velocity-electrons, whereas it would be better to carry out measurements of electrons whose velocity was neither too high nor too low. He then provided a sketch of how the information that Kaufmann was after could be obtained using cathode rays. Planck’s strategy thus came down to trying to draw apart the tight connection between Kaufmann’s data, the phenomenon of the velocity-dependence of mass and Abraham’s electromagnetic electron-model. He argued, more specifically, that while there was nothing particularly wrong with Kaufmann’s calculations on the basis of his data, the way in which these data were produced was possibly less reliable than expected, and hence we should not take them to provide direct insight into either the velocity-dependence of mass or the electron’s electromagnetic momentum. This in turn entailed that we should not take these data to form a direct argument in favour of Abraham’s electron-model. Planck’s attempt was not successful, however, as we can see from the discussion following his presentation: there, he was brought to resort to another strategy, which came down to arguing that while his preference for the principle of relativity was indeed subjective, the same was the case for the electromagnetic world view. The replies to Planck’s analysis show that at the time, Kaufmann’s experimental manipulations were still seen as reliable, in the sense that the data they produced were taken to provide actual information about the electron’s velocity-dependent mass and its electromagnetic momentum. While Planck’s analysis could not over- turn this characterization of Kaufmann’s experiments, his approach did bring others to investigate, in different ways, the charge-to-mass ratio of both low- and high- velocity electrons. All of these varied on one or more material aspects of Kaufmann’s set-up. Bestelmeyer and Bucherer applied cross-directional fields instead of fields with a parallel orientation. Bestelmeyer and Hupka employed cathode rays instead of Becquerel rays. Bucherer used a cylindrical set-up and measured the stability of /µ0 over different velocities. And all of them tried to improve the accuracy of their measurements by paying attention to the constancy and homogeneity of the applied fields, to the vacuum inside the set-up, and to the distance between capacitors and the photographic plate. While none of these experiments provided, in themselves, a final decision in favour of either theory, they did allow adherents of the relativistic approach to argue that Kaufmann’s experiments should not be seen as decisive after all. Planck used Bestelmeyer’s results to argue that Kaufmann’s applied electric field E was less constant than assumed, and that this could influence the measurements through ionization of the remaining air in the set-up. Likewise, Minkowski, as we have seen in footnote 148, used Bucherer’s results to argue that there was no room

92 Experiment, Time and Theory for a rigid electron.153 Raising doubts about the reliability of the set-up used by Kaufmann to manipulate the electron also problematized the supposed close connection between Kaufmann’s apparatus constants (E, B, /µ0) and the electromagnetic momentum obtained from them. In this way, the challenge raised by Kaufmann’s experimental results was defused, and the debate was open again. It was no longer necessarily the case that the experiments decided in favour of the electromagnetic interpretation. But, while Planck and others at first believed that further experiments could provide a decision, we have seen that this is not what happened. Each new experimental measurement gave rise to further issues, in such a way that Heil could conclude at the end of the decade that no real improvement had been made in the measurement of the electron’s charge-to-mass ratio, and that because of this we could perhaps not expect such a definitive decision from experiment (see the quote on page 91).154 In order to understand how the theory of relativity was able to definitely address the challenge raised by Kaufmann’s experiments, we thus have to look elsewhere besides experiments on the electron. The starting point for this will be Einstein’s (1907e) claim that a relativistic world view was not yet available, because it could not yet incorporate the most recent insights on radiation phenomena and the quantum (see page 76).

2.7 Planck’s Dynamics: Quanta, Relativity and the Electron

Black-Body Radiation and the Quantum The limitations of the Maxwell equations to which Einstein hinted were mainly based on his reading of Planck’s (1901a; 1901b; 1906c) work on thermal radiation and the study of black bodies.155 Thermal radiation is one of two ways, besides thermal conduction, in which heat is transmitted (Planck, 1906c, p. 1). Heat transfer occurs, more specifically, by means of electromagnetic waves, which are characterized in terms of a wavelength λ and a frequency ν. The main aim of research on thermal radiation in those days was to find a law for its spectral energy distribution, i.e. a law expressing how a ray’s energy or intensity (i.e. the energy it can deliver per unit of time) depended on its wavelength and frequency (Planck, 1906c, p. 6). In his (1906c) lectures, Planck’s focus was, more specifically, on the intensity of such

153 Minkowski’s claim relied, however, on a rather biased reading of Bucherer’s results: Bucherer himself immediately replied to Minkowski that his results, which did indeed form an argument in favour of the theory of relativity, should not be read as concerned with the rigid body (Bucherer, 1908, p. 762). 154 This does not mean that there were no attempts to do so after Hupka’s (1909) experiments. Günther Neumann (1914) and Charles-EugèneGuye and Charles Lavanchy (1915) both carried out experiments that, they claimed, confirmed the Einstein-Lorentz formula. While these experiments “provided broader grounds for a consensus view on the outcome of the experiments” (Staley, 2008a, p. 256, footnote 89), later review articles by C.T. Zahn and A.A. Spees (1938) and P.S. Faragóand L. Jánossy(1957) pointed out that none of the experiments were in fact precise enough to support such a decision. 155 In my short exposition of this earlier work, I will mainly rely on Planck’s (1906c) lectures on thermal radiation, black bodies and the quantum, which he gave in Munich during the winter of 1905 – 1906. Besides this, I have also made use of the historical works referred to in footnote 163.

93 Chapter 2. Experiment and the Electron thermal radiation in the case of systems at rest (1906c, p. 3 – 4).156 The properties of thermal radiation were often studied in terms of what is known as a black body, i.e. a “cavity with perfectly absorbing (i.e. black) walls” (Kuhn, 1987, p. 3).157 When such a body is heated to a specific temperature T and afterwards maintained in a state of thermal equilibrium (i.e. constant temperature T and no heat exchange with its environment), its interior will be filled with thermal radiation. That such bodies offered a very good way to study, both theoretically and experimentally, the general dependency of intensity or energy on wavelength and frequency, followed from earlier work carried out by Gustav Kirchhoff. He had shown that, for thermal radiation in general, the ratio between a body’s emission- capacity E and its absorption-capacity A was equal to the energy I of a ray reaching a surface dσ on the body’s interior from a cone of solid angle dΩ (Planck, 1906c, p. 43) (see figure 2.7).

Figure 2.7: Sketch from Planck’s lectures concerning the behaviour of thermal radiation where two diﬀerent media meet, e.g. the interior and the walls of a black body. Figure source: (Planck, 1906c, p. 35).

E = I = dσcosθ · dΩ · K dν (2.27) A ν

Here, Kν denotes the intensity of the radiation with a frequency between ν and ν + dν, and θ is the angle between dσ and the axis of the cone dΩ. Kirchhoﬀ had

156 Radiation in moving systems is the topic of Planck’s (1908b) article, which will be discussed in detail later, starting from page 98. 157 Planck lists three conditions for such bodies: its surface must be perfectly absorbing; it must be of a certain thickness, depending on the absorption-coeﬃcient of its materials; and its dispersion-coeﬃcient should be minimal, which means that the damping of the radiation should be very low (Planck, 1906c, p. 11 – 12).

94 Experiment, Time and Theory established, more specifically, that this equation (2.27) was a universal function, i.e. it was independent of the body’s specific constitution and depended only on the frequency ν and the temperature T , which determined the body’s emission-capacity E and its absorption-capacity A (Planck, 1906c, p. 43). When a black body is in thermal equilibrium, this formula tells us that its emission-capacity E is equal to the black-body radiation energy I (E = I), since it is a perfectly absorbing body (A = 1). By measuring the emission-capacity E of a black body,158 one could thus gain insight into the spectral energy distribution of such radiation, in order to determine an equation expressing the intensity of such radiation, i.e. how Kν depended exactly on the frequency ν, regardless of the body’s constitution. What Planck had obtained in his (1901a; 1901b) papers was exactly a law expressing the spectral energy density of the radiation emitted by a black body in thermal equilibrium at a particular temperature T . He had done this, more specifically, by means of a theoretical study of the thermodynamics of black bodies, since such bodies display the significant thermodyamical property of having an entropy S that is at its maximum:

When a system of bodies at rest, whose constitution, form and location does not even need to be speciﬁed, is enclosed by a heat-impermeable shell, it will transition over time from a random starting state to an equilibrium state, in which the temperature of all bodies of the system is the same. This is the state of thermal equilibrium, in which the entropy of the system takes on the maximal value of all the values that it can take, given the total energy determined by the initial conditions, and as such no further increase of the entropy is possible anymore. (Planck, 1906c, p. 23 – 24)159

Before Planck presented his law, Wien’s distribution law was mainly taken, by Planck as well as others working on thermal radiation, to adequately describe the spectrum. Experimental findings indicated, however, that Wien’s law could not account for the whole spectrum, but only for radiation with high frequency (i.e. short wavelength). As such, Planck set out to find an alternative law to account for the entire spectrum. His main guide in this search was Kirchhoff’s law, which, as we have seen, was a universal function, i.e. it did not depend on the body’s specific material constitution. This meant, Planck claimed, that in the theoretical construction of such a law, one could assume whichever mechanism one prefered as responsible for bringing about black-body radiation, as long as it was consistent with the laws of electrodynamics and thermodynamics:

158 Since a black body is, in the strict sense, an idealized body, they have to be approximated in experimental situations. For a general discussion of how such experiments were carried out at the time, see Hoffmann (2001). 159 The original German goes as follows: “Ein System ruhender Körper von beliebiger Natur, Form und Lage, welches von einer festen, fürWärmeundurchlässigenHülleumschlossen ist, geht, bei beliebig gewähltemAnfangszustand, im Laufe der Zeit in einen Dauerzustand über, bei welchem die Temperature in allen Körpern des Systems die nämliche ist. Dies ist der thermodynamische Gleichsgewichtszustand, in welchem die Entropie des Systems unter allen Werten, die sie vermöge der durch die Anfangsbedingungen gegebenen Gesamtenergie anzunehmen vermag, einen Maxi- malwert besitzt, von welchem aus daher keine weitere Vermehrung der Entropie mehr möglich ist”.

95 Chapter 2. Experiment and the Electron

The investigation of the properties of the state of black-body radiation is completely indiﬀerent to the precise nature of the bodies which one takes to be situated in the vacuum; it does not even matter whether such bodies actually exist somewhere in nature; the only thing that matters is that their existence and their properties are in fact compatible with the laws of electrodynamics and thermodynamics. (Planck, 1906c, p. 101)160

Because of this, Planck chose to work with the simplest emission- and absorption- system he could imagine under this constraint: oscillators,161 i.e. bodies with two equal but oppositely charged electric poles that can oscillate on the axis between the two poles (1906c, p. 101). Investigating, in terms of these oscillators, how a state of maximal entropy could arise for the energy of the black-body radiation ﬁlling a black body in thermal equilibrium then led Planck (1901a; 1901b) to the formulation of a law that provided the spectral energy density of black-body radiation for both high and low frequencies. It also led him, however, to quite a peculiar claim, namely that the energy of radiation emitted or absorbed by a black body was not continuous, but discontinuous. It could only be found in speciﬁc quantities of size E, which Planck called quanta of action.162 These were described by Planck in terms of the equation E = hν, where h refers to a new constant from Planck’s (1901a) law governing the energy density uν of a radiating black body:

8πhν3 1 u = (2.28) ν c3 ehν/kT − 1 Here, k refers to Boltzmann’s constant, which relates the temperature of a gas with the average kinetic energy of the particles in the gas, and e is the base of the natural logarithm. Planck presented this result without much elaboration or interpretation.163

160 The original German goes as follows: “Es ist also zur Untersuchung der Eigenschaften des Zustandes der schwarzen Strahlung ganz gleichgültig,welcher Art die Körper sind, welche man im Vakuum befindlich voraussetzt, ja es kommt nicht einmal darauf an, ob solche Körper in der Natur wirklich irgendwo vorkommen, sondern nur darauf, ob ihre Existenz und ihre Eigenschaften mit dem Gesetzen der Elektrodynamik und der Thermodynamik überhaupt verträglich sind”. 161 In the literature, these are often called resonators, which is the English translation of the word “Oszillator” that Planck used. 162 This was quite a peculiar result, since according to all accepted theories at the time (thermodynamics, electrodynamics, . . . ) energy was to be described in continuous terms. It would take us too far to go through the whole derivation of Planck’s law for the spectral energy distribution of black-body radiation. For this, I refer the reader to the sources listed in footnote 163. The term quantum was generally used at the time to denote a constant quantity: one often finds, for example, references to the quantum of electricity, i.e. electrical charge (see note 166 for an example from Planck’s work, and page 109 for one from Einstein’s work). Planck called his energy-elements quanta of action in reference to the principle of least action: “I will also refer to these elements as ‘elementary quanta of action’ or as ‘action elements’, since they have the same dimension as those quantities, to which the principle of least action owes its name” (Planck, 1906c, p. 154). (“Ich möchte dieselbe als ‘elementares Wirkungsquantum’ oder als ‘Wirkungselement’ bezeichnen, weil sie von derselben Dimension ist wie diejenige Größe,welcher das Prinzip der kleinsten Wirkung seinen Namen verdankt”). The relation between Planck’s quanta and the principle of least action will be discussed in more detail below, from page 98 onwards. 163 As Olivier Darrigol puts it, “in 1900 [Planck] did not know whether the energy elements were a mere computational fiction or should be ascribed direct physical significance” (2014, p. 121). Hence, a large part of the historical-philosophical debate on Planck’s work has concentrated on how to understand exactly his position. This debate has even spawned a kind of meta-investigation

96 Experiment, Time and Theory

Regardless of how Planck interpreted his quantum-result himself, what is important for our story here is that it led him to suggest a similarity between his oscillators and the electron. For large wavelengths λ (i.e. low frequency), Planck pointed out (1906c, p. 159), his spectral energy distribution equation (2.28) led to the Rayleigh-Jeans distribution law.164 Considerations pertaining to what this meant for the entropy and energy in the low-frequency spectrum then led Planck to an equation connecting these insights to electron-theoretical work concerning the kinetic energy of one-atomic molecules. This suggested to him the following:

From a very diﬀerent side, this equation, and with it also the identity of the constant k [i.e. Boltzmann’s constant] for molecular movement and radiation phenomena, is conﬁrmed in a very remarkable way, namely because of a consequence of the theory of the electron. For, according to the picture provided by this theory, the linear oscillations of the oscillators that we have been considering are to be represented as straight motions of an electron. (Planck, 1906c, p. 159 – 160)165

Planck’s quanta also provided him, as he had already shown earlier in his (1901b, p. 566) article, with a specific value for the electric charge (1906c, p. 163). This indicates that at the time, Planck was at least considering the idea that there is a relation between his quanta of action and the electron.166 What we see here, more specifically, is that the work on thermal radiation allowed Planck to draw a distinction between certain aspects of the electromagnetic approach that could be tolerated and even possibly accommodated, and other aspects that had to be abandoned. All mass could be, for example, electromagnetic in nature: this would not make a difference to the picture Planck sketched (Planck, 1906c, p. 102). But not everything could be accounted for in electromagnetic terms, as Planck showed by means of the example of the relation between the energy absorbed by a resonator and the intensity of the radiation it emits (Planck, 1906c, p. 130). As we will see in what follows, it is in this way – i.e. by picking apart, through the study of the limitations of the Maxwell equations, the electromagnetic world view – that on how historians have studied it. There is by now quite some extensive literature on the early stages of the quantum, especially regarding the interpretation of Planck’s early articles: see e.g. the work by Martin J. Klein (1962), Elizabeth Garber (1976), Thomas Kuhn (1987), Olivier Darrigol (2001; 2014), Clayton Gearhart (2002), Suman Seth (2010), and the references in these different papers. 164 This is a law for the spectral energy density of black-body radiation proposed independently by Lord Rayleigh and James Jeans on the basis of standard electrodynamical and thermodynamical considerations, i.e. without any discontinuity as in the case of Planck. The law only holds, however, for the low-frequency part of the spectrum (Gearhart, 2002, p. 191). The law is stated here as equation (2.34) on page 107. 165 The original German goes as follows: “Diese Beziehung, und damit auch die Identitätder Konstanten k fürdie Molekularbewegungen und fürdie Strahlungsvorgänge,wird von einer ganz anderen Seite her in sehr bemerkenswerter Weise bestätigtdurch eine Folgerung aus der Elektro- nentheorie. Nach den Anschauungen dieser Theorie hat man sich nämlich die von uns betrachteten linearen Schwingungen eines elementaren Oszillators vorzustellen als geradlinige Bewegungen eines Elektrons”. 166 In his lectures at Columbia University in 1909, published a few years later, Planck pointed out that his value for the electric charge “stands in noteworthy agreement with the results of the latest direct measurements of the electric elementary quantum made by E. Rutherford and H. Geiger, and E. Regener” (1915, p. 95).

97 Chapter 2. Experiment and the Electron a relativistic response to the issues raised by the Kaufmann experiments could be formulated.

Planck’s General Dynamics As was already pointed out, Planck’s (1906c) lectures were only concerned with thermal radiation in systems at rest. In his (1908a) article, ‘On the Dynamics of Moving Systems’, Planck turned to the study of thermal radiation in moving systems. His aim there, however, was not merely to offer a theory of such systems, but to present a complete reconceptualization of what he called dynamics or mechanics in the narrow sense.167 The main reason for carrying out such a revision, according to Planck, was that the motion of such systems called into question certain dynamical assumptions that were until then taken for granted. Overcoming these issues, by means of a study of the dynamics of moving thermal radiation, Planck argued, could lead to a general dynamics, i.e. one that covered not solely mechanics but also the newest insights in the fields of electrodynamics and thermodynamics (1908a, p. 728). Planck listed, more specifically, three ideas that, until then, were taken to be central to any study of the dynamics of physical systems, but which the study of thermal radiation showed to be merely approximations that were inexact with respect to the foundations of dynamics. The first was the idea that a body’s total energy is the sum of a velocity-dependent part, its kinetic energy, and a part, which Planck called its inner energy, that depends on the body’s constitution, i.e. its temperature, density and chemical composition. What the study of thermal radiation showed, Planck claimed, was that the inner energy of each body consisted in part of thermal radiation energy. When a body is set in motion, this thermal radiation energy will also move. For such thermal radiation energy in motion it is impossible, Planck claimed, to make the division between velocity-dependent and internal energy. This entailed that for the body as a whole this is not possible either (Planck, 1908b, p. 1 – 3). A second idea concerned a body’s inertial mass, which was generally taken, according to Planck, to form an absolute and unchangeable building block for the science of mechanics. Normally, according to Planck, this notion was defined in terms of kinetic energy. We have seen, however, that thermal radiation phenomena showed that it was impossible to draw a complete distinction between a body’s kinetic energy and its internal energy, which in part consists of thermal radiation energy. This thermal energy depends on the body’s temperature, which entailed that the body’s inertial mass no longer formed an absolute constant. It could vary according to how the body’s temperature changed. Abraham, Lorentz and Poincaré attempted to overcome this issue by drawing a distinction between ‘real’ and ‘apparent’ mass and ascribing constancy only to the first part. However, this did not really provide an actual solution, according to Planck. It maintained the idea of an absolute, constant mass, which the study of thermal radiation showed to be the real source of the problem, since it rendered unclear the concepts of kinetic energy and momentum (Planck, 1908b, p. 3 – 4). A final idea concerned the assumed general identity between inertial and ponder-

167 With mechanics in the narrow sense, Planck meant Newtonian mechanics, which he also often describes as ‘pure’ or ‘normal’ mechanics.

98 Experiment, Time and Theory able mass.168 While thermal radiation phenomena clearly had inertial mass, Planck argued, it was difficult to ascribe them ponderable mass. This issue in particular indicated that a new general dynamics was called for, since it showed the possibility of rigid bodies whose laws of motion completely differed from those of ordinary mechanics (Planck, 1908b, p. 4). Because of these issues, a thorough revision of the foundations of dynamics was required. Planck proposed to carry out such a revision under the guidance of the two principles that, he claimed, had not been challenged from the point of view of the most recent investigations. The first was the principle of least action, which, as Hermann von Helmholtz had shown according to Planck, covers mechanics, electrodynamics and thermodynamics in their application to reversible processes.169 The second was the principle of relativity, which, while it had received direct confirmation from only one experiment (Michelson-Morley), has not been contradicted at all, according to Planck: “at the moment no fact of the matter is known yet that directly prevents us from ascribing to it the most general and absolute precision” (Planck, 1908b, p. 6).170 Planck’s starting point in the formulation of his general dynamics guided by these two principles was the study of black-body radiation, since it displayed the following property:

Black-body radiation in a pure vacuum is of all physical systems the only one, whose thermodynamical, electrodynamical and mechanical properties can be determined with absolute precision, regardless of the contradictions between speciﬁc theories. Its study will therefore be given priority with respect to all other physical systems. (Planck, 1908b, p. 7)171

Planck characterized such a system as consisting, more specifically, of radiation in a vacuum of a certain volume V enclosed by absolutely reflecting walls (the size of the enclosure can be chosen as large as one wants, such that the mass of the walls will not make a difference). Assuming that all changes of the system took place in a reversible way (see footnote 169), the system’s total state could be described in terms of its velocity v, its volume V and its temperature T . Planck then showed how the first and second law of thermodynamics, which concern changes in the energy

168 Planck does not specify what he means by ponderable mass. Given his reconceptualization of mass in terms of energy at the end of the article, however, it seems that what Planck is trying to argue here is that a distinction needs to be made between the ponderable mass of material bodies and inertial mass, since radiation energy does have mass but is not ponderable in the sense of material. 169 Reversible processes, Planck points out a bit later in the article, are those changes to a system that are so slow that, for each instant of time, the system is in a stationary state (1908b, p. 7). What Helmholtz had shown is that when the principle of least action is applied to changes of a body’s state that are reversible, one can obtain diﬀerential equations for a body’s pressure p, entropy S and the force exerted on it expressed in terms of the body’s kinetic potential H, its velocity v, its volume V and its temperature T (Planck, 1908b, p. 10). 170 The original German goes as follows: “so ist doch andererseits bis jetzt keine Tat- sache bekannt, die es direkt hinderte, diesem Prinzip allgemeine und absolute Genauigkeit zuzuschreiben”. 171 The original German goes as follows: “Die schwarze Hohlraumstrahlung im reinen Vakuum ist unter allen physikalischen Systemen das einzige, dessen thermodynamische, elektrodynamische und mechanische Eigenschaften sich, unabh¨angigvom Widerstreit spezieller Theorien, mit absoluter Genauigkeit angeben lassen. Seine Behandlung ist daher der der Ubrigen¨ Systeme vorangeschickt”.

99 Chapter 2. Experiment and the Electron

E and entropy S of such systems, could be described in terms of these parameters, which in turn led him to expressions for the system’s pressure p and its momentum p. If such a system is accelerated in a way that keeps its volume constant and there is no heat added from outside, which ensures that the system’s entropy also remains the same, its temperature then transforms according to the following ratio: (1 − q2/c2)2/3 : 1, a result that Planck (1908b, p. 9) took from work by one of his doctoral students, Kurt von Mosengeil (1907).172 Planck then turned to physical systems more generally, which he characterized as bodies consisting of a number of molecules, equal or diﬀerent in kind, and which are in a stationary state that can be captured in terms of the independent variables V,T and the velocity-componentsx ˙ = dx/dt, y˙ = dy/dt, z˙ = dz/dt, such that v2 = x˙ 2 +y ˙2 +z ˙2.173 If the state of such a body is changed in a reversible way (see footnote 169), then Helmholtz’s formulation of the principle of least action provides us with equations expressing diﬀerent properties of the system – pressure, entropy, external force exerted on it, energy and momentum – in terms of partial derivatives of the kinetic potential H with respect to V,T, x,˙ y˙ andz ˙. In pure dynamics (see footnote 167), these results would then be analysed further by relating the system’s kinetic potential H to its kinetic energy (1/)2mv2, with m the body’s mass, and its inner energy F , through the following equation: H = (1/2)mv2 −F . But the case of black- body radiation had shown, we have seen (page 98), that this division was no longer tenable.174 To overcome this, Planck turned to the principle of relativity, which he took to state that the laws of mechanics, electrodynamics and thermodynamics that hold in a particular frame of reference (x, y, z, t) equally well hold good in all other frames of reference (x0, y0, z0, t0) that can be obtained by means of the following transformations (1908b, p. 12):

c(x − vt) c2t − vx x0 = √ , y0 = y, z0 = z, t0 = √ (2.29) c2 − v2 c c2 − v2 Planck used these equations, more specifically, to investigate how the different parameters obtained earlier through the study of thermal radiation in motion transformed between different frames of reference, following the procedure sketched in footnote 172. After obtaining equations for a system’s pressure p, entropy S, volume V , and temperature T , Planck then turned to the external force exerted on

172 The importance of this result lies in the fact that, as we have seen on page 94, a black body’s thermal radiation can be characterized, independently of the body’s specific constitution, in terms of temperature and frequency. Given this transformation ratio, the application of the principle of relativity can then inform us about how other properties, related through the theory of thermal radiation to T and ν, transform between different frames of reference in relative motion. Hence from the study of black-body radiation at rest, we can arrive at insights about how to describe such bodies in motion. Given that black-body radiation brings together the three theories that Planck wants to unify in his general dynamics, such knowledge of the dynamics of black-body radiation in motion informs him about how such a general dynamics should look like. Unfortunately, von Mosengeil died in a climbing accident before his paper was published. Planck, who was at that time editor of the Annalen der Physik, further elaborated the article and ensured its publication. See Goldberg (1976) for a discussion of von Mosengeil’s work and the way in which Planck elaborated it, and (Pyenson, 1985, chapter 8) and Pyenson (2008) for a discussion of Planck’s role as editor of the Annalen. 173 The number of molecules could be equal to zero, in which case we obtain black-body radiation. 174 This procedure derives, more specifically, from the idea that a system’s total energy is to be seen as a sum of its kinetic energy and its potential energy, which consists of its kinetic potential and its inner energy.

100 Experiment, Time and Theory a body. In order to obtain the transformation equations for this variable, Planck then considered a special case: “an infinitely small diathermal rigid body, charged with the electric substance e, which is located in an evacuated space filled with an electromagnetic field” (1908b, p. 17 – 18).175 The reason for proceeding in this way was that for this case, Einstein’s relativity paper (1905c) offered an easy way to calculate the transformation equations for the forces exerted on such a body. Hence, Planck could obtain transformation equations for the kinetic potential H, the energy E and the pressure p, which led him to the following transformation equation for the momentum p (where R = E + pV is Gibb’s heat function, which concerns the change in supplied heat for isobaric processes, i.e. with constant pressure p) (Planck, 1908b, p. 20 – 22):

c v2 p0 = √ p − R (2.30) c2 − v2 c2 This then led Planck to a whole list of quantities that are invariant under the relativistic frame transformations. It also brought him to draw the following connection between his quantum of action (see page 95) and his dynamics based on the principle of relativity and the principle of least action. One of the invariants obtained was Hdt (with H the kinetic potential), which the principle of least action links to the quantity of work W (“Wirkungsgr¨oße”)required to transition a system from a determined state 1 to a determined end state 2 in terms of the following equation:

Z 2 W = Hdt (2.31) 1 In his (1906c) lectures, Planck had shown that this quantity of work should be understood in terms of the Planck constant h that ﬁgures in Planck’s radiation equation (2.28), discussed on page 96.176 This entailed that changes covered by the principle of least action, as Planck used it here, could be understood in the following terms: “Any such change in nature derives from a determinate number of quanta of action, which is independent of the choice of the reference system” (Planck, 1908b, p. 23).177 At the time, Planck did not elaborate this suggestion further, however. He turned instead to a few consequences of his main result, i.e. his general dynamics, which he summarized as follows:

It can be shown, in a completely general way, that a system’s kinetic potential H and consequently all its state variables can be expressed directly as functions of its velocity, volume and temperature, insofar as these can be expressed, in the system’s state of rest, as functions of its volume and temperature. (Planck, 1908b, p. 24)178

175 A diathermal body is a body that can be penetrated by heat but not by mass. The original German goes as follows: “einen unendlich kleinen, mit der Elektrizitätsmenge e geladenen, diather- manen festen Körper, der sich in irgend einem evakuierten elektromagnetischen Felde befindet”. 176 Expressing W in terms of h had allowed Planck to obtain, among other things, the value for the electric charge discussed above (see page 97). 177 The original German goes as follows: “Einer jeden Veränderungin der Natur entspricht eine bestimmte, von der Wahl des Bezugssystems unabhängigeAnzahl von Wirkungselementen”. 178 The original German goes as follows: “Es läßtsich nämlich ganz allgemein zeigen, daß das kinetische Potential H und somit auch alle Zustandsgrößen sich unmittelbar als Funktio- nen der Geschwindigkeit, des Volumens und der Temperature angeben lassen, sobald sie fürdie Geschwindigkeit Null als Funktionen des Volumens und der Temperature bekannt sind”.

101 Chapter 2. Experiment and the Electron

One consequence that is of interest to us here concerns a body’s inertial mass, which Planck discussed in §16 – 18 (1908b, p. 27 – 33). As we have seen on page 98, in pure mechanics this quantity was considered to form an absolute and fundamental constant, determined by means of a body’s momentum p = mv. Planck’s general dynamics showed, however, that p was no longer proportional to its velocity, but rather to its temperature. This entailed that this mass could no longer be seen as constant. In fact, this showed, according to Planck, that the velocity-dependence of mass was primarily an issue of definition (“Definitionssache”), since depending on how one related mass to momentum, one would obtain a different velocity-dependence.179 Planck then elaborated further how we should understand the conceptualization of mass provided by pure mechanics (m = p/v) in terms of his new dynamics. In the body’s frame of rest (denoted by the subscript 0), its mass could then be expressed in the following terms, where R denotes Gibb’s heat function discussed earlier (see page 101): p R E + pV m = = 0 = 0 0 (2.32) v 0 c2 c2 When a body’s velocity v 6= 0, Planck pointed out, equation (2.32) provided its transverse mass, while differentiating it provided its longitudinal mass, as Abraham defined it: mk = dp/dv (see equation 2.8 on page 51). Planck immediately showed, however, that this distinction could not be the final word. Von Mosengeil’s study of the relativistic thermodynamics of black-body radiation had shown that the following velocity-dependent masses could be distinguished: transverse mass, longitudinal isothermal-isochoric mass (constant temperature and constant volume), longitudinal adiabatic-isochoric mass (no heat transfer and constant volume), and longitudinal adiabatic-isobaric mass (no heat transfer and constant pressure) (Planck, 1908b, p. 28). We should therefore not see equation (2.32) as a definition of mass in terms of the heat function R, but rather as suggesting a wholly different conceptualization of mass, in terms of a body’s energy:

According to equation [(2.32)], every absorption or emission of heat is accompanied by a change in the body’s intertial mass, and the increase of mass is moreover equal to the amount of heat which the body takes up from the outside during an isobaric change, divided by the velocity of light in a vacuum squared. What is especially remarkable is that this expression holds not only for reversible processes, but in general also for all irreversible changes of state; for the relation between the heat function R and the externally supplied heat is based directly on the ﬁrst law of thermodynamics. (Planck, 1908b, p. 29)180

179 Planck lists a few possibilities: one option conceives of mass as the ratio of the momentum to the velocity (p/v); another option is to differentiate the velocity v, in which case there are further options depending on how one differentiates; still another possibility is to represent a body’s mass not in terms of momentum but in terms of its energy E differentiated to v2/2 (Planck, 1908b, p. 27). 180 The heat function for constant pressure, as we have seen on page 101, goes as follows: R = E + pV . The first law of thermodynamics, on Planck’s formulation, states that a system’s change of energy is equal to the work A exerted on the system from the outside and the heat Q supplied from the outside: dE = A + Q (Planck, 1908b, p. 7). An isobaric change of state is one where the pressure remains constant. The original German goes as follows: “Denn nach der Gleichung [(2.32)] wird durch jede Wärmeaufnahmebzw. abgabe die trägeMasse eines Körpers

102 Experiment, Time and Theory

In a footnote to the quoted paragraph, Planck pointed out that this result was equivalent to the mass-energy equivalence that Einstein (1905a) had obtained (see the earlier footnote 129, and footnote 186, where this will be discussed further). Planck then claimed that instead of characterizing a body in terms of a constant inertial mass, as was done in pure mechanics, we should instead see a body as consisting fundamentally of energy: “according to the theory developed here, one has to presuppose in the interior of each body a particular energy supply” (Planck, 1908b, p. 30).181 This supply he then called a body’s latent energy.

Planck and the Principle of Action and Reaction In his (1908a) lecture to the Naturforscherversammlung, Planck further elaborated the general dynamics he had obtained in his (1908b) with respect to one particular issue, namely Newton’s third law, the principle of action and reaction. Planck characterized it as follows: “the actual content of the Newtonian principle of the equality of action and reaction is, as is well-known, the law of the conservation of momentum” (1908a, p. 828).182 Lorentz’s (1895) electrodynamics had endangered, however, the generality of this principle, since according to this theory, it was possible for ions to act on the ether without the ether acting back in accordance with the principle.183 It was Abraham’s concept of electromagnetic momentum, according to Planck, that presented a ﬁrst attempt to remedy this issue:

A sort of reassurance was ﬁrst introduced when it was shown, especially through the investigations of M. Abraham, that the reaction-principle could be saved after all, and moreover in its full generality, if one introduced, besides the only form of momentum known at the time, the mechanical one, another form of momentum, namely an electromagnetic one. (Planck, 1908a, p. 828 – 829)184

Abraham had introduced his electromagnetic conception of momentum, according to Planck, by means of an analogy with the conservation of energy. Just as the energy principle (see footnote 107) could only be upheld if one took into account the electromagnetic energy, the conservation of momentum could only be upheld if one took into account the electromagnetic momentum. There was a conceptual verändert,und zwar ist die Zunahme der Masse immer gleich der Wärmemenge,welche bei einer isobaren Veränderungdes Körpers von außen aufgenommen wird, dividiert durch das Quadrat der Lichtgeschwindigkeit im Vakuum. Dabei ist besonders bemerkenswert, daß dieser Satz nicht nur fürreversible Prozesse, sondern ganz allgemein auch fürjede irreversible Zustandsänderung gilt; denn die Beziehung zwischen der Wärmefunktion R und der von außen zugeleiteten Wärme gründetsich direkt auf den ersten Hauptsatz der Wärmetheorie”. 181 The original German goes as follows: “Nach der hier entwickelten Theorie hat man sich also im Innern eines jeden Körpers einen Energievorrat vorzustellen”. 182 The original German goes as follows: “Das Newtonsche Prinzip der Gleichheit von Aktion und Reaktion hat bekanntlich zum eigentlichen Inhalt den Satz der Konstanz der Bewegungsgröße”. 183 See (Miller, 1981, p. 42 – 43) and (Nersessian, 1984, p. 103 – 104) for discussions of how this issue arises in Lorentz’s electrodynamics. 184 The original German goes as follows: “Eine Art Beruhigung trat erst wieder ein, als sich zeigte, besonders durch die Untersuchungen von M. Abraham, daß das Reaktionsprinzip doch noch zu retten ist, und zwar in seinen vollen Allgemeinheit, falls man nur außer der bisher allein bekannten mechanischen Bewegungsgrößenoch eine neue Bewegungsgröße,die elektromagnetische, einführt”.

103 Chapter 2. Experiment and the Electron problem, however, with this approach, according to Planck, which rendered the analogy problematic. In the case of energy, many different kinds were known, which entailed that adding one more would not make that big a difference: it is not what Planck called a principled novelty (1908a, p. 829). The case of momentum, however, was different: there, the only kind known at the time was mechanical. This entailed that adding one more did make a big difference, conceptually speaking:

While energy already formed a universal physical concept before, momentum formed a specifically mechanical concept, and the reaction- principle a specifically mechanical law, and the required extension should therefore also be seen as a transformation of a principled kind, according to which the concept of momentum, which until recently was relatively simple and unified, becomes quite complicated in character. (Planck, 1908a, p. 829)185

Planck then argued that it was possible to address the issue raised by Lorentz’s electrodynamics, without comprising the unity of the concept of momentum, by accepting the theory of relativity. While this theory’s validity, according to Planck, had not yet been established in a completely definite way, its difference with other, non-named theories was so small that besides for these deviations, the theory could be taken as correct. According to this theory, Planck claimed, momentum was to be characterized in terms of the vector that expresses the flow of energy divided by the velocity of light squared. For a certain volume, as Planck showed by means of an example from fluid dynamics, this came down to a momentum density g per unit of volume, where α denotes the energy density moving with a velocity v, which exerts a pressure p on a surface element of the volume oriented normally to the direction of the energy flow (Miller, 1981, p. 366):186

v(α + p) g = (2.33) c2 This conceptualization of momentum in terms of a vector denoting a flow of energy was not new: in electrodynamics, there was already Poynting’s vector, which denotes the directional energy transfer per unit area per unit time of the electromagnetic field (see page 50, where Abraham makes use of this vector to conceptualize his electromagnetic momentum). What was new here, however, was that according to the theory of relativity, this expression applied to any kind of energy flow that can bring about momentum:

According to the theory of relativity, momentum can be reduced in a completely general way to such a vector, which gives expression to the

185 The original German goes as follows: “Währenddie Energie von vornherein schon einen uni- versellen physikalischen Begriff darstellt, war die Bewegungsgrößebisher speziell ein mechanischer Begriff, das Reaktionsprinzip ein speziell mechanischer Satz, und daher mußte die als notwendig erkannte Erweiterung immerhin auch als eine Umwälzungprinzipieller Art empfunden werden, durch welche der bisher verhältnismäßigeinfache und einheitliche Begriff der Bewegungsgröße einen erheblich komplizierten Charakter erhält”. 186 This equation also provides Planck with an expression for the flow’s density which is equal, he points out, to the equation (2.32) for the mass-energy equivalency he had obtained in his (1908b) general dynamics (see page 102). Miller describes this as “Planck’s generalization of Einstein’s mass-energy equivalence which included the flow of any sort of energy, and not just the total mechanical energy” (1981, p. 366).

104 Experiment, Time and Theory

flow of energy, but not solely to Poynting’s electromagnetic energy flow, but rather to the flow of energy in the most general terms. (Planck, 1908a, p. 829)187

Equation (2.33) expresses what Planck called the law of the inertia of energy, which states “that the effect of forces acting on a body [is] transmitted by a momentum density whose source [is] a flow of energy”, where the source v(α + p) can be of different kinds (Miller, 1981, p. 366). In the final part of his presentation, Planck then suggested a physical interpretation of his notion of momentum density in terms of the Maxwell stress tensor, which was originally introduced in order to study the interaction between electromagnetic forces and mechanical momentum.188 On Planck’s view, this tensor gave expression to the total flow of momentum between a body and its surroundings in terms of the different sources of energy that act on the surface of the body. In this way, equation (2.33) allowed one to determine whether the flow of momentum between a system and its environment obeys, in relativistic terms, the conservation of momentum, i.e. the principle of action and reaction. It is on the basis of these results that von Laue formulated his relativistic dynamics of the electron, as we will see on page 119.

Manipulability and Planck’s General Dynamics

What the discussion of Planck’s (1906c; 1908a; 1908b) work on his general dynamics has shown is that his study of thermal radiation, which led him to his quanta of action, suggested that those concepts that were central to Abraham’s electromagnetic account of the electron – the distinction between apparent and real mass, the velocity-dependence of mass, the notions of longitudinal and transverse mass, and electromagnetic momentum – were not that foundational at all. Within the framework of Planck’s general dynamics, they were rather derivative notions. Thus, Abraham’s notion of electromagnetic momentum becomes just one of many possible forms of momentum that could be expressed in terms of the law of the inertia of energy (equation 2.33, discussed on page 104). The velocity-dependence of mass became a special case of equation (2.32) (see page 102), which in turn showed that it is better understood directly in terms of the heat function R and a body’s inner store of latent energy, i.e. in terms of the relativistic mass-energy equivalence. The

187 The original German goes as follows: “In der Relativitätstheorieläßtsich nun die Be- wegungsgrößeganz allgemein auf denjenigen Vektor zurückführen,welcher die Energieströmung ausdrückt, aber nicht allein die Poyntische elektromagnetische Energieströmung, sonder die En- ergieströmung ganz im allgemeinen”. 188 To calculate the force exercised by a field on a system, one can use the Lorentz force law if the system is not too complex, such as a point charge. When the system becomes more complex, however, one makes use of what is known as the Maxwell stress tensor. A tensor is a multi- dimensional object, which is best understood in comparison with vectors and matrices. A vector such as s = (x, y, z) is a one-dimensional object, since all of its elements can be specified in terms of one dimension: si, with i = 1, 2, 3. A 4×4 matrix A, for example, is a two-dimensional object, since we need two dimensions to specify a particular element: Aij, with i = 1, 2, 3, 4 and j = 1, 2, 3, 4. Tensors now offer a generalization of such vectors and matrices in the sense that they form multi- dimensional objects. And just as matrices and vectors, tensors can be transformed by means of specific mathematical transformation rules. See (Steane, 2012, p. 164 – 170) for a discussion of how tensors are used in special relativity, and chapter 16 of the same book for an oversight of how the Maxwell stress tensor is conceptualized in special relativity.

105 Chapter 2. Experiment and the Electron longitudinal and transverse mass equations derived by Abraham and Lorentz were, finally, but a few of many different kinds of masses (see page 102). Moreover, as we have seen, Planck’s work on black-body radation also suggested to him that the electron could be studied in terms of the quantum. It led him to a later confirmed prediction for the electron’s charge (see footnote 166), and to an analogy between his oscillators and the electron (see the quote on page 97). In this way, Planck’s dynamics suggested that a relativistic model of the electron, and hence a response to the stability issue raised by Abraham and Ehrenfest on the basis of Kaufmann’s experimental results, could indeed be formulated. Planck himself did not elaborate such an account. That was mainly done by Einstein and von Laue. That Planck could present his general dynamics as overcoming and incorporating parts of Abraham’s electromagnetic approach, was not solely a result of the theory itself, however. It equally well relied on how Planck did, and did not, relate his work to that of others that was around at the time. Hence, Planck presented the principle of relativity as, up until that time, not refuted by any state of affairs (see the quote on page 99), even though at around the same time it was still open for debate whether Kaufmann’s experiments argued against the Lorentz-Einstein formulae. The same holds for the way in which Planck treated Abraham’s work. As we have seen, Abraham introduced his notion of electromagnetic momentum in order to correct Kaufmann’s interpretation of his experimental results, and it led him to the conviction that the electron’s mass was completely electromagnetic in nature. As such, Abraham’s notion should not be seen as an addition to the mechanical notion of momentum, as Planck claimed here, but rather as a replacement of it. Abraham’s goal was not to save the principle of action and reaction for Lorentz’s theory. It was rather to formulate an electrodynamical theory according to which the electron’s mass, momentum and all other notions that make up its dynamics were completely electromagnetic in nature. For this, he did not add this notion to the already existing notion of mechanical momentum, but rather proposed it as its replacement, in order to arrive at an electromagnetic alternative for Newton’s action-reaction principle. This now raises questions about Planck’s claim that Abraham’s electromagnetic momentum was problematic because it threatened the unity of momentum that reigned before. For, as Abraham (1903, p. 109) himself pointed out, his electrodynamical approach to the study of the electron was informed by a thorough-going analogy with Hertz’s mechanics. In fact, he put it on his head: where all Hertz’s notions were mechanical, Abraham attempted to turn them into electromagnetic ones. As such, it seems strange to claim, as Planck did, that Abraham’s notion threatened the unity of momentum, since Abraham in fact attempted to replace one kind of unity with another one. What we see here is that Planck is trying to reconceptualize the relation between Abraham’s work and the theory of relativity. No longer is it to be seen as a chal- lenger, but rather as a step in the progression towards the principle of relativity. This shows itself in the fact that Planck draws a historical progression from Lorentz over Abraham towards Einstein’s theory of relativity. This is a very significant change with earlier characterizations of the debate, where these three theories were seen as equal competitors with regards to Kaufmann’s experiments.189

189 The same can be said about Planck’s remarks about the distinction between apparent and real mass, discussed on page 98. He there distinguishes this approach, which he ascribes to Lorentz,

106 Experiment, Time and Theory

2.8 Einstein and von Laue on the Electron

Einstein and the Constitution of Radiation While Planck suggested certain similarities between his resonators and electrons, he was hesitant to draw any conclusions from this (see page 97). Einstein arrived at similar ideas in his (1909a; 1909b) work on the quantum,190 but was less hesitant. He proclaimed that he was working on a theory that would account for both the electron and the quantum.191 Both of these articles were concerned, more speciﬁcally, with the study of radiation. In his (1909b), Einstein discussed the way in which diﬀerent theories by Lorentz (1908), Jeans (1908) and Ritz (1908) at the time treated this subject. All of these led, on the basis of considerations arising out of statistical mechanics and Maxwell’s electrodynamics, to the same equation for the spectral energy distribution of black-body radiation, the Rayleigh-Jeans law (see footnote 164):

T u = 8πν2k (2.34) ν c3 The problem with this result, according to Einstein, was that this law could not account for speciﬁc radiation phenomena.192 This led him to claim that there was something wrong with the theoretical foundation on which this law was build, i.e.

Abraham, and Poincaré,with the one proposed by the theory of relativity and the study of thermal radiation. This ignores the fact that neither Abraham, Lorentz nor Poincarétook this distinction to be central. They all, at least for some time, attempted to provide a completely electrodynamic account of the electron’s mass, which meant that there was no ‘real’ (i.e. absolute, constant, mechanical) mass, but only ‘apparent’ mass. Again, we thus see how Planck tries to draw distinctions between earlier theories and the theory of relativity in order to sketch a progression towards the latter one. 190 I would like to thank Marco Giovanelli for sharing a manuscript of his paper ‘Like classical electrodynamics before Boltzmann. On the pre-history of Einstein’s distinction between constructive and principle theories’ with me, which concerns the relations between Einstein’s work on thermodynamics and the electron in the context of the development of the theory of relativity. It served in part as inspiration for my study of Einstein’s and Planck’s work on the quantum with regards to Kaufmann’s experiments. The abstract of this manuscript can be found at www.minkowskiinstitute.org/meeting/2017/abstracts/Giovanelli.pdf. 191 Einstein’s (1905b) was his first paper on what he called his light quantum. He presented it there as a theoretical hypothesis that was required in order to make sense of Planck’s radiation law (2.28) discussed on page 96, and showed that it could account for phenomena that the laws of electrodynamics, he claimed, could not account for, such as the photoelectric effect, i.e. the emission of electrons by a material when light shines upon it. In later work, he claimed the same for light emission and absorption (1906c) and specific heats (1907b). In the case of Planck, it is not clear, we have seen, how he conceptualized his quantum of action precisely (see the references in footnote 163 for the historical debate on this). For Einstein, on the other hand, it is more clear: while at first, he saw his quanta as just a hypothesis for theory formulation – in his (1905b), he called it a heuristic point of view –, over the years he came to see his light quantum as a new particle that was responsible for all light phenomena. For historical discussions of Einstein’s quantum work, see (Klein, 1964, 1965, 1967, 1979; Hendry, 1980; Kuhn, 1987; Bergia and Navarro, 1988; Navarro, 1991; Büttner et al., 2003; Darrigol, 2014). 192 Einstein provided the following list of issues that could not be accounted for, he claimed, by means of the Rayleigh-Jeans law: “Why, after all, do solids emit light only above a fixed, rather sharply defined temperature? Why are ultraviolet rays not swarming everywhere if they are indeed constantly being produced at ordinary temperatures? How is it possible to store highly sensitive photographic plates in cassettes for a long time if they constantly produce short-wave rays?” (Einstein, 1909b, p. 187; Beck, 1989, p. 361).

107 Chapter 2. Experiment and the Electron the equations provided by Maxwell’s electrodynamics and statistical mechanics that link the mean oscillation energy of the ions assumed to constitute radiation with the radiation’s energy density uν:

There can be no doubt, in my opinion, that our current theoretical views inevitably lead to the law propounded by Mr. Jeans. However, we can consider it as almost equally well established that formula [(2.34)] is not compatible with the facts. [. . . ] Thus, we will indeed have to say that experience forces us to reject either [the] equation [. . . ] required by the electromagnetic theory, or [the] equation [. . . ] required by statistical mechanics, or both equations. (Einstein, 1909b, p. 186 – 187; Beck, 1989, p. 360 – 361)

Planck’s radiation law (equation 2.28, discussed on page 96), on the other hand, was in accordance with the facts. But it was based on the same theoretical foundations as the Rayleigh-Jeans law, namely Maxwell’s electrodynamics and statistical mechanics. Planck should have arrived at the Rayleigh-Jeans law, according to Ein- stein, which indicated that “the Planck radiation formula is incompatible with the theoretical foundation from which Mr. Planck started out” (Einstein, 1909b, p. 188; Beck, 1989, p. 363).193 In line with his earlier radiation work (see the references in footnote 131), Einstein therefore proposed an alternative theoretical foundation, which retained the Maxwellian part but adapted the statistical mechanics part by introducing the following assumption:

A structure that is capable of carrying out oscillations with the frequency ν, and which, due to its possession of an electric charge, is capable of converting radiation energy into energy of matter and vice versa, cannot assume oscillation states of any arbitrary energy, but rather only such oscillation states whose energy is a multiple of h · ν. Here h is the constant so designated by Planck, which appears in his radiation equation. (Einstein, 1909b, p. 188; Beck, 1989, p. 363)

In contrast to Planck, who refrained from making any definite claims about how to see the constitution of his quantum of action or its relation to matter (see page 97), Einstein took the quantum to form an entity (“Ein Gebilde”) that was responsible for the transformation of matter energy into radiation energy.194 Einstein then showed how this hypothesis gained in plausibility by applying it to two specific cases concerning the energy and pressure fluctuations of thermal radiation. These considerations suggested, more specifically, that one could not take the quantum to concern merely the quantity of energy of radiation emitted and absorbed by matter.

193 See Norton (1987) for an extensive discussion of this inconsistency. 194 For a very extensive discussion of Einstein’s work on quanta between 1905 and 1911, see Klein (1979). Einstein himself saw this proposal as quite radical, since he believed that it would entail very fundamental revisions of what he called our physical theories: “the modiﬁcation of the foundations of Planck’s theory just described necessarily leads to very profound changes in our physical theories” (Einstein, 1909b, p. 188; Beck, 1989, p. 363). And already in a letter from 1905 to his good friend Conrad Habicht, in which he discussed the work that he was carrying out at that time – special relativity, Brownian motion, and the quantum – Einstein described his work on the quantum as “very revolutionary” in comparison with the other two topics (Klein et al., 1993, Document 27, p. 31 – 32).

108 Experiment, Time and Theory

It was rather “as if the radiation consisted of quanta of the indicated magnitude” (Einstein, 1909b, p. 191; Beck, 1989, p. 370). After indicating how this hypothesis could be elaborated experimentally, Einstein then turned, in his final section, to the question how a quantum theory of the constitution of radiation would look like. He did this by means of a discussion of how such a theory should treat a closed space, containing an ideal gas, radiation, and ions, which, because of their charge, are capable of mediating an energy exchange between the radiation and the gas. The theory would have to make use of the following quantities: the mean energy η of a molecular structure; the light velocity c; the electric charge ; and the frequency ν. Investigating how these quantities are to be related to the constants figuring in Planck’s radiation law (equation 2.28 on page 96) and Wien’s displacement law195 then led him, amongst other relations, to an equation that relates the light quantum constant h to the electric charge (Einstein also called the elementary quantum of electricity): h = 2/c. The significance of this equation, Einstein then pointed out, was that it indicated that such a theory could equally well account for the electron’s constitution:

The most important aspect of this derivation is that it relates the light quantum constant h to the elementary quantum of electricity. We should remember that the elementary quantum is an outsider in Maxwell- Lorentz electrodynamics.196 Outside forces must be enlisted in order to construct the electron in the theory; usually, one introduces a rigid framework to prevent the electron’s electrical masses from flying apart under the influence of their electric interaction. The relation h = 2/c seems to me to indicate that the same modification of the theory that will contain the elementary quantum as a consequence will also contain the quantum structure of radiation as a consequence. (Einstein, 1909b, p. 192 – 193; Beck, 1989, p. 373 – 374)

Einstein then listed four conditions for such a theory.197 While he could not oﬀer such a theory yet, he believed that it should be attainable. In fact, he concluded, there were not that many possible candidates (1909b, p. 193). In this way, Einstein’s work on the quantum suggested a way to address what he took to be the issue raised by Ehrenfest (see section 2.5): the formulation of

195 Attention, Wien’s displacement law is not the same law as Wien’s distribution law for the spectral energy density uν of black-body radiation, which was replaced by Planck’s law (equation 2.28), as we have seen on page 95. The displacement law is rather concerned with “how the curve for [uν , i.e. the spectral energy density] is displaced as the temperature of the cavity changes” (Kuhn, 1987, p. 6). It acted as a constraint on the formulation of the different distribution laws (by Wien, Rayleigh-Jeans, and Planck) for the spectral energy density of black-body radiation (Gearhart, 2002, p. 179). 196 Here, Einstein refers to an article by Tullio Levi-Civita (1907) which, according to the editors of the Einstein papers, presented “a solution of the field equations corresponding to the motion of a stable, isolated charge moving at the speed of light” (Stachel et al., 1989, p. 553; note 67). 197 Such a theory, according to Einstein, had to be constrained as follows: “The fundamental 1 ∂2φ ∂2φ ∂2φ ∂2φ equation of optics D(φ) = c2 ∂2t − ∂x2 + ∂y2 + ∂z2 = 0 will have to be replaced by an equation in which the universal constant (probably its square) also appears in a coefficient. The equations sought for (or the system of equations sought for) must be homogeneous in its dimensions. It must remain unchanged upon application of the Lorentz transformation. It cannot be linear and homogeneous. It must – at least if Jeans’ law is really valid in the limit of small ν/T – lead to the form D(φ) = 0 for large amplitudes in the limit” (Einstein, 1909b, p. 193; Beck, 1989, p. 374).

109 Chapter 2. Experiment and the Electron a dynamics of the rigid body, i.e. an account of the forces responsible for keeping the electron together. Einstein did not directly provide a response to Ehrenfest’s challenge, but he did defuse it as a challenge speciﬁcally for the theory of relativity. No longer was an account of the electron something that gave the electromagnetic world view an advantage over the theory of relativity. The radiation problem rather showed that the electron was equally well an outsider to the Maxwell equations (see the quote above), and as such, we should not expect an account of its constitution in purely electromagnetic terms. Ehrenfest’s issue therefore no longer formed a challenge to the theory of relativity, but rather an issue that was independent of any particular theory: no longer was the search for a dynamics of a rigid body required solely to respond to the stability issue originally raised by Abraham. Instead, it now formed a question that carried the promise of a foundation for both the quantum and the electron.

Einstein and the Constitution of Light The suggestion raised at the end of the (1909b) paper was not just any kind of issue. According to Einstein, it would form the next stage in the development of theoretical physics, as he put it in his first lecture to the Naturforscherversammlung (1909a, p. 817). He there presented, as title ‘Uber¨ die Entwicklung unserer Anschaaungen über das Wesen und die Konstitution der Strahlung’ indicates, a discussion of the historical development of what he called ‘our views’ (“unserer Anschauungen”) on the nature and constitution of radiation. Einstein began his lecture by drawing a historical lineage from the wave-conceptions of light to the theory of relativity. He started with early investigations on the nature of light, which involved a debate between wave- and particle-conceptions. Given that the particle-conception could not account for interference and diffraction phenomena, it was abandoned in favor of the wave-theory, which led to the introduction of the electromagnetic ether, as the medium required to carry light waves. The Michelson-Morley experiment then led Lorentz to develop his electrodynamics according to which bodies deform when they move with respect to the undetectable ether. For Einstein, this was an unsatisfactory response, however, since it did not pick up on what was the central point of the Michelson-Morley experiment, the principle of relativity (Einstein, 1909a, p. 817 – 819). He then pointed out that one particular consequence of the theory of relativity, the energy-mass equivalence, suggested a kind of particle-conception of light.198 For the equivalence entails that light is not a consequence of states of a hypothetical medium, but rather something that belongs to matter, and that the emission of light by a body and its absorption by another body can be seen as a transfer of inertial

198 Einstein presents the equivalence here in the following terms: “It turns out that the inertial mass of a body decreases by L/c2 when the body emits the radiation energy L” (Einstein, 1909a, p. 820; Beck, 1989, p. 385). Elaborating it by means of the energy principle – which states that the body’s energy before emission E0 is equal to the sum of L and the body’s energy E1 after emission: E0 = E1 + L – then leads him to widen its scope. It indicates, more speciﬁcally, an equivalence between energy, mass, heat and mechanical energy: “Energy and mass appear as equivalent quantities the same way that heat and mechanical energy do” (Einstein, 1909a, p. 820; Beck, 1989, p. 385). While Einstein thus still conceives of the equivalence itself in terms of the in- or decrease of mass and energy, as he did in his (1905a; 1907e) treatments of the claim (see footnote 129), he now widens its scope by following through on the idea that it is a consequence of the emission and absorption of radiation.

110 Experiment, Time and Theory mass. The theory of relativity in itself, according to Einstein, could not provide further insight into this process. For this he therefore turned to his quantum-work on the constitution of radiation. Wave-theories, Einstein points out, could not account for certain issues, which were the same as he had raised in his (1909b) article for the radiation theories of Jeans, Ritz and Lorentz (see footnote 192). These could be overcome, he then claimed, by means of Planck’s radiation equation (equation 2.28, discussed on page 96), which had received strong conﬁrmation by measurements of the electron’s charge by Rutherford, Geigener and Gegener (see footnote 166), and should therefore not be abandoned, even though its theoretical foundations were in need of replacement (Einstein, 1909a, p. 822). Einstein then argued that the only way to theoretically account for Planck’s equation (2.28) was by means of his light quantum. He showed this by means of a discussion of the pressure exerted, withinin a cavity, by radiation on a mirror (1909a, p. 823 – 824). This discussion led him to the following equation for the mean value of the square of the momentum (∆2) of the ﬂuctuations of the radiation’s pressure on the mirror (with ρ referring to Planck’s radiation equation (2.28) for the radiation’s spectral energy density, τ to the time, and f denoting the area of the mirror):199

1 c3 ρ2 ∆2 = hρν + dνfτ (2.35) c 8π ν2 What was peculiar about this equation, Einstein pointed out, was that the part between brackets consisted of two elements, which suggested that there were two different causes for radiation pressure fluctuations. Wave-theories of light could only c3 ρ2 account, according to Einstein, for the second part ( 8π ν2 ), while the first part (hρν) was accounted for by the light quantum hypothesis. As such, the equation suggested that light displays both wave- and particle-characteristics. A theory that described how this came about was still lacking, Einstein pointed out, but the most natural way to see it, according to him, was by means of an analogy with the electron. Just as the electron forms a particle that gives rise to a wave-structure, i.e. its electrostatic field, Einstein’s new particle-structure would give rise to light’s wave-properties, i.e. its electromagnetic field. While this analogy was nothing more than a suggestion, it does show that Einstein saw close parallels between the electron and his light quantum:

[F]or the time being the most natural interpretation seems to me to be that the occurrence of electromagnetic fields of light is associated with singular points just like the occurrence of electrostatic fields according to the electron theory. [. . . ] I am sure it need not be particularly emphasized that no importance should be attached to such a picture as long as it has not led to an exact theory. All I wanted is briefly to indicate with its help that the two structural properties (the undulatory structure and the quantum structure) simultaneously displayed by the radiation equation according to the Planck formula should not be considered as mutually incompatible. (Einstein, 1909a, p. 824; Beck, 1989, p. 394)

Einstein’s work on the constitution of radiation was thus, at least in part, inspired

199 See Klein (1964) for an extensive discussion of Einstein’s work on this equation.

111 Chapter 2. Experiment and the Electron by electron theories.200 As we have seen on page 109, this work on the constitution of radiation indicated to him a way to elaborate a relativistic account of the electron’s constitution, which enabled him to defuse Ehrenfest’s question regarding the stability of the electron’s motion as a challenge from the electromagnetic world view for the relativistic approach. Here, the electron offered him with a guide to develop a theory of the constitution of light that could account for the energy-mass equivalence, in line with his (1907e) claim that a general account of this equivalence could not be offered by electrodynamics, but only by a theory that would take into account the quantum as well (see page 76). Einstein now had a roadmap for such a theory, i.e. one that could account for both the Maxwellian electrodynamical wave-characteristics and the quantum and relativistic particle characteristics of light. In this way, Einstein’s work on the constitution of light and radiation again allowed him to incorporate parts of the electromagnetic program within the relativistic/quantum approach, as Planck had done earlier with Abraham’s notion of electromagnetic momentum (see page 106). In fact, the whole study of the electron’s constitution became part of this research program. Einstein’s work radically turned over, however, what such a study could provide. It would no longer lead to a completely electromagnetic conception of nature, but rather to a theory that, by providing an account of the constitution of both the electron and the quantum, would account for the equivalence between mass and energy that followed from the theory of relativity. And this showed itself, as in Planck’s (1908a) paper (see as well page 106), in the historical lineage drawn. No longer does Maxwellian electrodynamics lead to an ether-based theory of the electron, as was the case in Kaufmann’s (1901a) Naturforscherversammlung lecture. It rather led to the theory of relativity, the mass-energy equivalence and the quantum. By drawing such historical lineages concerning the way in which the theory of relativity emerged out of Maxwellian electrodynamics, Einstein was able to redraw the relationship between relativity and the theory of the electron. Earlier, Abra- ham’s theory and the Lorentz-Poincaré-Einsteinaccount of the velocity-dependence of mass formed rivalling electron-theories. Now, Einstein could present the theory of the electron, without specifying what he meant by this, as a source of inspiration and information for the development of his wave-particle account of the constitution of light (see the quote on page 111). As such, we see that Einstein’s historical lineages played the same role as the ones by Planck discussed earlier (see page 106 and footnote 189), i.e. to present the theory of relativity not as just one of many possible theories, but rather to present these other theories as stages in a progression leading towards the principle of relativity and the quantum.

200 During this period, the electron played a central role in Einstein’s work. As the quote above shows, it served him as inspiration for the elaboration of a theory of the constitution of light, and his work on the constitution of radiation aimed, in part at least, to provide a theory of the constitution of the electron as well, as the quote on page 109 shows. Moreover, Einstein also used electron theory, in two joint articles with Jakob Laub (1908a; 1908b), to discuss and indicate issues with Minkowski’s (1908) four-dimensional approach to the theory of relativity. See (McCormmach, 1970a) for a discussion of Einstein’s work on the electron during this period, and (Stachel et al., 1989, p. 503 – 507) on Einstein and Laub.

112 Experiment, Time and Theory

Manipulability and the Relativistic Electron Before we turned to the quantum, all electron-accounts discussed approached its dynamics in terms of Maxwellian electrodynamics. On such an approach, the electron was characterized in terms of charge and mass. The quantum-approach now allowed Planck and Einstein to reconceptualize this characterization. Already in his first quantum-papers, Planck (1901a; 1901b) had argued that a value for the electron’s charge could be derived from his quantum of action, one that was later confirmed experimentally (see footnote 166). And by means of his general dynamics, Planck could argue that a system’s mass was not to be conceptualized in terms of either a Newtonian absolute property m, nor as a completely electromagnetic velocity-dependent characteristic µe, but rather directly in terms of a body’s energy, which could have many sources according to Planck’s law of the inertia of energy (equation 2.33, discussed on page 104). The electron, on this view, was no longer to be characterized as a peculiar kind of entity, but rather as just one of many systems that, when in motion, could be characterized by means of Planck’s general dynamics in terms of its volume, temperature and velocity (see the quote on page 101). Both Planck (see the quote on page 97) and Einstein (see the quote on page 111) saw strong analogies between the theory of the electron and the theory of the quantum. And while Planck was hesitant to postulate the quantum as any kind of new entity, Einstein did see the quantum-theory as pointing towards the existence of a new entity, whose dynamics would be responsible for both the constitution of radiation and the constitution of the electron (see the quote on page 109). And, in line with his claims about a relativistic world view, the theory governing this entity’s behaviour was to offer a general account of the mass-energy equivalence that Einstein had originally obtained in a piecemeal way because of the limitations of his relativistic electrodynamics (see page 76). In this way, the quantum carried the promise of a theory that could respond, in a general way, to the theoretical aspects of the challenge raised by Kaufmann’s experiments: such a theory would allow for the elaboration of a relativistic account of the electron’s constitution – i.e. of an account of how the electron’s electromagnetic forces were kept in equilibrium – and of the precise way in which its mass depended on its velocity. This shows that the study of the quantum did not merely allow for the development of a relativistic alternative to the electromagnetic account of the electron offered by Abraham. What Planck and Einstein argued was that the concepts that were central to Abraham’s account of the electron’s mass and of the foundation of the electromagnetic world view, were merely derivative notions. The electron’s inertial mass, its velocity-dependency and its electromagnetic momentum, Planck argued, were all secondary with respect to its energy, its kinetic potential and its momentum. In this way, the relativistic approach was able to incorporate parts of the electromagnetic world view, in such a way that it could defuse the challenges it raised. And it is because the quantum allowed Planck and Einstein to incorporate aspects of the electromagnetic world view into their relativistic approach that they could write the historical trajectories they offered in their presentations at the Natur- forscherversammlung. On both historical trajectories, the electromagnetic approach was no longer presented as a rival or as an alternative, but rather as either a point on the way towards the relativistic approach (in the case of Planck) or as a source of inspiration (as Einstein does). This indicates that the relationship between the

113 Chapter 2. Experiment and the Electron relativistic approach and the electromagnetic world view had changed, in such a way that the theory of relativity could be presented as the new approach to the foundations of physics, and as the best bet for the future.201

Von Laue and the Electromagnetic World View

How much the context has changed with regards to Kaufmann’s (1906b) experimental results can be seen from Max von Laue’s (1911) handbook, which we already encountered in the beginning of this chapter (see page 42).202 The central question to which the theory of relativity oﬀered an answer, according to von Laue, was the question whether Maxwellian electrodynamics obeyed a principle of relativity. The theory showed that this was indeed the case, if we used the Lorentz transformations (equations 2.29, discussed on page 100) instead of the Galilean transformations to connect an inertial frame (x, y, z, t) with another inertial frame (x0, y0, z0, t0) moving with velocity v with respect to the ﬁrst:203

x0 = x = vt, y0 = y, z0 = z, t0 = t (2.36)

In his handbook, von Laue then attempted to answer the question what reasons we could have to accept this replacement. A ﬁrst, principled reason, was that while the Lorentz transformations are compatible with both mechanics and electrodynamics, the Galilean transformations are compatible only with mechanics (von Laue, 1911, p. 7 – 8). With regards to experimental reasons, von Laue claimed, as Planck had done earlier (see page 99), that while there was no direct experimental conﬁrmation of the theory of relativity yet, there was no experimental argument against it either: “not one empirical ground against the theory is available” (von Laue, 1911, p. V).204

Von Laue and Experiment Tthat there are no grounds against a theory does not yet mean that we should accept it. To argue for this, von Laue listed some experimental phenomena that, if the theory could provide an explanation of them, would form an argument in favour of the requirement of a principle of relativity for electrodynamics, and hence in favour of the theory of relativity:205 the phenomenon of electromagnetic induction, which, as Einstein had shown in the introduction of his original (1905c) relativity paper, gave rise to an asymmetry between theory and observation if it was not described in terms of the principle of relativity;206 experiments

201 What Planck and Einstein thus do is redraw what Staley calls research histories, i.e. “accounts of the past [. . . ] that scientists oﬀer in key papers and review studies[, which] play a substantive role in shaping understandings of new theory” (Staley, 2008a, p. 294). We will return to this concept of research histories in chapter 4. 202 For some historical and technical discussions of von Laue’s work, see (Miller, 1981, p. 367 – 374), Janssen and Mecklenburg (2006), (Staley, 2008a, p. 335 – 339), Rowe (2008) and (Janssen, 2009, p. 35 – 37). 203 The distinction between Lorentz transformations and Galilean transformations was ﬁrst made by Philipp Frank (1908) on the basis of Minkowski’s (1908) work (Staley, 2008a, p. 268). 204 The original German goes as follows: “kein einziger empirischer Grund [ist] gegen diese Theorie vorhanden”. 205 As von Laue (1911, p. 201) points out, this list is mainly based on Laub’s (1910) overview of the experimental grounds of the principle of relativity. 206 Together with Bert Leuridan, I have discussed this case in detail in our (2017) article.

114 Experiment, Time and Theory by Harold Wilson (1904) on the motion of a dielectric through a magnetic field;207 experiments by Henry Augustus Rowland (1878) on the magnetic characteristics of electric current; experiments by Wilhem Röntgen (1890) and Aleksandr Eichenwald (1904) on the electromagnetic properties of moving dielectrics; Hyppolite Fizeau’s (1851) experiment on the velocity of light in moving water; the stellar aberration phenomena first observed by James Bradley (1827); the Doppler effect, and especially recent experiments by Stark (1906) on this phenomenon in canal rays;208 the Michelson-Morley experiments (1886) on second-order effects of the motion of the earth with respect to the ether; the Trouton-Noble experiment (1903) on the ro- tationary moment of a charged capacitor in motion, and other experiments of this kind;209 and finally, the dynamics of the electron, with Kaufmann’s experiments and the issue of the electron’s constitution (von Laue, 1911, p. 8 – 18). It is on von Laue’s discussion of this last item that we shall focus here. Kaufmann’s experiments promised, according to von Laue, a decision between Lorentz’s and Einstein’s predictions for the electron’s longitudinal and transverse mass (1911, p. 17 – 18).210 They now showed, according to von Laue, that there was indeed a velocity-dependence of the electron’s transverse mass. Neither these exeri- ments, nor later replications of them, could, however, provide a definitive decision between the theories involved:

Now, an electron will experience forces when moving in electric and magnetic fields, in such a way that its dynamics can be investigated experimentally. Kaufmann, who was the first to attempt such investigations, was able to prove the velocity-dependence of the transverse mass in the case of β-rays. The accuracy was not sufficient however, for a decision between both theories. And even though later, very significant experiments by Bucherer and Hupka seemed to argue in favour of the theory of relativity, the opinions on their evidential value are still divided, such

207 Einstein and Laub (1908a) had already discussed these experiments as offering a possible way to differentiate between Einstein’s theory of relativity and Lorentz’s relativistic electrodynamics. 208 These experiments provided a possible new way to test the principle of relativity, according to Einstein (1907d), since the moving positively charged ions that constitute canal rays emit line spectra whose frequency, if the theory of relativity was indeed correct, would dilate, i.e. slow down when put in motion, in line with the time dilation effect. 209 See Janssen (1995, 2009) for an extensive discussion of these experiments. 210 At first, I thought this characterization of the Kaufmann experiments as concerning a decision between Lorentz’s electrodynamics and the theory of relativity had to be a mistake, since everybody at the time took these experiments to concern a choice between Abraham’s electromagnetic account and the Lorentz-Einstein relativistic approach, as Einstein’s theory of relativity entailed the same equations for the velocity-dependency of mass as Lorentz’s theory. Von Laue repeats his claim, however, in later editions of his textbook as well (I have checked the fourth edition, which is from 1921). For Lorentz’s equation, von Laue refers to work by Abraham (1903; 1905), Karl Schwarzschild (1903) and Sommerfeld (1904a; 1904b; 1905) on the dynamics of the electron. This is an interesting use by von Laue of these works, since all three of them discussed the Kaufmann experiments as involving, essentially, a choice between Abraham’s rigid and Lorentz’s deformable electron, and while all three of them pointed out that both theories were compatible with Kauf- mann’s (1903) results, they also all discuss Abraham’s work on the electron’s stability, which, as we have seen, was taken to be an issue for Lorentz’s electron (see section 2.3). Schwarzschild (1903, p. 245 – 246), for example, states that it is doubtful whether Lorentz’s purely electromagnetic electron could address this issue. While Sommerfeld does not seem to discuss Lorentz’s electron in detail, his discussion of the electron theory is very much in line with Abraham’s, which, according to Sommerfeld (1904b, p. 366) provides the theoretical interpretation of Kaufmann’s observations.

115 Chapter 2. Experiment and the Electron

that the theory of relativity has not yet obtained unconditional reliable support from this side. (von Laue, 1911, p. 17 – 18)211

Von Laue and the Electron’s Stability Throughout his handbook, von Laue investigated what the implications were of the theory of relativity for the dynamics of the electron. His starting point (1911, p. 79) for this were the transformation equations for the electric and magnetic fields that Einstein already obtained in his (1905c). On the basis of Minkowski’s (1908) four-dimensional geometrical approach to the theory of relativity, von Laue then expressed the total force density of the electromagnetic field on the electron in terms of what he called the four-force, which is a specific four-vector that specifies the Lorentz transformations for this force.212 In terms of this framework, von Laue then elaborated what this meant for the conservation of energy, momentum and angular momentum, which he then in turn used to obtain transformation equations for energy, energy flow and stresses. These transformation equations served von Laue to study further the influence of electromagnetic fields on charged bodies in motion: what was the precise contribution of the electron’s self-induced fields on the total force experienced by the electron? He started with a charged body in uniform motion, which, in its rest frame K0 (i.e. the frame that moves with the same velocity in the same direction as the body) gives rise to an electrostatic field, but no magnetic field. This entailed, von Laue showed, that the total force from its own self-induced fields experienced by such an electron would be zero. Given the transformation equations for forces obtained earlier, the same had to be the case for the total force from its self-induced fields for such an electron in uniform motion. This entailed that no external force was required for stationary motion, i.e. motions that are equal to rest in the electron’s rest frame (von Laue, 1911, p. 96). This was not the whole story, however, for as von Laue pointed out, the rotational momentum of the electromagnetic force is not zero (1911, p. 96). This led again to the stability-issue originally raised by

211 The original German goes as follows: “Nun erfährtein bewegtes Elektron sowohl im elektrischen als im magnetischen Feld Kräfte,so daß man seine Dynamik experimentell untersuchen kann. Kaufmann, der zuerst an diese Versuche herantrat, konnte auch die Abhängigkeit der transversalen Trägheitvon der Geschwindigkeit bei den β-strahlen nachweisen. Zu einer Entschei- dung zwischen beiden Theorien reichte aber die Genauigkeit nicht aus. Und wenn auch spätere, sehr bedeutende Experimente von Bucherer und Hupka zugunsten der Relativitätstheoriezu sprechen scheinen, so sind doch die Meinungen über ihre Beweiskraft noch so geteilt, daß die Relativitätstheorievon dieser Seite eine unbedingt zuverlässige Stützewohl noch nicht erhalten hat”. 212 The four-force is a four-vector, i.e. a vector consisting of four elements (x, y, z, t), which denotes a force in a particular inertial frame of reference. Minkowski’s (1908) work offered a particular formalism for investigating how different four-vectors, denoting different physical properties, changed under the Lorentz transformations, which formed a group (see footnote 109) and could be represented by a 4 × 4 matrix. In this way, Minkowski’s formalism was able to capture the way in which a system’s properties, expressed in terms of four-vectors, transform under the relativistic transformations characterized in terms of four-dimensional matrices. On this view, a body’s motion is no longer visualized as a trajectory between different space-coordinates in a particular space-frame (x, y, z), which can be transformed relativistically by means of the Galilean transformations, with an absolute, unchangeable time t in the background; it is rather conceptualized as a worldline, i.e. a line of events (points in a particular spacetime frame (x, y, z, t)) which gives the location of a body as a function of time, and which can be transformed relativistically by means of the Lorentz transformations. See (Steane, 2012, p. 25 – 39) for a short, technical discussion of four-vectors, and (Miller, 1981, p. 238 – 243) for a short overview of Minkowski’s work.

116 Experiment, Time and Theory

Abraham:

When the electromagnetic momentum of the ﬁeld of a moving charged body is not in the direction of the velocity, electromagnetic forces will exercise a rotational momentum on the electron [Abraham (1903; 1905)]. Still, no rotation should occur, since in [its rest frame] K0 the electrostatic forces do not bring about any change of place. It is to be the task of mechanics to show, how this electromagnetic rotational momentum is cancelled. We want to point out here already that it is the mechanical stresses that keep the electromagnetic forces in the body in equilibrium. (von Laue, 1911, p. 97)213

As von Laue pointed out, this issue could not be answered in a completely satisfactory way yet. That would require a mechanics of stresses, which would be developed later in the book (see page 119). Still, an outline for how this stability was to be obtained from a relativistic point of view could already be given, by means of a discussion of a spherical electron at rest. Following Abraham’s treatment of such an electron (see pages 51 and 60), von Laue showed that its electromagnetic momen- e e tum G was equal to the GEM Abraham calculated for Lorentz’s electron from its self-induced fields (see equation 2.16 on page 60). He also showed, equally well in line with Abraham’s work, that the forces and energy of its self-induced electromagnetic fields were such that there would be no rotational momentum because of its symmetrical form. Von Laue pointed out that, strictly speaking, these results only applied to non-acceleratory motion. They could also be used, however, von Laue then claimed, to approximate the contribution of the self-induced electromagnetic forces to the total force for motions with accelerations that are so small that they have no influence on the field, i.e. quasi-stationary accelerations (von Laue, 1911, p. 98). Carrying out this approximation could then inform us, according to von Laue, about how the electron’s motion remained stable. To accomplish this, von Laue introduced a new kind of four-vector, namely the four-potential, which allowed him to formulate an expression for the potential flow of the field induced by a point charge that displays an arbitrary motion.214 Integrating over the totality of point charges that make up a charged body then provided von Laue with four-dimensional equations for such a body’s field potentials A and φ.

213 The original German goes as follows: “Liegt der elektromagnetische Impuls [. . . ] des Feldes eines bewegten geladenen Körpers nicht in der Richtung der Geschwindigkeit, so üben die elektromagnetischen Kräfteein Drehmoment auf ihn aus [Abraham (1903; 1905)]. Trotzdem darf keine Drehung eintreten, da in K0 die elektrostatischen Kräftekeine Anderung¨ der Lage bewirken. Es wird die Aufgabe der Mechanik sein, nachzuwiesen, wodurch dies elektromagnetische Drehmoment aufgehoben wird. Wir wollen schon hier bemerken, daß dies die mechanischen Spannungen sind, welche im Körper den elektromagnetischen Kräftendas Gleichgewicht halten”. 214 Besides their formulation in terms of the electric and magnetic field E and B, the Maxwell equations can also be formulated in terms of the magnetic potential A, which denotes the potential energy per unit of current (with B = ∇ × A = 0), and the electric potential φ, which denotes the potential energy per unit charge (with E = −∇φ − ∂A/∂t). The four-potential combines both the magnetic potential and the electric potential in one four-vector, in line with the procedure outlined in footnote 212. This four-vector provided von Laue with the field’s potential flow, which is an expression for the velocity field, i.e. a vector field expressing the velocity and direction of the total field, derived from the electric potential, for a charge in arbitrary motion. See chapter 8 of (Steane, 2012, p. 171 – 204) for an extensive discussion of electrodynamics within the four- dimensional relativistic framework.

117 Chapter 2. Experiment and the Electron

In trying to obtain from these equations the values for the electromagnetic self- forces induced by these fields, however, von Laue stumbled upon the issue that given the state of mathematical physics at the time, this was only possible for the non-deformable, i.e. rigid, electron, but not for a deformable one (von Laue, 1911, p. 105).215 To overcome this, von Laue proposed to constrain his study of the electron’s motion. He would only consider those motions in which the acceleration, from the point of the view of the K0 frame, remained the same, which in Minkowskian terms is called hyperbolic motion. Considering only such motions was sufficient for what he is after since they allowed for the approximation of any kind of world line (1911, p. 107). Investigating the transformation properties of such motion then led him to the claim that an electron performing such motions was to be conceptualized as if it were a rigid body in its rest frame:216 A body, whose points are represented by such hyperbolas as world lines, has therefore, at the time that it is at rest, in each such system the same form; it moves as if it were a rigid body. With regards to one and the same system its form changes of course following the Lorentz- contraction. It is this motion that we will ascribe in what follows to the electron. (von Laue, 1911, p. 107)217 Von Laue then elaborated equations expressing the four-potential and the forces exercised by it on such an electron displaying hyperbolic motion. Transforming the equations for the self-induced forces from the rest frame to a frame in which the electron’s motion is hyperbolic then showed him that the self-induced force experienced by the electron, in this frame, was equal to the negative rate of change of its electromagnetic momentum: Fe = −dGe/dt (von Laue, 1911, p. 115). He thus obtained the same expression for the velocity-dependent contribution of the electromagnetic self-induced forces to the electron’s inertia as Abraham and Lorentz had already obtained (see footnote 75), although, as von Laue himself pointed out, he obtained it in a way that differed quite profoundly. While Abraham and Lorentz focused solely on the electron’s electromagnetic momentum, and then tried to infer which forces were required to keep the electron in equilibrium, he started from the total momentum required for the electron to remain in equilibrium, and then inferred which part was contributed by the electron’s self-induced fields (von Laue, 1911, p. 116).218

215 The problem was that, at the time, the theory of relativity did not have the mathematical tools to express the influence of acceleration on a body’s deformation. 216 Following von Laue himself, I use the expression ‘as if’ here, since strictly speaking, the Minkowskian formulation of special relativity did not allow for a rigid body. Ehrenfest (1909) had argued that the introduction of the concept of a rigid body into this framework led to contradictions. Minkowski himself had suggested in his (1909, p. 80) lecture that introducing the concept would allow for the possibility of an experimental detection of the ether. And Von Laue indicates here that the concept would lead to the possibility of infinitely high velocities within his relativistic theory of stresses. For historical discussions of relativity and the rigid body, see (Miller, 1981, p. 243 – 257), Maltese and Orlando (1995) and (Staley, 2008a, p. 271 – 293). 217 The original German goes as follows: “Ein Körper, dessen Punkte durch derartigen Hyperbeln als Weltlinien dargestellt sind, hat daher in jedem dieser Systeme, in dem Moment, da er in ihm ruht, genau dieselbe Form; er bewegt sich wie ein starrer Körper. Bezogen auf ein und dasselbe System veränderter natürlich seine Form entsprechend der Lorentz-Kontraktion. Diese Bewegung wollen wir im folgenden dem Elektron zuschreiben”. 218 As he puts it: “While the equation [Fe = −dGe/dt] is, for all systems in quasi-stationary

118 Experiment, Time and Theory

Von Laue and the Electron’s Constitution Later on in his book, Laue then made use of these results in a discussion of what they entailed for the electron’s constitution. He did this, more specifically, in terms of Planck’s (1908a; 1908b) general dynamics and its law of the inertia of energy, translated into the Minkowskian v(α+p) formalism. As did Planck, von Laue took the equation (2.33) g = c2 (discussed on page 104) to cover any kind of momentum transfer, and he similarly tried to conceptualize it as a generalization of the Maxwell stress tensor. Bodies, on this view, are elastic entities formed by stresses of the electromagnetic field surrounding them. This “relativistic dynamics of elastic bodies stated axiomatically that stresses existed to maintain a body of any shape in uniform translation” (Miller, 1981, p. 374), which meant that it generalized the stresses introduced by Poincaré(see section 2.3) and discussed by Planck (see page 104) to any kind of physical bodies. It thus provided an account for the deformation of relativistic bodies: a body is deformed by the stresses of e.g. the electromagnetic field surrounding it in such a way that its motion would remain stable in accordance with the principle of relativity.219 Within this framework, von Laue turned to the elaboration of a relativistic dynamics, i.e. an account of the behaviour of systems when they are brought into (quasi-stationary) acceleration as a consequence of an external force. He investigated, more specifically, whether there was any difference depending on the shape one ascribed to such systems. The first shape he investigated was that of a point particle, subject to a constant pressure p and characterized in terms of its mechanical energy E0, its stress tensor P0 and its volume V 0 (with the superscript 0 referring to its rest frame).220 Von Laue then showed that, in the case of quasi-stationary acceleration, the particle’s longitudinal and transverse mass could be expressed as a particular instance of Planck’s law of the inertia of energy (equation 2.33, discussed 0 on page 104), with the momentum density g capturing the mk and m⊥, α = E , p = p0V 0 and v the particle’s velocity in the rest frame. As we have seen (see page 104), Planck’s law expressed the effect of forces acting on a body as a momentum density whose source is a flow of energy. In this case, von Laue argued, the sources of energy were the particle’s mechanical energy and the work carried out by the acceleration, a necessary consequence of the law of conservation of momentum, Lorentz, and before him Abraham for the rigid electron, could infer in the opposite direction from the momentum to the self-induced force Fe” (von Laue, 1911, p. 116) (“Weil Gleichung [Fe = −dGe/dt] füralle derartigen Bewegungen eine notwendige Konsequenz des Impulssatzes ist, so konnte Lorentz und vor ihm fürdas starre Elektron Abraham umgekehrt von dem Impuls auf die innere Kraft Fe zurückschließen”). 219 In this way, von Laue obtains a relativistic dynamics for the electron in line with Planck’s general dynamics: the interactions between charged particles are to be conceptualized, by means of Minkowski’s (1908) formalism, in terms of Planck’s notions of momentum and energy. In fact, this dynamics is not restricted to the electron or to electrodynamics, given that Planck’s general dynamics remains silent on which kinds of forces there can exist. As Rowe puts it, “Planck made an important breakthrough by associating a momentum density with any energy flow (elastic, heat, chemical, gravitational)” (2008, p. 235). Minkowski translated this insight into his geometrical formulation of special relativity, which von Laue then used in “his proposal that the state of a physical system could be described completely through [an] equation [. . . ] [which] contained the [. . . ] tensors for mechanical, chemical, thermal, elastic, etc. processes” (Miller, 1981, p. 368). 220 Important here is that von Laue does not state that this is a charged point particle; he rather speaks about a point particle in general. This is in line with Einstein’s (1905c) approach, which, as we have seen, also concerned not solely electrons, but all point particles in general (see the quote on page 65). A pressure p is an external force exercised on a body which gives rise to a stress inside the body. Hence, if we know the pressure p, we can ascribe to it a stress tensor P.

119 Chapter 2. Experiment and the Electron pressure p (von Laue, 1911, p. 164). He then turned to the dynamics of an electrically charged sphere. In its state of rest, it has spherical shape and its electric charge is distributed evenly over its surface. When accelerated, the electromagnetic field will not only exert self-induced electromagnetic forces on such an electron, but equally well a negative pressure, so that the electron’s dimensions contract in line with the theory of relativity. Since this electron’s motion can be described in quasi-stationary terms, we can find a precise expression for this pressure by calculating its stress in its rest frame K0, which 0 0 1 Ee led von Laue to the following result: p = − 3 V 0 . By making use of the expression for the electromagnetic contribution to the electron’s inertia he had obtained earlier (see page 118), he then obtained a description of the electron’s longitudinal and transverse mass when it is accelerated, which, again, could be expressed as an instance of Planck’s law of the inertia of energy (equation 2.33). This gave the following expression for the total energy of the forces exerted on the spherical electron: 0 0 0 0 E + p V + (4/3)Ee , which, with the expression for the negative pressure obtained 0 0 earlier, reduced to E + Ee . The sources of energy were thus the mechanical energy and the electromagnetic energy (von Laue, 1911, p. 166).221 The equations that this dynamics provided for the spherical electron’s longitudinal and transverse mass had recently been confirmed by the experiments of Bucherer and Hupka, according to von Laue, which led him to claim that also from the side of the electron’s dynamics, the theory of relativity had received confirmation (in line with his list of phenomena that the theory had to account for, see page 114): Many currently conceive of the electron as an electrically charged sphere.222 In this way, we obtain (under the constraint of surface charge, which is however not significant) that dependency of both masses on velocity that corresponds to the experiments by Bucherer and Hupka. For the dynamics of the electron as well, the theory of relativity is thus in agreement with experiment; however, it should be pointed out again that the latter has not yet been carried out in a flawless way yet. (von Laue, 1911, p. 166)223 Some of these electron theories went even further, Laue continued, and conceptualized the electron’s mass as completely electromagnetic in nature. While there is nothing in the theory of relativity that strictly forbids this,224 neither the dynamics

0 221 The energy-element contributed by the electromagnetic field, (4/3)Ee , is the same as the one obtained by Abraham (see page 62), which led Abraham to claim that there was an issue with 0 Lorentz’s completely electromagnetic electron, since there was a difference of (1/3)Ee between the energy obtained from the electromagnetic field and that obtained from the electron’s Lagrangian. We have seen, on page 61, that Poincaréwas able to overcome this issue by postulating the existence of a negative pressure, the Poincaréstress. What von Laue thus does here is use the same manoeuvre as Poincaréproposed. 222 Von Laue refers here to the work of Poincaré(1905; 1906b), Lorentz (1909), and Abraham (1905). 223 The original German goes as follows: “Als elektrisch geladene Kugel fassen viele zurzeit das Elektron auf. Wir finden so (freilich unter den Einschränkungauf Oberflächenladung, was aber nicht wesentlich ist) diejenige Abhängigkeit der beiden Massen von der Geschwindigkeit, welche den Versuchen von Bucherer und Hupka entspricht. Auch bei der Dynamik des Elektrons steht die Relativitätstheoriein Ubereinstimmung¨ mit dem Experiment; doch mag nochmals darauf hingewiesen werden, daß das letztere wohl noch nicht ganz einwandfrei ausgeführt worden ist”. 224 As he puts it at the end of his textbook, the theory of relativity does not make any claims about the electron’s mass (1911, p. 186).

120 Experiment, Time and Theory of the electron nor recent experiments into the electron’s charge gave reasons to believe this claim. Regarding the electron’s dynamics, it would require introducing an extra contribution of energy besides the electron’s electromagnetic energy (1911, p. 166 – 167).225 Moreover, recent investigations into the electron’s charge and charge-to-mass ratio gave no reason to believe that the electron had to be such as the electromagnetic view assumed.226 And while the electromagnetic view had to ascribe a particular form to the electron, in order to account for its velocity- dependent mass in purely electromagnetic terms, the theory of relativity offered the advantage that it leaves open different possibilities for the electron’s shape, as he then showed.227 What von Laue (1911, p. 167) did, more specifically, was conceptualize the electron as a body shapen by indeterminate stresses (“Körper mit beliebigen Spannun- gen”). This again raised Abraham’s issue, i.e. how to explain away the rotational momentum of the electron (see the quote on page 117). To address this issue, von Laue assumed that such an electron formed a completely static system, which meant that in its rest frame K0, it was in static equilibrium (i.e. all the forces working on it balance each other out). This assumption allowed him to address the issue strictly in terms of the total force the electron experiences, and hence without having to investigate which different sources contributed to this force. Proceeding in this way provided him with expressions for the electron’s energy and momentum that were equal to the general equations that he obtained earlier in the elaboration of his dynamics, which showed that the dynamics of such a completely static system was the equal to that of the mass point as well (von Laue, 1911, p. 170). The electron too formed a completely static system, von Laue then claimed, which entailed that the shape we ascribe to it does not make a difference for its dynamics. The total force that is exercised on the electron can be captured in terms of Planck’s law of inertia of energy, without any specification of the sources of energy that contribute to it. As such, we arrive at the claim with which we opened this chapter (see page 42), namely that experiments on the electron’s quasi-stationary acceleration could not provide us with any insight into its dynamical constitution:

225 This is a very ironic twist. As we have seen (page 61 and footnote 221), Abraham argued, on the basis of the expression for the electromagnetic momentum he had obtained from his purely electromagnetic dynamics of the electron, that Lorentz’s electron required a non-electromagnetic negative contribution, which was provided later by the Poincaréstress. Here, von Laue’s relativistic dynamics argues, on the basis of the expression for the electromagnetic energy he has obtained for an electron with such stresses, that Abraham’s electron requires a positive contribution. 226 Von Laue does not refer to any specific experimental investigations. He only states that the most recent value for the electron’s charge, which was the one obtained by Planck in his work on thermal radiation (see page 97), has been determined in different ways (von Laue, 1911, p. 167). 227 This, again, is quite an ironic twist, for the fact that the theory of relativity did not provide a definite answer regarding the precise constitution of the electron was only a few years earlier taken as a big problem for that theory, as we can see from the discussion of Ehrenfest’s paper in section 2.5).

121 Chapter 2. Experiment and the Electron

tum. (von Laue, 1911, p. 170)228 In this way, von Laue claimed, he had shown that the Kaufmann experiments aimed at something unattainable, i.e. providing an experimental decision regarding the electron’s constitution on the basis of investigations into its quasi-stationary acceleration. We cannot reason back from the dynamics of the electron, on von Laue’s formulation, to the electron’s constitution, since whatever form we ascribe to the electron would lead to the same dynamics, as expressed by Planck’s law of the inertia of energy. As such, the question of the electron’s constitution was outside of the domain of the theory of relativity. The theory does not provide us with an account of the electron, but, on von Laue’s view, only with a criterion – the principle of relativity – that allows us to investigate whether particular theories that do try to give such a constitution-account are admissible or not (von Laue, 1911, p. 186).

Manipulability and von Laue’s Relativistic Electron Einstein (1907a; 1907e) had to admit to Ehrenfest, we have seen on pages 75 and 77, that the theory of relativity could not yet provide an answer to the stability-issue raised by Abraham. Such an answer required a relativistic world view, and that was not yet available at the time: the only secure ground available was that of relativistic electrodynamics. It was only after Planck’s work on black-body radiation, and his development of a general dynamics on that basis, that an outline for such an account of the electron’s dynamics could be given. This shows that both Planck and Einstein believed that the theory of relativity had to provide such an account of the electron’s constitution. That they believed this to be one of the questions to which the theory had to respond is a consequence of the fact that Kaufmann’s experiments, which were taken to provide insight into the electron’s electromagnetic momentum, dominated the discussion. When von Laue’s textbook (1911) appeared, however, this had changed. What the electron’s constitution was – whether it was completely electromagnetic in nature or not, what kind of shape we whould ascribe to it, etc. – was no longer a question to which the theory of relativity had to respond. On the assumption that the electron is a completely static system, which means that it behaves in its rest frame as if it is a rigid body, its motion can be described in terms of hyperbolic world lines, which entails that in a frame in which its motion can be described as quasi-stationary, it will deform in such a way that its mass changes in line with the relativistic formulae for the velocity-dependence of mass (i.e. Lorentz’s equations 2.14 and 2.15 with l = 1, discussed on page 58), and this independently of the speciﬁc shape we ascribe to it in its frame of rest. As such, investigating the electron’s acceleration, on von Laue’s view, does not inform us about its dynamics. This claim should not be seen, however, as a relativistic response that ﬁnally overcomes the challenges raised by Kaufmann’s experiments, since von Laue does not really address these challenges. With regards to the experimental challenge, he puts it to the side rather than providing an argument for why the relativistic formulae for the velocity-dependence of the electron’s mass were not in correspondence with Kaufmann’s results: the quote on page 120, where he states that Kaufmann’s experiments were not accurate enough, is the only statement he makes in his handbook about these results. This shows that, as a consequence of Bucherer’s and

228 For the original German, see footnote 55.

122 Experiment, Time and Theory

Hupka’s experiments, Kaufmann’s experimental results did not pose such a pressing issue for the relativistic approach anymore, in contrast to a few years earlier, when Einstein could only admit that Planck’s re-analysis showed that Kaufmann’s calculations were essentially correct, and that they therefore could indicate that the foundations of the principle of relativity did not correspond to the facts (see the quote on page 82). And von Laue does not precisely respond to the theoretical challenge either, since he does not really offer an account of how the relativistic electron can remain stable under deformation. His discussion of the electron rather started, as Miller puts it, from his “axiomatic claim that the relativity theory had to be in agreement with the electron’s stability” (1981, p. 374). Since the electron behaves as if it is a rigid bod in its rest frame, “the electron’s energy and momentum obtained from the world-tensor formalism ab initio contained contributions from every force necessary for its equilibrium” (1981, p. 373). Von Laue does not specify which forces ensure its stability in its rest frame, but rather assumes that there have to be such forces. This then allows him to argue, by means of the principle of relativity, that it will also remain stable in any frame, connected to the rest frame by means of the relativistic transformation equations, in which it is in motion. Regardless of which shape we ascribe to the electron, von Laue argued, we end up with the same dynamics, i.e. Planck’s general dyamics as characterized by his law of inertia of energy. One advantage of this was that we do not need to specify which sources of energy are responsible for the electron’s momentum, since as we have seen on page 104, this law covers all kinds of energy sources. This shows how von Laue is able to put aside the stability-issue raised by Abraham, which exactly concerned which sources of energy were required to ensure the stability of a deformable electron, i.e. one whose shape could change (see page 62). Von Laue thus sidesteps the experimental and theoretical challenges raised by Kaufmann’s experiments by arguing that they are not really specific issues at all, from the point of view of the theory of relativity. Insofar as the results of the different experiments discussed in this chapter can provide information about the electron’s velocity-dependent mass, on von Laue’s view, they do not inform us about the electron’s constitution, since the same velocity-dependence will arise for any kind of physical system: in line with Planck’s law of the inertia of energy, different sources of energy can be involved, depending on the specific system under consideration.229 With regards to the data produced in the experiments that von Laue considers, i.e. Bucherer’s and Hupka’s, his work can thus be taken to offer the following relativistic interpretation of the manipulations carried out:

[von Laue’s Relativistic Interpretation]: 0 0 0 c i dp i i (p&E &V &P ) + (E&B) −→ hyperbolic motion −→ F = dt −→ µ⊥ −−→ (α+p)/c2 y0,ρ

This interpretation provides a conceptualization of how manipulating an electron by means of electric and magnetic fields produces a particular effect that can provide information about the electron’s velocity-dependence of mass as follows. Whatever its specific constitution may be, applying electric and magnetic fields to it will endow

229 Recall that von Laue argued that the same dynamics applied to both a non-charged point particle and to an electron conceptualized as a charged body shapen by indeterminate stresses.

123 Chapter 2. Experiment and the Electron it with motion that can be characterized as hyperbolic motion. This entails that it can be treated as if it is a rigid body (see the quote on page 118). This allows us to conceptualize the total force F experienced by the body in its rest frame in terms of p, E0,V 0, and P0, from which we can then obtain the electron’s total momentum p. Hyperbolic motions, we have seen on page 117, can also be used to approximate quasi-stationary motion, which entails that the body’s dynamics can be taken to be the same as that of a point particle (see the quote on page 121). Transforming the electron back to the frame where its motion is that induced by the electric and magnetic fields and calculating the electron’s total momentum there will provide us with a difference in momentum, which is due, following Planck’s law of the inertia of energy, to the flow of energy that is embodied by the moving electron. It is this energy flow that can be called the velocity-dependent part of the electron’s mass µ⊥. Applying this to the data (y0, ρ) obtained by Bucherer and Hupka, then provided von Laue with the information that its dynamics was the same as for other physical systems, namely Planck’s general dynamics: its charge-to-mass ratio /µ is to be seen as (α+p)/c2 , where the mass µ is reconceptualized in terms of Planck’s law of the inertia of energy (equation 2.33, discussed on page 104).

Because this interpretation is so generic, in the sense that it can be used without specifying the dynamical constitution of the system under study, von Laue could claim that experiments such as Kaufmann’s could never provide information about the electron’s dynamics. It also allowed him to claim that the electron’s mass could be either completely electromagnetic in nature or not, but that this would not be of importance for the relativistic study of the electron. In this way, we come to see how von Laue, in line with Planck’s and Einstein’s work on black-body radiation, the quantum and the electron, redraws the way in which the theory of relativity relates to the study of physical systems such as the electron. At the time of Kaufmann’s ﬁnal experiments, the theory of relativity was often conceived as one of many proposals for an account of the electron, and these experiments were taken to provide information about the validity of the principle of relativity (see, for example, Ein- stein’s claim that the experimental results could mean that the principle of relativity did not correspond to the facts on page 82). Now, however, von Laue presents the theory as a kind of meta-theory, which lays down principles for the formulation of theories regarding physical systems such as the electron: “the principle of relativity presides over all domains of physics in the same way as, for example, the energy principle, and it equally well proclaims itself as a criterion for the acceptability of any physical theory” (1911, p. 185 – 186).230 In this way, the challenges raised by the electromagnetic world view were deﬁnitely defused, in the sense that its most central element – an electron with a completely electromagnetic mass – could in principle be admitted as a possibility within the bounds laid down by the principle of relativity.

230 The original German goes as follows: “Tatsächlich steht das Relativitätsprinzipin demselben Sinne über allen Gebieten der Physik, wie etwa das Energieprinzip, und beansprucht ebenso wie dies, bei allen physikalischen Theorien ein Kriterium fürderen Zulässigkeit zu enthalten”.

124 Experiment, Time and Theory

2.9 Investigating the Electron’s Dynamics

This chapter has shown how the experimental manipulations carried out by Kauf- mann, Bucherer, Bestelmeyer and Hupka can be characterized in terms of experimental inferences. These inferences express how the manipulation of supposedly stable properties of the electron by means of the experimental set-up should produce data that provide information about more hypothetical properties of the electron. In order for experimental manipulations to provide such information, however, the inferences that characterize them have to be interpreted. Such an interpretation, provided by a model of the entity manipulated, provides a conceptualization of the influence of the manipulation on the entity, in the sense that it tells us which specific effect we can expect if the manipulations are carried out correctly. If the data produced are in line with this expectancy and with other, earlier and similar experiments, this interpretation is then taken to show that the experiment has indeed functioned as it was supposed to. The electromagnetic interpretation (see page 56) thus provides an account of how applying electromagnetic fields to an electron would deflect it in such a way that it would acquire quasi-stationary acceleration. This would then endow the electron with an electromagnetic momentum, from which its transverse electromagnetic mass could be calculated. Applying these interpretations to Kaufmann’s experimental results then showed both that the results were in line with earlier experiments on the electron (i.e. Simon’s and Kaufmann’s earlier experiments on cathode rays) and that the electron’s mass was completely electromagnetic in nature. As such, as long as the electromagnetic interpretation of the experimental manipulations carried out by Kaufmann was in line with the results produced by these manipulations, these manipulations could be seen as reliably providing information about the electron’s electromagnetic momentum. The relativistic interpretation of Kaufmann’s inference (see page 123), on the other hand, provided an account of how applying electromagnetic fields to an electron would deflect it in such a way that the data produced could provide information about the velocity-dependence of its momentum, expressed in terms of Planck’s law of the inertia of energy. On this view, the electrons would be deflected so that their motion could be described in terms of the principle of relativity, which would endow them with a momentum from which its transverse mass, expressed in terms of the kinetic potential, could be calculated. Applying this information to Kaufmann’s experimental results entailed, for those who adhered to the principle of relativity, that these results had to be problematic, and that it were rather the experiments by Bestelmeyer, Bucherer and Hupka that provided insight into the electron’s mass. Moreover, once one accepted that the relativistic interpretation of these later experimental manipulations was in line with the results, these manipulations were to be seen as reliably providing information not about the specific dynamics of the electron, but rather about the dynamics of all physical systems in general. During the period discussed, there were thus different interpretations of how these manipulations produced informative data. These interpretations were offered from particular theoretical standpoints, and could thus be taken as an illustration of Morrison’s claim that for manipulation to provide information about what is manipulated, theoretical information about what is supposedly manipulated is already required. This entails that it is difficult to state which information was provided

125 Chapter 2. Experiment and the Electron by Kaufmann’s experimental manipulations in themselves: it depends on how one interprets these manipulations. This shows that whether the experiments provide information about the electron’s dynamics or not is a question that one cannot answer independently of the historical context. As long as Kaufmann’s experiments were taken to be successful, they were seen as providing information about the electron’s constitution. Von Laue and others took the experiments to provide no such insight, however, because they had a different interpretation of how the data produced by the experiments came about. For them, such data could be produced by any physical system that was given the same motion as the electrons in Kaufmann’s experimental set-up. As such, in line with Arabatzis’ argument that the causal claims supposedly provided by manipulation are also subject to theoretical change, we see here that there was a significant reconceptualization over time of how the experiments were taken to function. That the relativistic approach was able to reconceptualize the interpretation of Kaufmann’s experiments offered by the electromagnetic approach was not solely a consequence, however, of the theory addressing the theoretical and experimental challenges raised by these experiments. Rather, what really opened up the debate where the results by Bestelmeyer, Bucherer and Hupka. Their experiments should not be taken as establishing that the relativistic formulae for the velocity- dependence of mass was in fact the correct one. All experiments, we have seen, were open to serious criticism. They could be used by the adherents of the relativistic approach, however, to argue that Kaufmann’s experimental results were perhaps not as reliable as it was assumed. As such, what these new experimental results primarily accomplished was that the relativistic interpretation was considered, again, as equally plausible as the electromagnetic interpretation. In this way, the experimental challenge was defused rather than directly addressed. This opened up a space for the further development of a relativistic account of the electron, based on Planck’s general dynamics. We should not read this account, however, as providing a comple response to the theoretical challenge of Abraham’s stability-issue. Einstein could only offer a programme for a future theory of the electron’s dynamics, and von Laue’s account of the electron had to assume that there were forces that would ensure the electron’s stability. What the development of these accounts made possible, however, was the incorporation of certain aspects of the electromagnetic electron into the relativistic approach. Von Laue, for example, could claim that it was possible that the electron’s mass would be completely electromagnetic in nature; and Planck could argue that the notions that were central to Abraham’s electrodynamical account of the electron, such as its electromagnetic momentum, were only approximations of those notions that were really fundamental. As such, what these theoretical elaborations primarily accomplished was that the relativistic approach could present itself as a next step in the development of a theory of the electron. In this way, the theoretical challenge as well was defused rather than directly addressed. These reconceptualizations, however, also raise questions about Arabatzis’ claim that in the Kaufmann case, the experiments proceeded in a cumulative fashion and provided a refinement of the electron’s charge-to-mass ratio (see the quote on page 43). As we have seen, this was not how Heil evaluated the measurements of this ratio at the end of the decade. He claimed that there had been no improvement at all

126 Experiment, Time and Theory since Becker’s 1905 measurement. What one rather saw was that both values that were lower than Becker’s and values that were higher were available, and that which value one took to be correct often depended on one’s position within the debate on Kaufmann’s experimental results. As such, Arabatzis’ claim does not seem to hold: rather than a refinement of the measurements, we have a polarized situation where each measurement was read in terms of the debate between the electromagnetic world view and the relativistic approach. What this history of the measurement of the electron’s charge-to-mass ratio also shows, is that even the empirical regularity that one can identify in the experimental results, depends on how one interprets the experimental manipulations. Where adherents of the electromagnetic world view saw the higher charge-to-mass ratio measurements as evidence for the electromagnetic velocity-dependence of mass and the lower measurements as incorrect, those working under the relativistic approach saw the lower measurements as evidence for the the relativistic velocity-dependence and the higher measurements as incorrect. And the way in which they took measurements to be ‘correct’ or ‘incorrect’ was influenced by the way in which they interpreted the experimental manipulations carried out, since it was this interpretation that told them which experimental set-up functioned reliably and which did not. We thus have an even stronger version of Massimi’s argument: whereas she claimed that it was only by means of theory that scientists could recognize what was responsible for the phenomenon produced, here we see that theory even influenced which empirical regularity was recognized. As such, neither what one would now take to be the ‘unsuccessful’ manipulations by Kaufmann, nor the ‘successful’ manipulations by Bucherer and others,231 can be taken to provide any information in themselves. Rather, it is only within a certain interpretation that they can be taken to do so. And moreover, the information that they do provide under such an interpretation is not to be characterized as any kind of factual information. Kaufmann’s (1906b) experiments did not show that the electron had the properties Abraham ascribed to it, such as a spherical form or rigidity. Rather, on the electromagnetic interpretation of the experimental manipulations carried out, these manipulations endowed the electron with a specific kind of electromagnetic momentum, and it was this momentum-value that was then taken to determine the bounds of which properties one could possibly ascribe to the electron. As long as these experiments could be taken to show, in terms of the electromagnetic interpretation, that the electron’s momentum was brought about in a completely electromagnetic way, it could be either rigid (as was Abraham’s) or deformable (as was the Bucherer-Langevin electron). This shows that, given a particular interpretation of how the experiment works, the information provided by the manipulation is to be seen as delineating what could plausibly be responsible for the effect produced by the manipulation. As long as one took Kaufmann’s experiments to be successful, the electromagnetic models could be taken as plausible accounts of which properties of the electron were

231 I take it that normally, one would consider the latter experiments to be successful, given that they provided data that could be seen as evidence in favour of the theory of relativity, a theory that is still taken as successful. Kaufmann’s experiments would generally be seen as unsuccessful, given that they provided data in favour of the electromagnetic world view, an approach that has been abandoned. This, of course, shows that the evaluation of whether an experiment is successful, i.e. whether it works reliably in such a way that we can take its data to provide us information, is not independent of any kind of theoretical considerations, as Cartwright and Hacking assume.

127 Chapter 2. Experiment and the Electron manipulated in such a way that the experiment could produce the results that it did. From the moment that one took these experiments as no longer successful, however, either because of a commitment to the principle of relativity on other experimental or theoretical grounds or because of the results of the experiments by Bestelmeyer, Bucherer and Hupka, one could take the relativistic interpretation, in terms of the Lorentz-Poincar´eelectron, to be an equally plausible account of the experimental manipulations. As such, the information provided by an experimental manipulation, which delineates the boundaries of plausible interpretations of the experiment’s functioning, depends on how one interprets the manipulations carried out.

128 Chapter 3

Experiment and the State of Magnetization of Superconductors

3.1 Introduction

The second historical episode to be discussed concerns a whole series of experiments on the state of magnetization of superconductors. These are metallic substances that, when a magnetic field H0 with a strength below a certain critical field threshold HC is applied, while their temperature T is below a certain critical temperature threshold TC , will transition to the superconducting state, in which they are able to carry a current that behaves as if it experiences zero resistance.232 According to Maxwell’s equations, bodies with zero resistance (R = 0), which are called perfect conductors,233 will display what was known at the time as frozen in magnetic fields, i.e. a magnetic flux B equal to the field H0 applied before the transition to the superconducting state. Our starting point will be certain experiments carried out by Heike Kamerlingh Onnes and Willem Tuyn (1924), which were taken at the time to show that all superconductors have frozen in fields. This chapter will be concerned, more specifically, with how these experiments and their results fared in the years afterwards. While they were very widely accepted at first,234 they were completely

232 In contrast to the previous chapter, a distinction needs to be made between an externally applied magnetic field H, a magnetic flux B (sometimes also called magnetic flux density in the literature), and a body’s state of magnetization M. The flux density B is connected to the applied magnetic field H by means of the following expression: B = H + 4πM, where M = χH. The symbol χ refers to the material’s volume magnetic susceptibility, which concerns how much a material will become magnetized upon application of a magnetic field (see footnote 236 for a discussion of different kinds of magnetization). The relation between flux density and applied field is also expressed in terms of the material’s permeability µ, i.e. its capacity to allow for the formation of a magnetic field within itself: B = µH. Bold symbols denote a vector, i.e. a physical quantity with a direction. When we are speaking solely about the value of a property, no bold symbol will be used. 233 When a material is rendered superconducting, there will be electrical conduction through it, i.e. charged particles that flow and constitute a current I. The direction and force of this current is determined by the voltage difference between two points on the material. The resistance of the material is the ratio of the voltage across the material to the current: R = V/I. It is determined by the type of material and its geometry. The resistivity η characterizes the resistance of a material independently of its geometry. Its inverse is called the material’s conductivity σ: a material with high resistivity has low conductivity, and vice versa (Matricon and Waysand, 2003, p. 31). 234 Hendrik Casimir, one of the researchers whose work will be discussed below, later described the idea of frozen in fields as one of the two superstitions that haunted superconductivity research

129 Chapter 3. Experiment and Superconductivity overturned in later years by other experiments, according to, Fritz London, one of the central ﬁgures in what is to follow:

In a conductor with infinite conductivity (in this way, it was believed at the time, superconductors had to be characterized), it is not possible to bring about any change in the magnetic flux; this entailed, it was believed, that the magnetic field present inside the superconductor on the moment of transition would ‘freeze in’, so to say. Important experiments, in particular the famous experiment by Kamerlingh-Onnes and Tuyn on the persistance of supercurrents in a sphere, seemed until now to confirm this conception, according to which the state of a superconductor is not defined uniquely in terms of the customary variables (temperature, magnetic field value, etc.), but rather characterized, among other things, in terms of a sort of remembrance of the state during which the superconductivity arose the previous time. According to this conception, the actual state of a superconductor depended on the path it followed during its history. Recently, our ideas have undergone a profound revolution which was brought about primarily by an experiment first carried out by Meissner and Ochsenfeld (1933), which was repeated afterwards by other investigators. Under ideal conditions, this experiment seems to show the following: A superconductor cooled in a magnetic field below its transition point, expels the magnetic field outside of the superconducting region. (London, 1937b, p. 9 – 10)235

Because superconductors were taken to display such frozen in fields, they were often conceptualized in terms of a ferromagnetic state of magnetization:236 even after the at the time. The other superstition was the idea that superconductivity was to be explained in terms of the free path of the superconducting electrons (Casimir, 1977, p. 174). 235 As in the previous chapter, all quotes in the text will be given in English. If no translation is available, I will give my own translation and add the original quote in footnote. Here, the original French states the following: “Dans un conducteur de conductibilitéinfinie [c’est ainsi que l’on se croyait obligéde caractériser un supra-conducteur], il n’est possible d’effectuer aucun changement du flux magnétique; on croyait pouvoir en déduireque le champ magnetique qui règne dans le supra-conducteur au moment du passage au point de transition, se ‘congèle’,pour ainsi dire. Des expériences importantes, particulièrement la fameuse expériencede Kamerlingh-Onnes et Tuyn sur la persistance des supra-courants dans une sphère,semblaient jusqu’àprésent confirmer cette conception, suivant laquelle l’étatd’un supraconducteur n’est pas uniquement définipar les variables habituelles [comme la température,la valeur du champ magnétique, etc.], mais caracterisé en outre par une sorte de souvenir de l’étatau cours duquel la supra-conductibilités’est établie la fois précedente. Selon cette conception, l’étatactuel du supra-conducteur dépendait du chemin qu’il a suivi pendant son histoire antérieure.Récemment, nos idéesont subi une profonde révolution due àune expériencequi fut d’abord réaliséepar Meissner et Ochsenfeld (1933) et répétéeensuite par plusieurs chercheurs. Réalisée dans des conditions idéales,cette expérienceparaˆıtdémontrer ce qui suit: Un supra-conducteur refroidi dans un champ magnétiqueau-dessous de son point de transition, refoule le champ magnétiqueen dehors de la régionsupra-conductrice”. 236 With regards to the state of magnetization M of a substance, we can distinguish different categories of magnetic susceptibility χ, depending on how they behave under application of an external magnetic field. In what is to follow, three different such states will be of importance: diamagnetism, paramagnetism and ferromagnetism. Diamagnetic substances have a negative magnetic susceptibility, which means that an applied magnetic field tends to get expelled from the substance’s centre. Paramagnetic substances have a positive magnetic susceptibility, which means that they attract the applied field. Both of these substances lose their magnetization when the

130 Experiment, Time and Theory applied field H was removed, they would still display magnetic properties as a consequence of the frozen in fields. What Walther Meissner and Robert Ochsenfeld’s experiment showed, according to Fritz London, was “that a supraconductor behaves not only like an ideal conductor, but in addition also like a very strongly diamagnetic metal” (1937a, p. 793).237 This meant, according to Fritz London, that we should normally not expect any frozen in fields in superconductors, since diamagnetic materials will expel any magnetic flux. The central aim of this chapter will thus be to investigate how these experiments led to the claim that superconductors are not ferromagnetic materials with frozen in fields, but rather diamagnetic materials without frozen in fields. The main reason for investigating this issue is that it can provide even more insight into the epistemology of experimental manipulations. This case offers a good way to study this issue, since at the time there were divergent opinions about what Meissner and Ochsenfeld’s experiments entailed. Fritz London’s diamagnetic interpretation of the experiments was not generally shared at the time: Meissner and Ochsenfeld themselves, for example, ended their (1933, p. 788) article with a restatement of the ferromagnetic analogy, and Meissner (1935, p. 15) claimed that later experiments raised issues with the validity of Fritz London’s interpretation, which he had formulated together with his brother Heinz. Willem Keesom and Johannes Kok stated that the experimental results suggested primarily that “one must be cautious as to the appreciation of the value of the magnetic field in the neighbourhood of a supraconductor” (1934b, p. 503). Moreover, even Fritz London himself, together with Heinz, had earlier described Meissner and Ochsenfeld’s results as a “still very uncertain experimental finding” (1935b, p. 341).238 As such, this chapter will be concerned, more specifically, with how it came about that Kamerlingh Onnes and Tuyn’s experiments were no longer seen as providing the information that superconductors are ferromagnetic materials of some kind, and how Meissner and Ochsenfeld’s experiments came to be seen as showing that they are instead diamagnetic materials of some kind. Investigating how to characterize the information provided by these experiments seems beneficial, since Meissner and Ochsenfeld’s experiments are at the center of a philosophical debate that has been going on for quite some time now, concerning the model of superconductivity that Fritz London constructed with his brother Heinz. This debate was sparked by Steven French and James Ladyman’s (1997) reaction to a short article by Nancy Cartwright, Mauricio Suárezand Towfic Shomar (1995) about the model.239 Both sides assume that Meissner and Ochsenfeld’s experiments applied field is removed. Ferromagnetic substances, finally, are substances that have a far stronger magnetization than the others, and can even, under some conditions, remain magnetized in the absence of an applied external field (Keith and Quédec,1992, p. 364). For a contemporary overview of the study of diamagnetism, paramagnetism, ferromagnetism and other states of magnetization such as antiferromagnetism, see chapters 11 and 12 of (Kittel, 2005, p. 297 – 360). 237 At the time, the term supraconductor, which derived from the French word ‘supraconducteur’, was often used instead of the English ‘superconductor’, even in English or German (Matricon and Waysand, 2003, p. 52). 238 Here, the original German states “den noch sehr unsicheren experimentellen Befund”. 239 Since then, both sides have responded to each other in quite a few articles. From the side of Cartwright, Suárezand Shomar we have two articles: (Suárez,1999; Cartwright and Suárez, 2008). From the side of Ladyman and French, we also have two papers, together with Otávio Bueno, directly responding to Cartwright et al.: (Bueno et al., 2012a,b). Besides these papers, French, Ladyman and Bueno, sometimes together with Newton C.A. da Costa, have also discussed

131 Chapter 3. Experiment and Superconductivity provided a diamagnetic insight. French, Ladyman and OtávioBueno, for example, write that “[w]hat [the Meissner effect] drove was a shift in the over-riding analogy, from that with ferromagnetism in the case of the old ‘pre-Meissner’ model, to that with diamagnetism in the case of London and London’s” (Bueno et al., 2012b, p. 44). Suárez,who is part of the other side of the debate, equally well writes that “[the Meissner effect] means that a superconductor is a kind of diamagnet” (Suárez,1999, p. 186).240 On the basis of this assumption, they then argue over how the London brothers were able to translate this insight into a model of superconductivity: was it diamagnetic theory or the experimental insight that superconductors are diamagnetic that drove them? Investigating how we are to characterize the information provided by Meissner and Ochsenfeld’s experiments will show that neither side of the debate characterizes them correctly: it was neither experiment nor theory on its own that entailed that Meissner and Ochsenfeld’s experiments became seen as providing the information that superconductors are diamagnets of some kind.

3.2 Lippmann’s Theorem, Perfect Conductors and Frozen In Fields

It was Heike Kamerlingh Onnes (1911) who first presented a description of a new phenomenon that was brought about in his laboratory in Leiden: superconductivity.241 He came into contact with this phenomenon during his investigations on the liquefaction of helium, which required him to bring about extremely low temperatures (a bit above 0K, so around −273◦C).242 He observed, more specifically, that when certain substances are cooled under a certain critical temperature treshold TC (a bit above 0K) while applying a magnetic field H0, their resistance R drops to almost zero. This was shown by the currents that were induced on the surface of the superconducting material by varying the strength of the applied magnetic the model in quite a few other papers: (Bueno, 1997; French and Ladyman, 1998; Ladyman, 1998; French, 1999; French and Ladyman, 1999; Costa and French, 2000; Bueno et al., 2002; Costa and French, 2003; Ladyman, 2002). Furthermore, one can also find discussions of the topic in (Landry, 2007; Schindler, 2007; Morrison, 2008; Bailer-Jones, 2009; Le Bihan, 2012). It is because of this debate that my historical discussion will end with the work of the London brothers, since this chapter is based on, and an elaboration of, an article of mine (2019b), in which I discussed the use of this historical episode as a ‘historical case study’ within philosophy of science. 240 This view is not confined to this philosophical debate: one can equally well find it in some textbooks on superconductivity, such as Chandrasekhar (1969), (Tinkham, 1996, p. 2), (Kittel, 2005, p. 262). 241 For historical discussions of Kamerlingh Onnes’ work and his laboratory see (Gavroglu and Goudaroulis, 1989; Dahl, 1992; Reif-Acherman, 2004; van Delft and Kes, 2010; van Delft, 2014). His laboratory, which Jean Matricon and Georges Waysand describe as “the forerunner of the in- stitutions of big science” (2003, p. 18), was, until 1923, the only place on earth where the extremely low temperatures required for superconductivity could be reached (Matricon and Waysand, 2003, p. 47). 242 It was Michael Faraday who first succeeded in liquefying a gas, i.e. turning it into a liquid by compressing it. During his investigations, he stumbled upon a few gases that did not turn liquid, even though they were compressed enormously. These became known as the permanent gases, and it became a challenge for the scientific community to find ways to liquefy them. Helium was the last of the permanent gases to be liquefied, and it was Kamerlingh Onnes who first achieved this by lowering its temperature to almost zero Kelvin. Temperatures in this range afterwards became known as liquid helium temperatures (Matricon and Waysand, 2003, p. 2 – 23).

132 Experiment, Time and Theory

field. These currents were persistent currents, i.e. currents that can, in principle, continue to flow ad infinitum, without experiencing any resistance.243 This finding put him on a long program of determining both the different materials that could be made superconducting and the characteristic properties of this phenomenon.244 These investigations soon showed him that it was only when a magnetic field with a strength H below a temperature-dependent critical threshold HC was applied, that persistent currents could be induced; when H > HC , the superconducting state would be destroyed (see figure 3.1 on page 133).

Figure 3.1: The superconducting domain, characterized in terms of the two critical tresholds: the applied magnetic ﬁeld HC and the temperature TC . Figure source: (Tinkham, 1996, p. 4).

Because materials in this state could carry a finite current with zero resistance, it seemed natural to conceptualize them as Maxwellian perfect conductors, i.e. bodies that are governed by Maxwell’s equations with resistance zero (R = 0). More than twenty years earlier, in 1889, Gabriel Jonas Lippmann had already elaborated the electrodynamics for such a perfect conductor. Because of Kamerlingh Onnes’ success, Lippmann republished his account in his (1919) article. He approached the new phenomenon as follows: suppose we have a closed circuit, i.e. a conducting ring, with a finite resistance R that carries a current of intensity I, and which is surrounded by a magnetic field. Both the applied external magnetic field and the current’s self-induced magnetic field will, according to Maxwell’s equations, exert an electromotive force on the conductor, which Lippmann expressed as the number of magnetic field lines that crossed the conductor per unit time dt for each field: dn for the applied magnetic field, and dn0 for the self-induced field. Ohm’s law then entails, Lippmann continued, that the sum of these two electromotive forces (dn/dt+dn0/dt0) is equal to the product of the resistance and the current:245 RI = dn/dt + dn0/dt0

243 Michael Tinkham points out that, in reality, such currents have been observed to continue flowing “without measurable decrease for a year”, and that “under many circumstances we expect 10 absolutely no change in field or current to occur in times less than 1010 years” (1996, p. 2). 244 Kamerlingh Onnes’ scientific adagium was, not for nothing, “Door Meten tot Weten” (through measuring to knowledge) (Matricon and Waysand, 2003, p. 18). 245 Lippmann uses Ohm’s law here in its formulation IR = V , with V denoting the voltage, i.e.

133 Chapter 3. Experiment and Superconductivity

(Lippmann, 1919, p. 6). When certain materials are cooled below TC in the presence of a magnetic field HC , Kamerlingh Onnes had shown, according to Lippmann, that their resistance becomes zero: R = 0. In this case, Ohm’s law states that 0 = dn/dt + dn0/dt0, which entails that the sum of the variations in number of field lines (∆n + ∆n0) remains constant. This in turn implies that n+n0 also remains constant: the number of magnetic field lines that cross a superconductor remains the same (Lippmann, 1919, p. 6). As such, Lippmann argued, if the strength of the applied field were to change, i.e. if its number of magnetic field lines would in- or decrease, the strength of the superconductor’s persistent current would change in such a way that the magnetic field resulting from this change would exactly compensate the variation in the external applied field. The total number of magnetic field lines would therefore remain for ever constant:

When the number of force lines, due to the external ﬁeld, which cross the circuit undergoes a variation ∆n, the induced current that is the result of this will produce a variation ∆n0 which compensates exactly the ﬁrst. In other words, the total number of magnetic lines of force remains the same; and everything happens as if the superconducting circuit remains impenetrable for lines of force. This conclusion holds in particular for the experiments by Kamerlingh Onnes. (Lippmann, 1919, p. 6 – 7)246

This statement became known in the literature as Lippmann’s theorem. In later terminology, he had shown that when a material was rendered superconducting, its magnetic flux would remain forever equal to the field H0 applied before the transition, because the superconductor’s persistent currents would prevent it from changing in response to a changing applied magnetic field. The original applied magnetic field H0 was said to be frozen in (Gavroglu and Goudaroulis, 1989, p. 74).247

3.3 Kamerlingh Onnes and Tuyn’s Experiments

The experiments by Kamerlingh Onnes and Tuyn that will be the subject of what is to follow were presented by Willem Keesom at the Solvay Conference (1924).248 the difference in potential energy, between two points of the conductor. Another formulation of Ohm’s law states that the current density J, i.e. the amount of current per unit volume, is equal to the product of the electric field and the material’s conductivity σ, which is the opposite of the material’s resistivity (see footnote 233): J = σE. The current density of a conducting material in turn concerns the electric current flowing through a certain cross section area of the material at a given time. It is formed by the product of the velocities v of the charges present in that area, and the area’s charge density ρ, which denotes the amount of charge in that area: J = ρv. 246 The original French goes as follows: “[Q]uand le nombre des lignes de force dues au champ extérieuret qui traversent le circuit subit une variation ∆n, le courant induit qui en résulteproduit une variation ∆n0 qui compense exactement la première.En d’autres termes, le nombre total des lignes de force magnétiquedemeure invariable; et tout se passe comme si le circuit hyperconduc- teur demeurait infranchissable aux lignes de force. Cette conclusion s’applique en particulier aux expériencesde Kamerlingh Onnes”. 247 For a discussion of Lippmann’s work in the light of later work on superconductivity, see Essén and Fiolhais (2012). 248 The experiments were carried out by Kamerlingh Onnes and Tuyn, Kamerlingh Onnes was listed as the paper’s author, and it was Keesom who presented it at the 1924 Solvay conference,

134 Experiment, Time and Theory

They were carried out in the context of investigations of a hypothesis presented by Kamerlingh Onnes at the earlier 1921 Solvay conference. The hypothesis was that when materials are rendered superconducting by cooling below TC and after applying and removing HC , they would still display what he called a micro-residual resistance, i.e. a temperature-independent resistance of a metal in its purest state (1921, p. 167).249 To a ﬁrst approximation, the temperature-dependency of a material’s resistance could be expressed, according to Kamerlingh Onnes (1921, p. 167), in terms of the following equation, where α and φ are two constants, T denotes the material’s temperature and 273K is equal to 0◦C:

R T = α(T − φ) (3.1) R273K When one reaches the superconducting state, the temperature-dependent part of the resistance will go to zero, and the body will only display what Kamerlingh Onnes called its minimal resistance. This resistance could still be higher than the body’s microresidual resistance because of, for example, impurities or stresses. In his first attempts to obtain a value for the ratio of the microresidual resistance to a body’s temperature-dependent resistance, Kamerlingh Onnes had used cadmium. This material has a very low minimal resistance, and hence one could take this resistance value to be very close to its microresidual resistance. The resistance of superconducting cadmium, at liquid helium temperature, was measured by bringing about persistent currents on the material, in line with Lipp- mann’s theorem.250 The theorem entails that the application of a precise magnetic field allows one to bring about persistent currents with a precise strength I = V/R. Measuring the voltage V , which was done by a bismuth wire attached to the material, then provided one with the resistance. For cadmium, the minimal resistance, taken to be very close to the microresidual resistance, was measured to be 0.0005 times that of the resistance at 273K (Onnes, 1921, p. 168). Further investigations with improved accuracy and very pure samples of other materials (mercury, lead, and tin) allowed Kamerlingh Onnes to obtain an even much lower value that was very similar for the different materials (0.5 · 10−10), which he took to indicate that there was indeed such a thing as a superconducting material’s microresidual resistance (Onnes, 1921, p. 172). Kamerlingh Onnes and Tuyn embarked on their (1924) measurements because these earlier measurements were possibly not completely reliable. Theoretical and experimental considerations suggested that the persistent currents were perhaps not completely invariable over time, i.e. there was the possibility that their strength or direction had changed during the measurements. Before more accurate measurements of the microresidual resistance could be undertaken, the degree of invariability of the persistent currents thus first had to be established. To investigate this, Kamerlingh Onnes and Tuyn proceeded as follows: since “Onnes’ health was declining at the time” (Dahl, 1992, p. 107). 249 See (Dahl, 1992, p. 101 – 106) for a discussion of the presentations of Kamerlingh Onnes and others at the 1921 conference. 250 As Kamerlingh Onnes pointed out later in his presentation, it was common procedure at the time to use Lippmann’s theorem as the basis for experimental investigations of the properties of superconductors (1921, p. 178 – 179).

135 Chapter 3. Experiment and Superconductivity

With regards to the measurement methods that we have in mind, they make use of the persistent currents that one can establish in a superconductor by means of appropriate variations in the applied magnetic field, and they consist of the determination of the ponderomotive forces produced by the electrodynamical action of these currents among themselves, or by the action of a field on these currents. [. . . ] Indeed, if one makes use of a persistent current in a fixed conductor, one possesses a field that, all other circumstances remaining equal, will not vary except within the precision range with which one can render observable the invariability of the persistent current. (Onnes and Tuyn, 1924, p. 252)251

Kamerlingh Onnes and Tuyn would thus investigate whether the ponderomotive forces produced by the interaction between the persistent currents would change over time, which would indicate, in line with Lippmann’s theorem, that there was variation in the persistent currents induced. Ponderomotive forces are forces that put matter in motion, and Kamerlingh Onnes and Tuyn would thus investigate whether any variation could be observed in the motion of superconducting objects. They carried out these experiments, more specifically, with two different objects: one involving a leaden ring (see figure 3.2), the other a hollow leaden sphere (see figure 3.3). In both cases, the objects were suspended within a fixed leaden ring by means of a spring. Rotating the object by a specific angle with respect to its original position would then bring about a torsion in the spring, i.e. a mechanical energy proportional to the angle of rotation. After the objects were rendered superconducting, they would be rotated by a specific degree, which would bring the spring to exercise a force (a torque) counteracting both the torsion and the ponderomotive forces exercised by the persistent currents, in such a way that the object would remain in a stationary state with respect to its axis of rotation. If there were to be any variation in the persistent currents, this would give rise to changing magnetic fields, and hence to changes in the ponderomotive forces exerted on the superconductor. These would then manifest themselves in a change in the superconducting object’s angle of rotation with respect to its original position. The objects were rendered superconducting by placing them within a dewar 252 containing liquid helium, which had a temperature T < TC . A magnetic field H > HC was then applied, and its value was decreased until it was lower than the critical field value. In the case of the suspended ring this gave rise to a frozen in field and persistent currents, as was to be expected from Lippmann’s theorem (which conceptualized a superconductor as a closed conducting ring): “From the moment

251 With a fixed conductor, Kamerlingh Onnes and Tuyn here mean a superconductor that was suspended within their set-up. The original French goes as follows: “Quant aux méthodes de mesure que nous avons en vue, elles font usage des courants persistants qu’on peut établirdans les supraconducteurs àl’aide de changements appropriésd’un champ magnétique,et consistent dans la déterminationdes forces pondéromotricesproduites par l’action électrodynamique de ces courants entre eux, ou bien par l’action d’un champ sur ces courants. [. . . ] En effet, si l’on fait usage d’un courant persistant dans un conducteur fixe, on dispose d’un champ qui, toutes les autres circonstances restant les mêmes,ne varie que dans les limites de la précision avec laquelle on pourra mettre àl’épreuve l’invariabilitédu courant persistant”. 252 A dewar is “a double-walled glass container with a vacuum in the space between the walls”. Filled with liquid helium, these were used as insulators in order to maintain the very low temperature required for superconductivity (Matricon and Waysand, 2003, p. 15).

136 Experiment, Time and Theory

Figure 3.2: Frontal and top-down view of the first set-up, involving a leaden ring suspended within another leaden ring. The suspended leaden ring could rotate, as pictured on the top-down view. Figure source: (Onnes and Tuyn, 1924, p. 253). that we obtain the critical field value the distribution of the lines of force inside the rings does not change anymore, and the surfaces of the rings are covered with the current distribution required for this effect” (1924, p. 255).253 These persistent currents continued to increase until the applied field was lowered in such a way that it completely disappeared.254 The inner ring was then rotated by 30◦ with respect to the outer ring. Because this constituted a change in the direction of the currents, it would induce a change in their magnetic field, which, in turn, induced new persistent currents, in line with Lippmann’s theorem. Any change in the inner object’s position with respect to the outer ring, measured in terms of a change in angle, would then indicate a variability in the persistent currents. In the case of the leaden ring, only a very minimal variation was observed over 6 hours (Onnes and Tuyn, 1924, p. 255). The second experimental set-up, involving the hollow leaden sphere, was employed not only to measure the invariability of the currents, but also the invariability of their distribution, i.e. whether “the paths of persistent currents in a superconducting body, his ‘tubular filaments,’ are rigidly fixed in the body” (Dahl, 1992, p. 109).255 The reason for investigating this property derived from attempts at the

253 The original French goes as follows: “A partir du moment oùl’on atteint la valeur du champ seuil la distribution des lignes de force àl’interieur des anneaux ne varie plus, les surfaces des anneaux se couvrent chacune de la distribution de courant nécessaire àcet effet”. 254 The complete removal of the applied magnetic field was required in order to ensure that any change in the motion of the superconductor was indeed brought about by the persistent currents. 255 This hypothesis was first raised by Kamerlingh Onnes in his previous Solvay lecture (1921, p. 182). He introduced it there to account for the fact that the lengths of the free paths of the

137 Chapter 3. Experiment and Superconductivity

Figure 3.3: Frontal and top-down view of the second set-up, involving a hollow leaden sphere suspended within a leaden ring. The sphere could rotate, as pictured on the top-down view. Figure source: (Onnes and Tuyn, 1924, p. 253). time to formulate a theory of superconductivity, which all conceptualized the phenomenon of superconductivity in terms of free electrons, i.e. electrons not bound to any atoms. When the material was rendered superconducting, they would somehow be put in motion, hence giving rise to the observed currents. How to understand this mechanism of electrons being put in motion was one of the central theoretical questions raised by Kamerlingh Onnes in his previous Solvay lecture (1921, p. 186). The experiments on the sphere were thus carried out in order to obtain further insight into the precise paths of the free electrons constituting the persistent currents. The sphere was made superconducting by means of the same procedure as in the case of the ring. This gave rise to observations that were completely analogous to that case. When the sphere was rotated 30◦ with respect to the outer circle (see figure 3.3 on page 138), persistent currents would arise that would give the sphere a specific magnetic moment, i.e. a particular direction and strength of the magnetic field induced by the persistent currents with respect to the outer circle. As in the previous experiment, the torque exercised by the spring would counteract the torsion induced by the rotation and the ponderomotive forces exercised by the persistent currents. The aim was to observe whether there were any changes in the sphere’s position, which would indicate a change in the magnetic moment with respect to the suspension axis. In terms of Lippmann’s theorem, this would mean that there was variation in the persistent currents induced on the superconducting sphere, which would in turn suggest that the conduction electrons could change their direction, hence presenting an argument against the idea of tubular filaments. electron calculated from earlier measurements were far too long to be compatible with results obtained earlier.

138 Experiment, Time and Theory

Almost no variability was observed over the course of several hours, which meant that there was no change of the magnetic moment. This provided Kamerlingh Onnes and Tuyn both with evidence for the idea of tubular ﬁlaments and with more precise measurements of the microresidual resistance (1924, p. 257). Kamerlingh Onnes, Tuyn nor Keesom gave any theoretical interpretation of these results, since Hendrik Antoon Lorentz discussed them in detail in the overview of theoretical research on electric conduction that he presented at the same conference.

Lorentz’s Analysis: Perfect Conductivity and Frozen In Fields Lorentz showed, more specifically, how the behaviour of the superconducting sphere could be accounted for in terms of the electron-theory of conduction in metals.256 According to this conceptualization of conduction, which was first presented by Paul Drude (1900), the electrons responsible for the conduction of currents through a metal were to be studied as a gas, in the sense of the kinetic theory of gases: the electrons were conceived as particles that, through their free motion, were endowed with a certain kinetic energy that is carried over, through collisions, to the atoms constituting the metal. In this way, Drude’s account attempted to explain, in terms of the collissions of the electrons, the electric and thermal effects that arise when a current is conducted through a metal (Lorentz, 1924a, p. 1 –3).257 In the first part of his lecture, Lorentz presented and elaborated Drude’s theory, without going into too much detail about other proposals and contributions.258 The theoretical elaborations that Lorentz did mention, led him to the following summary of the consensus on the constitution of metals at the time:

Modern investigations leave little doubt about how the structure of a metal needs to be pictured. We conceive of the atoms as each composed of a central, positively charged nucleus and a number of electrons, which circulate around this core under the inﬂuence of the attractive force it exercises and of their mutual repulsion. The nuclei are arranged in a crystalline network and are maintained in their position by forces which manifest themselves in the rigidity and elasticity of the body. (Lorentz, 1924a, p. 15)259

256 It is stated in a footnote of Lorentz’s paper that part of his discussion, in casu his account of the experiments by Kamerlingh Onnes and Tuyn, was added after the presentation and the discussion (1924a, p. 40). Lorentz also presented the same results in another paper (1924b). Given, however, that his Solvay presentation (1924a) provides a more extensive discussion of the experiments within the context of his electron-theory, I have decided to follow the Solvay paper. 257 See (Hoddeson and Baym, 1980, p. 8 – 9), (Dahl, 1992, p. 25 – 27) and (Matricon and Waysand, 2003, p. 32 – 34) for discussions of Drude’s electron theory of metals. 258 For such a historical discussion of the development of the electron theory of metals until 1924, see (Hoddeson and Baym, 1980, p. 9 – 11). Lorentz’s elaboration of Drude’s theory was, as Matricon and Waysand point out, not completely successful, but no real improvements were made during this period: “Lorentz’s failure stopped most theoretical attempts to understand metals” (2003, p. 34). The problems with Lorentz’s theory will be discussed on page 143. 259 The original French goes as follows: “Les recherches modernes ne laissent guèrede doute sur l’image qu’on doit se former de la structure d’un métal.Nous considéronsles atomes comme composéschacun d’un noyau central positif et d’un nombre d’électronsqui circulent autour de ce noyau sous l’influence de l’attraction qu’il exerce et de leurs répulsionsmutuelles. Les noyaux seront arrangésdans un réseaucristallin et seront maintenus dans leurs positions par des forces qui se manifestent dans la rigiditéet l’élasticitédu corps”.

139 Chapter 3. Experiment and Superconductivity

On the basis of this conception,260 Lorentz then turned to a discussion of the motions of free electrons, i.e. those that are outside the crystalline structure.261 A current could be conceptualized, Lorentz claimed, in terms of the expression Nev, where N is the number of electrons, e their charge and v the mean velocity of the current. Its movement was taken to be governed by Ohm’s law (J = σE) (Lorentz, 1924b, p. 16 – 17). After elaborating how this conceptualization of the motion of electrons in metals could account for different conduction phenomena, Lorentz turned to a discussion of the influence of an external magnetic field H to a conductor carrying a current. 1 Such a field would exercise a force c [v · H] on an electron belonging to a current moving with a velocity v. This force would not only be an electromotive force, in the sense that it would influence the motion of the electrons in such a way that the Hall effect would arise (see footnote 42 of chapter 1). It would equally be a ponderomotive force influencing the body’s motion (Lorentz, 1924b, p. 35). By means of the example of a conducting sphere,262 Lorentz showed how these effects could be conceptualized. The force exercised by the field at a specific point on the sphere could be characterized in terms of three directions, h, k and n, where h and k point in the surface of the sphere, whereas n is the normal direction outside of the sphere, i.e. it is at right angles to the surface. The different components of this force exercised by H could then be expressed in terms of the following equations, where C denotes the current, the subscript 1 concerns the sphere’s interior and 2 its exterior:

1 1 H − H = − C ; H − H = C ; H − H = 0 (3.2) h1 h2 c k k1 k2 c h n1 n2 These equations thus expressed how the difference between the force exercised on the in- and outside of the sphere would influence the currents. This allowed Lorentz to compute the stresses on the in- and the outside of the sphere. These stresses on both sides of the sphere’s surface would give rise to a couple, i.e. two forces acting in opposite directions, which would put the sphere in rotational motion around its vertical axis. The sphere would not rotate, however, when the body’s total moment with respect to the axis of rotation would not change over time, a state which Lorentz called stationary (1924b, p. 35 – 36). Lorentz then asked what could bring about this stationary state, i.e. what could keep the conductor’s moment constant over time (Lorentz, 1924a, p. 36). In the case of an ordinary conductor, Lorentz argued by means of his electron theory, the answer was quite simple: the currents induced by the external field would themselves give rise to to a magnetic field that could ensure that the couple would be counteracted, in such a way that the stationary state could arise (1924a, p. 36 – 37).

260 In 1912, Max von Laue had shown by means of experiments involving x-rays that atomic nuclei form symmetric crystalline structures held together by certain forces, which could be conceptualized in terms of lattices with vector forces between their nodes (Eckert et al., 1992, p. 46 – 52). For an extensive discussion of the history of the physics of crystalline structures, see Eckert et al. (1992). See (Kittel, 2005, chapter 1, p. 1 – 22) for a fairly recent overview of the study of crystalline structures. 261 Those inside the atom, which were called bound electrons, were governed by quantum conditions, Lorentz pointed out, but since these did not play a role in electric conduction, he did not take them into consideration (1924a, p. 16). 262 For the moment, we are considering a normal conducting sphere, not a superconducting one.

140 Experiment, Time and Theory

Lorentz then investigated how this issue could be handled in the case of perfect conductors (i.e. conductors with resistance zero R = 0). How does the required magnetic field arise there in such a way that we arive at the stationary state? To calculate the complete magnetic field that arises in this case, he first made abstraction of the external magnetic field, which means equating 1/c[v·H] with zero. By means of Lippmann’s theorem, Lorentz argued that in that case, only a frozen in magnetic field Hn would be present. If we first apply a magnetic field (H < HC ) whose Hn = α, and then lower the temperature (T < TC ), the magnetic components Hn = α at different points on the sphere will remain, even if the applied magnetic field is removed, because the persistent currents will ensure that the original value of the applied field at each point, α, remains constant:

We apply an external field, of which the Hn-components have particular values α, and we leave the induced currents the time to fade out. If, afterwards, we make the resistance disappear by lowering the temperature, we will still have these values α, and they will maintain themselves when we remove the external field. A system of induced currents then arises in such a way that the magnetic force that belongs to it will, at each point of the surface, have exactly the normal component α. This suffices to determine the electricity’s circulation, which we can therefore designate with the symbol C(α). (Lorentz, 1924a, p. 37 – 38)263

This allowed Lorentz to calculate the total influence of an external magnetic field, either an applied field or a field induced by the motions of the electrons, that was required in order to bring about the stationary state. This showed him that if the electrons’ state of motion was conceptualized in terms of a distribution of free electrons moving completely freely, the net couple on the surface of the sphere would not be zero, and the stationary state would not arise. A superconductor, perceived as a perfect conductor, could only be in such a state if the electrons that constitute its current cannot not move freely, but only in particular rigid paths, i.e. tubular filaments. In this way, Lorentz argued, the electron-theory of conduction could account for the stationary state recently observed by Kamerlingh Onnes and Tuyn (Lorentz, 1924a, p. 43 – 44).

Manipulability and the Hollow Sphere Experiments As in the previous chapter, I will analyse the experiments discussed in terms of experimental inferences and their interpretations. The experimental inferences link the manipulation of an entity by means of an experimental set-up to the production of an eﬀect. As was the case with Kaufmann’s inference, the experimental inference discussed here – which characterizes the manipulations carried out by Kamerlingh Onnes and Tuyn – had to be interpreted, using a theoretical model of the entity manipulated, in order to obtain speciﬁc information about the properties of the

263 The original French goes as follows: “On applique un champ extérieurdans lequel les com- posantes Hn ont certaines valeurs α et on laisse aux courants induits le temps de s’éteindre. Si, ensuite, par un refroidissement, on fait disparaˆıtrela résistance, on aura toujours ces valeurs α, et elles se maintiendront quand on fera disparaˆıtrele champ extérieur.Il s’établiraalors un système de courants induits tel que la force magnétiquequi lui est propre aura, en chaque point de la surface, exactement la composante normale α. Cette condition suffit pour déterminerla circulation de l’électricité,que nous pouvons donc convenablement désignerpar le symbole C(α)”.

141 Chapter 3. Experiment and Superconductivity entity, which was the goal of the experiments. See the appendix A for a short overview of the different inferences and interpretations discussed in this chapter and the previous one, and how they are to be read. The materials studied by Kamerlingh Onnes and Tuyn were first brought into the superconducting state by lowering the temperature T below TC while applying a magnetic field H with a strength below HC . This gives us the entity studied, namely a material in the superconducting state (T < TC &H < HC ). This entity was then manipulated by varying the applied magnetic field (∆H), which Kamerlingh Onnes and Tuyn did by removing the original applied field and rotating the body. This manipulation would induce persistent currents I(∞) on the superconducting body. These currents allowed for the measurement of different properties which in turn could be taken to provide information about the magnetic flux B present in the superconducting body.264 This experimental procedure can be represented in terms of the following inference, where −→c denotes a causal link, −→i an inferential link, + an interaction and & the occuring together of different properties:

[Kamerlingh Onnes and Tuyn’s Experimental Inference]: c i (T < TC &H < HC ) + (∆H) −→ I(∞) −→ B

Kamerlingh Onnes and Tuyn were looking for changes in the position of the superconducting body with respect to the fixed outer ring, which would indicate that the ponderomotive forces exercised by the persistent currents would change over time. In this way, they could obtain insight into the variability of the strength and distribution of the currents, which, when combined with measurements of changes in their voltage by means of bismuth wires, could in turn inform them about the microresidual resistance. Neither the ring nor the sphere displayed any change in position over a long period of time, which was taken to mean that the strength and distribution of the persistent currents was invariable, and thus that their earlier measurements of the microresidual resistance could be taken as reliable. Their results were long taken, as we have seen in section 3.1, to indicate that all superconducting bodies would display frozen in fields. The reason for this was Lorentz’s account of the experiments in terms of his electron-theory of conduction. On this view, the stationary state observed by Kamerlingh Onnes and Tuyn had to be accounted for in terms of magnetic fields influencing the motion of the electrons constituting the currents in such a way that their total state of motion would give rise to such a state. The sources of these magnetic fields were the applied magnetic field and the magnetic field produced by the persistent currents. To be able to calculate the magnetic contribution of these currents, Lorentz conceptualized superconductors as perfect conductors (R = 0). In that case, Lippmann’s theorem entailed that any variation in the applied magnetic field (∆H) would induce changes in the persistent currents, in such a way that the magnetic field brought about by the motions of

264 And, as we have seen in footnote 250, it was common procedure at the time, according to Kamerlingh Onnes, to investigate the properties of superconducting bodies by measuring the induced currents. This is also shown by Matricon and Waysand, who claim that even experiments to measure the precise critical field treshold HC were carried out in this way: “[I]t was known that a sufficiently strong magnetic field could destroy superconductivity. This property was also observed by measuring the resistivity; no magnetic measurements were done” (Matricon and Waysand, 2003, p. 50).

142 Experiment, Time and Theory the electrons constituting these currents would compensate the variation: C(α ± ∆H). On the basis of this, Lorentz could then represent these currents in terms of his electron-theory as streams of currents (Nev) that could only move in rigid paths. Applying his electron-theory to the observations of Kamerlingh Onnes and Tuyn, which I represent with an inferential arrow with subscript I(∞), −−−→i , then I(∞) entailed that the magnetic flux inside the superconducting body was equal to the field applied before the superconducting transition: B = H0. As such, Lorentz offered the following perfect conductivity interpretation of Kamerlingh Onnes and Tuyn’s experimental inference:

[The Perfect Conductivity Interpretation]: c i i (R = 0) + (∆H) −→ C(α ± ∆H) −→ Nev −−−→ B = H0 I(∞)

Lippmann formulated his theorem, we have seen on page 133, for superconducting rings. Kamerlingh Onnes and Tuyn’s experiments on the leaden ring confirmed that in this case, there was indeed frozen in flux. Their experiments on the hollow sphere, which showed the same behaviour as the ring, suggested that such frozen in flux was also to be found in superconductors with other shapes. This suggestion was then reinforced by Lorentz’s analysis, since it showed that the behaviour of such superconductors could also be accounted for in terms of perfect conductors with frozen in fields. As such, frozen in fields became a general characteristic of all superconducting materials. In what follows, we will see how this generalization led the theoretical study of superconductivity in an impasse, and how Fritz London could proclaim that experiments had brought about a revolution, in the sense that they had shown how to overcome this impasse (see the quote on page 130).

3.4 Overturning the Classical Electron

As was already mentioned, Lorentz’s theory suffered some problems (see footnote 258), which led scientists to turn to the newly emerging quantum theory in order to elaborate an alternative electron-theory of conduction in metals. A first problem with the Lorentz-Drude electron-model of conduction in metals concerned the issue of the specific heats of metals.265 On the free-electron model, we have seen, there are free electrons moving around the atoms of the metal which can be conceptualized as a gas, in line with the kinetic theory of gases. According to this theory, both the electrons and the atoms should contribute to the material’s specific heat. Experimental determinations of the specific heats of different materials indicated, however, that these consisted solely of the part that, according to the free-electron model, was contributed by the atoms (Hoddeson and Baym, 1980, p. 9) (Matri- con and Waysand, 2003, p. 36). A second issue was that the theory could not explain magnetic properties such as diamagnetism, ferromagnetism and paramagnetism (Hoddeson and Baym, 1980, p. 11). Finally, while the Drude-Lorentz theory entailed the Wiedemann-Franz law, which states that “the thermal conductivity [K] divided by the electrical conductivity [σ] is proportional to the absolute temperature

265 A material’s speciﬁc heat is the amount of energy that is required to raise the temperature of a speciﬁc amount (per unit mass) of it with one degree (Matricon and Waysand, 2003, p. 35).

143 Chapter 3. Experiment and Superconductivity

[T ]” (K/σ = 3(k/e)2T , with e the charge and k the mean kinetic energy of electron) (Dahl, 1992, p. 26, 88), its computations of σ and K separately were not so adequate (Hoddeson et al., 1987, p. 288 – 289).266 For these reasons, scientists started looking for an alternative electron-theory of metals, several of which were already proposed before Kamerlingh Onnes and Tuyn’s (1924) experiments. Here, we will focus on the later proposals, which attempted to give an account of the conduction of electrons in metals in terms of the newly emerging quantum mechanics.267 The main reason for focusing on the quantum-theoretical developments is that, as Felix Bloch pointed out in the introduction of his (1928) article on the electron- theory of metals, the application of quantum theoretical principles allowed scientists to overcome most of these problems. The ﬁrst of these principles was Pauli’s exclusion principle, originally formulated by Wolfgang Pauli for the electrons that are bound to atoms in a metal (1925). It concerns the diﬀerent quantum numbers that specify the characteristics of particles such as the electron whose interactions are subject to quantum constraints, and which together make up such a particle’s quantum state. According to this principle, it is not possible to have two electrons with exactly the same quantum numbers bound to a particular atom:268

It is not possible to have two or more equivalent electrons in an atom, for which in strong ﬁelds the values of all the quantum numbers n, k1, k2, m1 (or, what comes down to the same, n, k1, m1, m2) correspond. If an electron is present in an atom, for which these quantumnumbers (in the external ﬁeld) have determinate values, then this state is ‘occupied’. (Pauli, 1925, p. 776)269

The second quantum-principle that played a central role, according to Bloch, was embodied in the use of Fermi-Dirac statistics.270 This form of quantum statistics was developed through the application of Pauli’s exclusion principle to the particles

266 The problem with these computations was that they involved two unknowns, namely the electron density and mean free path (Hoddeson et al., 1992, p. 91). 267 I am only giving a very schematic overview of these quantum-theoretical developments here, focusing on those elements that are of importance to the later story. For a more comprehensive overview, see e.g. (Darrigol, 1992; Cushing, 1994; Kragh, 1999; Massimi, 2005; Bacciagaluppi and Valentini, 2009; Seth, 2010). 268 For an extensive historical and philosophical discussion of Pauli’s principle, see Massimi (2005). Before Pauli’s formulation of the principle, electrons bound in an atom were characterized by the following quantum numbers: the energy state n, the orbital angular momentum k1 (with k2 denoting a relativistic correction), and the orientation with respect to a magnetic field m1. These quantum numbers could only take on integer values, and hence it was believed at the time that all quantum numbers had to be of integer values. Certain spectroscopic results, however, forced the introduction of a half-integer quantum number, i.e. spin m2 = ±1/2, which came to be interpreted, following work by George Uhlenbeck, Samuel Goudsmit and Pauli, as meaning that the electron has an intrinsic angular momentum which is either positive or negative. See Michela Massimi’s entry on Pauli’s Exclusion principle (2009, p. 220 – 222) and Klaus Hentschel’s entry on Spin (2009, p. 726 – 731) in the Compendium of Quantum physics for short overviews of these subjects, and chapter 8 of Arabatzis (2006) for the history of the electron’s spin. 269 The original German goes as follows: “Es kann niemals zwei oder mehrere äquivalente Elek- tronen im Atom geben, fürwelche in starken Feldern die Werte aller Quantenzahlen n, k1, k2, m1 (oder, was dasselbe ist, n, k1, m1, m2) übereinstimmen. Ist ein Elektron im Atom vorhanden, fürdas diese Quantenzahlen (im äußerenFelde) bestimmte Werte haben, so ist dieser Zustand ‘besetzt’.” 270 This form of statistics was one of the quantum-statistics available to compute the probabilities of particular quantum states arising for systems with many particles. The main difference

144 Experiment, Time and Theory that make up an ideal gas, first carried out by by Enrico Fermi (1926) and later elaborated by Paul Dirac for the case of the emission and absorption of radiation (1926).271 In contrast to classical Boltzmann statistics, which gives us the probability that an individual particle is in a particular state, Fermi-Dirac statistics gives us the probability of a particular distribution of a number of identical particles over different states (Hoddeson and Baym, 1980, p. 13). On the basis of this framework, Pauli (1927) first proposed a new conceptualization of paramagnetism as a particular state of magnetization. Sommerfeld (1927; 1928a; 1928b) used these two quantum-principles to elaborate both a theoretical mechanism accounting for the specific heats of different substances and a theory of the Wiedemann-Frantz law that offered a way to compute separately a substance’s thermal conductivity K and its electrical conductivity σ in a satisfactory way (Hod- deson and Baym, 1980, p. 16). And Werner Heisenberg (1928) showed how it could provide insight into ferromagnetism. We thus see how the new quantum formalism led to the resolution of many problems that plagued the classical Lorentz-Drude electron-theory.272 These successes indicated that a general electron-theory of metals also had to be formulated in quantum-mechanical terms. We will focus here on one particular proposal, namely Bloch’s electron-lattice theory of conduction in metals, which, as he himself pointed out, elaborated recent applications of the quantum-theoretical principles listed above to the electrons conceived as a gas (1928, p. 555). His aim was, more specifically, to investigate how the conductibility of a metal depended on the bonding strength (“Bindungsstärke”) of the electrons, i.e. in how far the electrons were to be seen as either bounded to the crystal lattice or free. In this way, Bloch attempted to find a middle way between Sommerfeld’s (1928a; 1928b) electron theory, which started from the assumption of electrons being able to move completely freely in and through the crystal lattices that constitute the metal, and Heisenberg’s (1928) electron theory, which conceived of them as completely bound to with classical statistics can be characterized as follows: suppose we have a system consisting of 2 particles with identical properties, a and b, and 2 energy states, s1 and s2, and we express e.g. particle a occupying state s1 as s1(a). Classical statistics assumes that the particles a and b, while identical, are still distinguishable, and hence it tells us that there are two different possible configurations of the system: (s1(a), s2(b)); (s1(b), s2(a)). Fermi-Dirac statistics, by contrast, drops the distinguishability-assumption, since Pauli’s exclusion principle tells us that we cannot have two identical but distinguishable particles. Hence, it provides us with only one possible configuration of the system: (s1(one particle), s2(one particle)). Particles that obey Fermi-Dirac statistics are called fermions. These particles have half-integral spin (see footnote 268). Those particles that do not have half-integral but rather integral spin obey the other form of quantum statistics, called Bose-Einstein statistics, and the systems governed by it, whose particles are called bosons, do not fall under the exclusion principle. Classical Boltzmann statistics forms an approximation of Fermi- Dirac and Bose-Einstein statistics, which holds in the high temperature region. For an intuitive illustration of how Fermi-Dirac statistics works and how it was applied in all kinds of work at the time, see (Matricon and Waysand, 2003, p. 36 – 42). See the entries in the Compendium of Quantum physics by Arianna Borelli on quantum statistics (2009, p. 611 – 612), on Bose-Einstein statistics (2009, p. 74 – 87) and on the Spin Statistics Theorem (2009, p. 733 – 736), and by Simon Saunders on Fermi-Dirac statistics (2009, p. 230 – 234), as well as (Hoddeson et al., 1992, p. 93 – 97) for more elaborate discussions. 271 For an English translation of Fermi’s paper, originally in Italian, see Zannoni (1999). 272 See Hoddeson et al. (1992) for an extensive historical overview of this work, especially concerning Sommerfeld’s role in what Carl Eckart later described as his big project “to rework the Lorentz theory of electrons using the Fermi statistics” (Hoddeson et al., 1992, p. 103).

145 Chapter 3. Experiment and Superconductivity the crystal lattices. He conceptualized this middle way, more speciﬁcally, as follows:

Here an intermediate position between the two approaches mentioned above will be taken, which, insofar as the interaction between electrons is not taken into consideration, conceives them not simply as freely moving, but rather as situated in a force-ﬁeld, which has the same periodicity as the lattice structure itself. On the basis of this assumption, it will be shown how and up until which degree the facts regarding free conduction electrons can be justiﬁed in quantum mechanical terms. (Bloch, 1928, p. 555 – 556)273

Bloch decided to ignore the interaction between the electrons in order to simplify the calculation of the bonding between an electron and the lattice. To an electron bound within the lattice, he ascribed a wave function Ψ, which was composed out of the periodicity of the crystal lattice and a momentum-like vector which he called the crystal wave vector (Hoddeson et al., 1992, p. 108). By plugging this wave function into the time-independent Schr¨odingerequation,274 Bloch could compute the wave function describing the probability amplitude of the electron’s energy. This showed him that besides the periodicity of the lattice, something else also had to contribute to the electron’s periodicity, which he took as evidence for the electrons being capable, at least in part, to move freely between the nodes of the crystal lattices:

The fact, that there is always a factor [. . . ] which is split off from the eigenfunctions [. . . ], where the rest now only denotes the periodicity of the lattice, can be clarified as follows, that we are dealing with flat de

273 The original German goes as follows: “Hier soll ein Zwischenstandpunkt zwischen den beiden oben erwähnten Behandlungsweisen eingenommen werden, insofern, als der Austausch der Elektronen unberücksichtigt bleibt, sie dagegen nicht einfach als frei beweglich, sondern in einem Kraftfeld gedacht werden, das dieselbe Periodizitäthat, wie der Gitteraufbau selbst. Auf dieser Annahme fußend, soll gezeigt werden, wie und bis zu welchem Grade sich die Tatsache freier Leitungselektronen quantenmechanisch rechtfertigen läßt”. 274 The Schrödingerequation, developed by Erwin Schrödingerin his work on wave mechanics, allows one to describe the evolution of a system that is subject to quantum constraints over time. Schrödingerdeveloped it in response to Louis de Broglie’s (1925) claim that matter displays wave properties. This entailed that its behaviour could be described in terms of a wave-function Ψ, where, as Helge Kragh puts it in his entry in the Compendium of Quantum Physics on the wave function, “[t]he wave function of a quantum system is the quantity that allows calculation of the various outcomes of an experiment or observation involving the system” (2009, p. 812). When we experiment on or observe a quantum system, we interact with it, which means that we change its wave function. This is represented formally by the application of an operator to the system’s wave-function, which then leads us to predictions for the possible outcomes of the measurement. If the result of this operation is a product of a real constant and a wave function, then this new wave function is called an eigenfunction of the operator, and the constant an eigenvalue. If this is the case, there is no uncertainty about the outcome of the measurement. If this is not the case, however, we do not achieve certainty: we rather end up with the probabilities for the measurement of different possible values of the observable characteristics of the system. What the Schrödinger equation now tells us, is how a system’s wave function evolves between measurements. See the entries in the Compendium of Quantum Physics by Leslie E. Ballentine on ‘States, Pure and Mixed, and their Representations’ (2009, p. 744 – 746), by Marianne Breinig on the Schrödingerequation (2009, p. 681 – 685) and on wave mechanics (2009, p. 822 – 827), and by Helge Kragh on the wave function (2009, p. 812 – 813) for a more extensive discussion.

146 Experiment, Time and Theory

Broglie-waves, which are modulated in the rhythm of the lattice structure. It is this similarity with the eigenfunctions of force free motions that gives the lattice electrons the freedom required for electrical conduction. (Bloch, 1928, p. 559)275

In the rest of his paper, Bloch then showed how this result provided a way to conceptualize electrons with different bonding strengths and their dynamics, and to study their contribution to the specific heats and conductivity of metals. In this way, Bloch provided a quantum-theoretical foundation for what was known at the time as Sommerfeld’s semi-classical electron-theory (Hoddeson et al., 1992, p. 109).276 Reflections on what his account entailed for the relation between a material’s resistivity, conductivity and temperature then indicated, as Bloch pointed out at the end of his paper, that there was one issue that he could not yet account for, namely superconductivity (Bloch, 1928, p. 600).

Quantum-theory and superconductors One attempt to formulate a quantum-theoretical account of superconductivity, which tried to incorporate the phenomenon into Bloch’s quantum-mechanical electron theory of conduction in metals, was the spontaneous current approach, elaborated by Bloch himself, together with Lev Landau and Yakov Frenkel.277 The central idea of this programme was that superconductors were analogous with ferromagnetic materials.278

275 What Bloch shows here is that electrons, as matter particles, display wave-like properties that can be described as de Broglie-waves. The original German goes as follows: “Die Tatsache, daß sich von den Eigenfunktionen [. . . ] stets ein Faktor [. . . ] abspalten läßt,wobei der Rest nur noch die Periodizitätdes Gitters aufweist, läßtsich anschaulich so formulieren, daß wir es mit ebenen de Broglie-wellen zu tun haben, die im Rhytmus des Gitteraufbaus moduliert sind. Diese Ahnlichkeit¨ mit dem Eigenfunktionen der kräftefreienBewegung ist es, die den Gitterelektronen die zur elektrischen Stromleitung notwendige Beweglichkeit gibt”. 276 Sommerfeld’s electron-model was taken to be semiclassical since, while it used Pauli’s exclusion principle and Fermi-Dirac statistics, it did not offer a fully quantum-mechanical treatment of electrons in metals. It rather used these principles to have the classical Drude-Lorentz electron model approximate the empirical results available at the time (Hoddeson et al., 1992, p. 104). As Friedrich Bopp puts it in his part of an overview article with Sommerfeld on fifty years of quantum theory: “The Fermi-Dirac statistics, already known in older quantum theory, is also based on the Pauli principle. Its application to conduction electrons in metals, which, in a first approximation, are treated as free particles, led Sommerfeld (1927; 1928a; 1928b) to a successful revival of P. Drude’s theory of conductivity” (Sommerfeld and Bopp, 1951, p. 91). 277 Besides the spontaneous current approach, there was also another programme, elaborated by Niels Bohr and Ralph de Laer Kronig, which was known as the electron lattice approach. This programme will not be discussed here, since it was the spontaneous current approach that, according to Fritz London, “seemed to be indicated by the facts”, but which in fact gave rise to what seemed as an “insoluble problem” (London, 1935, p. 25). For discussions of the electron lattice approach, see (Gavroglu and Goudaroulis, 1989, p. 75 – 77), (Dahl, 1992, p. 151 – 153), (Hoddeson et al., 1992, p. 146 – 150), (Leggett, 1995, p. 917), (Matricon and Waysand, 2003, p. 45 – 48) and (Schmalian, 2011, p. 45 – 48). 278 Ferromagnetic materials, as we have seen, are substances that have a far stronger magnetic susceptibility than those endowed with other states of magnetization, and can even, under some conditions, remain magnetized in the absence of an applied external field. See footnote 236 for a short overview of the differences between the different states. For historical overviews of the study of states of magnetization at the time, see (Hoddeson et al., 1992, p. 123 – 140) and Keith and Quédec (1992). Bloch, Landau and Frenkel had all worked earlier on the magnetic susceptibility of metals: Landau (1930) on diamagnetism, and Frenkel (1928) and Bloch (1929; 1930) on ferromagnetism.

147 Chapter 3. Experiment and Superconductivity

Heisenberg, as was already mentioned on page 145, had been able, through the use of quantum-theoretical principles, to overcome one of the issues of the Drude- Lorentz electron theory, namely that it could not account for the ferromagnetic properties of certain metals. One property of electrons, we have seen in footnote 268, is their spin, i.e. their intrinsic angular momentum, which is expressed in terms of a positive or negative half-integral quantum number. Heisenberg suggested that the magnetic moment responsible for a material being ferromagnetic was a consequence of the alignment of the spin vectors of all the electrons within the metal in the same direction, and that this alignment was brought about by what he called the exchange interaction (Hoddeson et al., 1992, p. 129 – 130).279 According to Bloch, however, there was a specific issue with Heisenberg’s treatment of the phenomenon: on Heisenberg’s view, all electrons were bound to the lattice, which entailed that it was in disagreement with most electron-theories of conduction in metals, which included the movement of free electrons within the crystal lattice (Bloch, 1929, p. 545). Bloch therefore proposed to reconceptualize Heisenberg’s account of ferromagnetism in terms of his own conduction-account, which, as we have seen, characterizes conductivity in terms of a gas of electrons whose periodicity is constituted by both a free wave and the periodicity of the crystal lattice (see the quote on page 146). Proceeding in this way led him to an account of ferromagnetism according to which “remanent magnetization [was] explained by recognizing that parallel orientation of the magnetic moments of atoms leads to a lower energy than random orientation”, as he put it in his recollections of this period (Bloch, 1966, p. 27). Because of the success of this approach in accounting for the characteristics of ferromagnetic materials, and because of the similarity of superconductors with ferromagnetic materials – in both cases, it was believed at the time, there was retention of magnetization below the critical temperature TC (superconductivity) or below the Curie point (ferromagnetism) after the removal of an applied magnetic field –,280 Bloch, Landau and Frenkel took it as their starting point for the conceptualization of superconductors.281 Bloch’s earlier work on conduction, we have seen, ignored the interactions between electrons (see the quote on page 146). If one wanted to account for the persistence of currents in superconductors, however, it would be necessary to take these into account, for extrapolating from the energy of a single electron would entail zero current (Sommerfeld and Bethe, 1967, p. 224). By means of these interactions, it was thought at the time, it would then be possible to “obtain a minimum of the free energy in a state of the metal with finite current”, which would allow for the persistence of currents (Bloch, 1980, p. 27). In analogy with ferromagnetism,

279 This exchange interaction, also called resonance, comes down to a transfer of energy from one electron to the other. See Simon Saunder’s entry on Fermi-Dirac Statistics in the Compendium of Quantum Physics for a short exposition (2009, p. 234). 280 The Curie point is “the temperature above which the spontaneous magnetization vanishes”, i.e. the point above which ferromagnetic materials are no longer magnetized after an applied ﬁeld has been removed (Kittel, 2005, p. 323). 281 Bloch never published his work on this theory (Hoddeson et al., 1992, p. 143). For the discussion, I will thus necessarily have to rely, in part, on secondary and later sources. Besides (Smith and Wilhelm, 1935, p. 260), (Dahl, 1992, p. 151), Leggett (1995), (Matricon and Waysand, 2003, p. 40 – 46) and Schmalian (2011), I have used those that Hoddeson, Baym and Eckert (1992, p. 178, note 380) mentioned in their discussion of the spontaneous current approach: (Brillouin, 1935; Sommerfeld and Bethe, 1967; Bloch, 1966, 1980).

148 Experiment, Time and Theory which was explained by the parallel orientation of the spin vectors of the electrons leading to a minimum state of energy, superconductivity was to be explained by the interactions between electrons leading to a similar minimum state of energy: “[t]he problem was [. . . ] the question whether it is possible, by means of such an interaction, to explain the existence of an energy minimum in the presence of current flow” (Bloch, 1966, p. 28). Bloch therefore set out to investigate different possible interactions, by checking whether the Schrödingerequation “would allow stationary states of the electrons with non-vanishing current and a minimum of the energy” (Bloch, 1980, p. 27).282 And while Bloch and others thought, at different moments, that this approach was on the right track, he never succeeded in obtaining a definite solution, which led him to formulate his famous impossibility-theorem:

I was so discouraged by my negative result that I saw no further way to progress and for a considerable time there was for me only the dubious satisfaction to see that others, without noticing it, kept on falling into the same trap. This brought me to the facetious statement that all theories of superconductivity can be disproved, later quoted in the more radical form of ‘Bloch’s theorem’: ‘Superconductivity is impossible’. (Bloch, 1980, p. 27)283

For each interaction bringing about a minimal energy state orientation of the electrons, Bloch found that the minimum energy state could bear no current. The reason for this was pointed out a few years later by Leon Brillouin in a presentation at the Royal Society (1935) on the issues plaguing the formulation of a theory of superconductivity.284 The first, general problem was that the conceptualization of the superconducting state that was common at the time, i.e. as a state of zero resistance reached by lowering the temperature, could in fact never be obtained. For, Brillouin argues, there are two sources of resistance in a material – thermic agitation disturbing the lattice, and impurities in the lattice –, and even at absolute zero, there would still be resistance as a consequence of the material’s impurities. As such, we should not expect to obtain a state of zero resistance just by lowering the temperature: “[f]or ordinary metals, the thermic effect disappears at zero temperature, while the impurity effect always persists, thus preventing the resistivity from falling to naught” (Brillouin, 1935, p. 19).285

282 A particle being in a stationary state means that it is in a quantum state with all observables being time-independent, i.e. remaining the same over time (Greenberger et al., 2009, p. 825). 283 It is in this more radical formulation, for example, that Fritz London presents Bloch’s theorem: “The present theoretical situation may be characterized in such a way that it is rigorously demonstrable that, on the basis of the recognized conceptions of the electron theory of metals, a theory of supraconductivity is impossible” (London, 1935, p. 24). A page later he then states the other, more moderate version. 284 This presentation was part of a symposium on superconductivity. Other participants included, amongst others, Walther Meissner, who presented his newest experimental results (discussed on pages 155 and 182), and Fritz London, whose contribution will be discussed on page 176. 285 Bloch himself acknowledged this point in his quantum-theory of conduction, which, as we have seen on page 146, conceptualized the free electrons as having a periodicity that was equal to the crystal lattices. Zero resistance could be obtained, on this view, if one had a strictly periodic lattice, but such lattices were not to be found in nature, since there would always be temperature- independent impurities: “[i]n nature, no strictly periodic lattices, i.e. perfect single crystals, are to be found, as is supposed here, yet the lattice defects and impurities will only show themselves in a small, temperature-independent residual resistance” (Bloch, 1928, p. 578) (“Nun kommen

149 Chapter 3. Experiment and Superconductivity

And even if this state of zero resistance was actually possible,286 Brillouin then argued, such a state could never be expected to be a minimum energy state carrying persistent currents:287 when a current I flows through a part of a metal, the metal’s energy will be E; applying a voltage, i.e. a potential difference P , to two ends of the conductor will then increase this energy, for a very short time dt, by an amount IP dt; however, Brillouin points out, the sign of the potential difference can always be changed, which means “that there is always a possibility of decreasing the total energy E, which cannot be a minimum” (Brillouin, 1935, p. 20) As such, on Bril- louin’s argument, there is no lowest energy stable state for the current, i.e. a minimal energy state in which the current can persist without any outside interference (which is what stability comes down to). The only way that this issue could be overcome from the point of view of what Brillouin called classical theories, was by taking the current to “not be stable but only metastable” (1935, p. 20). This would mean that, while in the lowest energy state, no current would be possible, there would somehow be a higher energy state where it would be possible (Leggett, 1995, p. 918; Schmalian, 2011, p. 48). The question was then, however, how such a current was to be conceptualized. Brillouin did not elaborate this idea further, since, as he himself pointed out, such metastable states seemed to be in conflict with experimental results. As such, it was unclear how superconductivity was to be conceptualized, and in this way, Bloch’s and Brillouin’s work led to a kind of impasse in superconductivity research, since it seemed to confirm Bloch’s impossibility-theorem:288

[A]gainst this conception [i.e. the spontaneous current approach] a general theorem of the theory of electrons was quoted, even by Bloch himself, according to which the most stable state of any mechanism of electrons for general reasons may very probably have no current, and, as Professor Brillouin has just shown us; this argument can essentially be reinforced. So Bloch concluded that any theory of superconductivity is refutable, and until now experience has always verified the theorem. (London, 1935, p. 25) zwar in der Natur niemals streng periodische Gitter, d. h. vollkommene Einkristalle vor, wie hier vorausgesetzt wurde, doch werden die Gitterstörungensich ähnlich wie Verunreinigungen nur in einem kleinen, temperaturunabhängigenRestwiderstand geltend machen”). 286 As Brillouin himself points out, such a state is, while very improbable, not completely impossible: “To avoid the temperature effect proved quite as difficult. I tried to imagine a very peculiar type of energy-momentum curve, which had electrons with high kinetic energies and low velocities but insensible to thermic agitation. The possibility of such unusual conditions was not actually proved: they appeared impossible in cubic or body-centered cubic lattices, but could perhaps be found in face-centred cubic or hexagonal crystals. This feature was rather satisfactory, on account of the fact that most of the supraconductors belong to these last two crystalline types” (1935, p. 20). 287 According to Brillouin, this assumption “was proved impossible by a very general reasoning of Bloch himself” (1935, p. 20). This reasoning is found in an appendix to Brillouin’s (1933) article, in which he sketches a discussion he had with Bloch about this topic. I have chosen to follow Brillouin’s (1935) formulation, because of its generality and simplicity. 288 Landau (1933) and Frenkel (1933) proposed elaborations and refinements of Bloch’s original approach. Given that Brillouin’s argument equally well targets their attempts, these will not be discussed here. For an overview of how they tried to improve on Bloch’s work, see e.g. (Smith and Wilhelm, 1935, p. 260), (Dahl, 1992, p. 151), (Hoddeson et al., 1992, p. 144 – 145) and (Matricon and Waysand, 2003, p. 44 – 45).

150 Experiment, Time and Theory

Manipulability, Superconductors and the Quantum

What the discussion in this section has shown, first of all, is that the quantum- reformulation of the electron-theory of conduction was very much a continuation of the classical approach. Just as Lorentz conceptualized conduction in terms of the motion of free electrons, Bloch’s quantum-theory also conceptualized it as possible only when the electrons were not completely bound to the lattice (see the quote on page 146 and Bloch’s evaluation of Heisenberg’s quantum-account of ferromagnetism, page 148). What Bloch accomplished in this way was a quantum-theoretical foundation for Lorentz’s theory of the electron, in line with Sommerfeld’s goal to revive the Drude-Lorentz theory in quantum-mechanical terms (see footnote 276). And this theory was very successful with respect to the different issues that plagued the classical theory of conductivity (see page 143). As such, we could expect that Bloch’s theory would equally well be successful in providing an account of superconductivity, given that Lorentz’s theory could successfully account, we have seen on page 143, for their frozen in fields. This meant searching for an interaction between the electrons that would allow for a minimum energy state in which the currents induced could persist after the applied field had been removed, in order to maintain the frozen in fields supposedly present, in line with Lippmann’s theorem and the ferromagnetic analogy. Hence, the search for such an interaction could be seen as a further investigation into how the causal mechanism responsible for the results produced by Kamerlingh Onnes and Tuyn could be conceived, since their experimental procedure both essentially relied on these persistent currents and could be seen as an indication that superconducting bodies of all shapes displayed frozen in fields maintained by these currents. What Bloch was thus looking for was how the electrons could bring about a superconducting state with frozen in fields. The problem, however, was that no such interaction could be found, and that it was probably impossible to find one, since Bloch and Brillouin had argued that the state in which a stable persistent current could arise could never be a minimal energy state. This was a problem, since it made it unclear how data such as those produced by Kamerlingh Onnes and Tuyn could have been produced, and how these data could be taken to provide information about the phenomenon of superconductivity conceptualized as perfect conductors displaying frozen in fields.289 Brillouin’s formulation of the impossibility-theorem already hints at what was responsible for the impasse, namely the fact that superconductors are conceptualized as perfect conductors, i.e. purely in terms of the electrons giving rise to a current. Even if perfectly pure materials displaying no temperature-independent resistance were to be found, Brillouin argued, these would not be able to carry persistent currents in their minimal energy state. As we will see now, doubts had already been raised about this conceptualization by the time Brillouin published his formulation

289 The electron lattice approach was not successful either, since “[t]he model that Bohr proposed was never published – Bloch had too many strong reservations” (Matricon and Waysand, 2003, p. 42). And while Kronig did publish his attempt to oﬀer a theoretical account in terms of the electron lattice approach, Bloch pointed out that these could not be successful either (Dahl, 1992, p. 153). The result of this was that “[n]either Kronig nor Bohr progressed further with electron lattice theories[, and that] [e]ven while making no substantial progress himself, Bloch through his role of critic emerged from the debate as the main authority of the time in the microscopic theory of superconductivity” (Hoddeson et al., 1992, p. 150).

151 Chapter 3. Experiment and Superconductivity of the theorem (1935), and an alternative was already in the making. This was not primarily a consequence of theoretical work on Bloch’s theorem, however, but rather of experimental work on the phenomenology of superconductivity.

3.5 Experiment and Superconducting Phenomena

That the development of a theory of superconductivity had reached an impasse does not mean that all research on the phenomenon came to a complete halt. In line with Kamerlingh Onnes’ adagium that through measurement, one could arrive at knowledge (’Door Meten tot Weten’, see footnote 244), measurements on the specific characteristics of superconducting materials did continue.290 In what follows we will discuss a whole list of experiments: Meissner and Ochsenfeld’s (1933) experiments on a superconductor’s magnetic field distribution, and the replications of these by Kurt Mendelssohn and J.D. Babbitt (1934; 1935) and by G.N. Rjabinin and Lew Schubnikow (1934); Wander de Haas and Josina Casimir-Jonker’s (1934) experiments on the influence of the applied magnetic field’s direction on the transition to and from the superconducting state; experiments by de Haas, J. Voogd and Casimir-Jonker (1934) on the influence of applied magnetic fields to a superconductor’s resistance; and Willem Keesom and Johannes Kok’s experiments on the specific heats of tin and thallium at the superconducting transition temperature. Their importance lies in the fact that they served as the inspiration for two new phenomenological accounts of superconductivity:291 Gorter and Casimir’s thermodynamical account (1934) and the Londons’ electromagnetic account (1935a). In this way, we will arrive at a better understanding of how these new phenomenological accounts brought Fritz London to proclaim a revolution in the study of superconductivity (see the quote with which we opened this chapter, page 130).

Meissner and Ochsenfeld’s Experiments

When, above TC , a magnetic field is applied to a material that can be rendered superconducting, Walther Meissner and Robert Ochsenfeld start their (1933) paper, the magnetic field lines will penetrate the material, given that it has a very low magnetic susceptibility χ (see footnote 232). According to previous views, they continue, we would expect the magnetic field lines to remain the same when the temperature was then lowered beneath TC : the magnetic field lines should remain frozen in. Their experiments on lead and tin, however, suggested that this was not necessarily the case (Meissner and Ochsenfeld, 1933, p. 787). Meissner and Ochsenfeld made use of two different experimental set-ups. The first involved two parallel cylindrical superconductors, sometimes made out of lead, sometimes out of tin, between which they placed a search coil parallel to the axes of the cylinder. This search coil could be rotated, which would induce a change in the applied magnetic field (see figure 3.4). The search coil was connected to a ballistic

290 These experiments were no longer carried out solely in Leiden. By the end of the 1920s, low-temperature laboratories had opened in Toronto, Berlin, Kharkov, Berkely and Washington (Matricon and Waysand, 2003, p. 47). 291 A phenomenological investigation, as Daniela Monaldi puts it, is “one that describes the observed phenomena without attempting to explain them or derive them from microscopic mechanisms” (2017, p. 39).

152 Experiment, Time and Theory

Figure 3.4: The set-up of the first kind of experiments carried out by Meissner and Ochsenfeld, which involved two cylinders a1 and a2 (both made of either lead or tin), with a measurement coil b placed in between them. Figure source: (Meissner and Heidenreich, 1936, p. 451). galvanometer, which allowed them to measure precisely the change in magnetic flux B between the two cylinders induced by changes in the applied magnetic field as a consequence of the motion of the coil. At room temperature (T > TC ), they would first apply an external magnetic field (below HC ) to the cylinders, and carry out a first measurement of the magnetic flux B. In line with the procedure sketched in the previous paragraph, they would then lower the temperature below TC , hence rendering the body superconducting. They measured the magnetic flux again, and calculated the ratio of the magnetic flux before and after the transition, in order to obtain insight into whether it changed during the transition. This value was then compared with the ratio provided by Max von Laue and Friedrich Möglich’s (1933) theoretical study of the magnetic field surrounding Maxwellian perfect conductors, which suggested that after the transition, the cylinders’ magnetic permeability was close to zero:

On cooling below the transition temperature the ﬁeld-line pattern in the region outside the superconductor changes almost to that which would be expected if the permeability of the superconductor was zero, or the diamagnetic susceptibility was −1/(4π). (Meissner and Ochsenfeld, 1933, p. 788; Forrest, 1983, p. 118)292

That the material’s permeability seemed to reduce to zero was observed in terms of an increase of magnetic ﬁeld lines around the exterior of the cylinder’s surfaces (see ﬁgure 3.5). In the second experiment, Meissner and Ochsenfeld applied the same procedure to a cylindrical leaden tube, with a hollow interior in which they placed the search

292 As we have seen in footnote 232, magnetic ﬂux is described by the following equation: B = H + 4πM, with M = χH and B = µH. Expressing this equation purely in terms of the applied ﬁeld H gives us µH = H + 4πχH. When we would have a permeability µ of zero, as Meissner and Ochsenfeld claim, then we would have 0 = H + 4πχH, or −(1/4π)H = χH. Hence, permeability zero is equal to a susceptibility χ = −1/4π. I will make use of Allister Forrest’s (1983) translation of Meissner and Ochsenfeld’s original paper. As in the previous chapter, I will provide the pages of both the original and the translation.

153 Chapter 3. Experiment and Superconductivity

Figure 3.5: Graphical depiction of the difference in internal magnetic flux between the non- superconducting and the superconducting state, in the case when first a magnetic field is applied, and then the temperature is lowered. Figure source: (Meissner and Heidenreich, 1936, p. 455)

coil. After applying a magnetic field (H < HC ) and then lowering the temperature (T < TC ), the coil indicated a very small increase in magnetic flux at the inside of the cylinder, while the field variation on the outside was as in the previous experiment, i.e. as if the material’s permeability was zero. When the applied field was turned off while the material remained in the superconducting state, the field at the inside remained the same, while there was some remaining field strength on the outside: most of the applied field had thus disappeared. Finally, if they proceeded in the reverse order – i.e. first cooling and then applying the magnetic field – the field strength at the inside would be zero, while on the outside we would again have a field variation as if the body’s permeability was zero. Meissner and Ochsenfeld did not give any real interpretation of these results, besides a short hint in their final paragraph to some kind of analogy with ferromagnetism. The main reason for abstaining from such an interpretation, it seems, was that it was completely unclear how the results of the two experiments together could be reconciled into one macroscopic representation in terms of a superconductor’s permeability:

The representation of the results in terms of a statement about the changes in the macroscopically defined permeability perhaps gives rise to difficulties concerning the processes inside the lead cylinder since possibly no unique connection any longer exists between the induction [i.e. flux density B] and the field strength. (Meissner and Ochsenfeld, 1933, p. 788; Forrest, 1983, p. 119 – 120)

The problem was that the magnetic permeability differed between the two experiments, contrary to what one would expect. In the parallel cylinders-experiment, the permeability seemed to reduce to zero, since a change in the external field, in the sense of an increase in field lines, was measured. This suggested that in this case, the magnetic flux was expelled from the superconductor and reduced to zero. This was not observed, however, in the hollow cylinder-experiments. If the magnetic field was really completely expelled, one would expect an increase in the magnetic field lines both in the hollow of the cylinder and on the outside. Instead, it was observed that the field in the hollow remained practically the same. This rendered it unclear how the magnetic behaviour of the two experiments could be captured in terms of one description of the superconducting state. This issue, of how to interpret the different results together, plagued not only Meissner and Ochsenfeld. Gorter as well raised it in a letter to Meissner. Unfor- tunately, Meissner replied, he could not provide more insight into the issue, since

154 Experiment, Time and Theory

Ochsenfeld had just left and he did not have the required materials for new experiments yet.293 The only thing he could remark was that it seemed implausible to him that his experiments indicated that in general, after transition to the superconducting state, a material’s flux density would reduce to zero, as Gorter had suggested (we will come back to this suggestion on page 170). Meissner took his experiments rather to point, again, in the direction of an analogy with ferromagnetism: “For now I must question the general assumption B = 0; perhaps conditions similar to those of ferromagnetism are involved here, where again no clear connection exists between field strength and induction” (Dahl, 1992, p. 187).294 In his (1935) presentation to the Royal Society (see footnote 284), Meissner described the results of his earlier experiments with Ochsenfeld as follows: “only for a solid cylinder (i.e., without interior holes) of pure metal cooled in a magnetic field can one say that it behaves as if its permeability is reduced to zero when it becomes supraconducting” (1935, p. 13). The experiment with the hollow lead cylinder, on the other hand, indicated that in general, the phenomenon was more complicated. This was confirmed, he continued, by further experiments by Heidenreich (see footnote 293) on the magnetic field in- and outside a hollow tin tube. These experiments showed, more specifically, that for both the tin and the lead cylinder, there is a remaining magnetic field outside the object after rendering it superconducting by applying a magnetic field, cooling it down and then removing the applied field (Meissner, 1935, p. 14 – 15).

Replications: Mendelssohn and Babbitt The main characteristics of Meiss- ner and Ochsenfeld’s original (1933) article, according to Dahl, were “its extreme brevity, seeming contradictions, and obvious importance” (1992, p. 182). Because of this, other physicists soon set out to replicate the experiments, which did not immediately lead to more clarity, however. A first attempt was carried out by Kurt Mendelssohn and J.D. Babbitt, who started their first paper on their replications by pointing out that until recently, it was believed “that it was possible to predict, by the ordinary electromagnetic equations, the persistent current produced in a supraconductor cooled below the transition point in a constant external magnetic field after the field was switched off” (Mendelssohn and Babbitt, 1934, p. 459). An example of such an approach, according to Mendelssohn and Babbitt, could be found in Lorentz’s (1924b) article on Kamerlingh Onnes and Tuyn’s hollow sphere-experiment, where he “calculated the current induced in a supraconducting sphere, that is, the effective magnetic dipole when an external magnetic field is established” (Mendelssohn and Babbitt, 1934, p. 459). According to Mendelssohn and Babbitt, however, Meissner and Ochsenfeld’s experiments indicated that this

293 After the ﬁrst series of measurements, Ochsenfeld was replaced by F. Heidenreich, since Ochsenfeld left Berlin, where the experiments were carried out, for a teaching position in Potsdam. In fact, Meissner himself also left Berlin soon after, for an academic position in Munich, leaving Heidenreich to carry out the measurements by himself (Dahl, 1992, p. 195). The results of these later experiments are published in (Meissner, 1935; Meissner and Heidenreich, 1936). 294 Meissner had already formulated a similar reply earlier to the same question, regarding the interpretation of his measurement of zero permeability, in a letter to John McLennan (Dahl, 1992, p. 182). And Kurt Mendelssohn and J. D. Babbitt, in their (1935) paper on their replications of Meissner and Ochsenfeld’s experiments, also state that the result of the second experiment “appears to us not entirely in accordance with the assumption that the induction in the whole body became zero” (1935, p. 316).

155 Chapter 3. Experiment and Superconductivity calculation might not be so simple as expected.

Figure 3.6: The experimental set-up employed by Mendelssohn and Babbitt in their attempts to replicate Meissner and Ochsenfeld’s (1933) experiments, here with a solid tin sphere. Figure source: (Mendelssohn and Babbitt, 1935, p. 317).

Meissner and Ochsenfeld’s experiments suggested, more specifically, that instead of the magnetic field being frozen in, there was an increase in magnetic field lines surrounding the superconducting body, which in turn suggested that the body behaved as if it had a magnetic permeability of zero. This would mean that “the flux of induction [B] in the superconductor should be zero and one might expect, in contradistinction to the old view, that no persistent current or effective induced dipole would be produced by switching off the external field” (Mendelssohn and Babbitt, 1934, p. 459). In order to acquire more insight into this issue, Mendelssohn and Babbitt investigated whether there were any differences in the magnetic field surrounding the body depending on whether the superconducting state was reached by first cooling down, and then applying a magnetic field, or vice versa. They carried out these measurements on two objects: a solid tin sphere and a hollow tin sphere. They conceived their measurement set-up (see figure 3.6) in such a way that “[t]he moment of any residual induced dipole was measured with a test coil” (Mendelssohn and Babbitt, 1935, p. 317). This would allow them to investigate experimentally whether superconducting bodies behave as Meissner and Ochsenfeld had observed, in which case we would expect no residual magnetic moment, or as Lorentz’s account told us, according to which the body should be a magnetic dipole at the end of the experiments. When they first applied a magnetic field and then lowered the temperature, their measurements indicated that there was a difference between the two objects: the exterior magnetic field distributions measured were two to three times bigger for the superconducting hollow sphere than for the solid sphere. These results were, however, in accordance with neither of the two views: “[t]he following experiments seem to show that although superconductors do not conform

156 Experiment, Time and Theory to the older theory, neither do they behave as though they had zero permeability” (Mendelssohn and Babbitt, 1934, p. 459). And the same result, Mendelssohn and Babbitt point out in their more elaborate (1935) paper, was obtained when they proceeded in the opposite direction, i.e. by first cooling and then applying a magnetic field (1935, p. 319). They summarized their findings as follows:

The experiments both with constant external field and at a constant temperature completely confirm the results of the preliminary [Mendelssohn and Babbitt (1934)] experiments. When the specimen is cooled in an external field below its threshold value, lines of force are pressed out and the induction decreases; but part of the flux remains in the specimen and this residual flux is greater for the hollow sphere than for the solid sphere. If we could place a perfectly diamagnetic sphere, i.e., one for which the induction is zero in a homogeneous field, then the intensity of the distorted field at the equator of the sphere would be 50% greater than the original homogeneous field. Now for the solid supraconducting sphere the field at the equator was only 18% above the external field, and for the hollow sphere only 10%. The control experiments on the other hand showed that under special circumstances a supraconducting sphere can behave as if it were perfectly diamagnetic. Indeed, a field excess at the equator of about 50% can be obtained, when the sphere has been cooled to supraconductivity in zero field, if an external field, never greater than the threshold value, is applied. (Mendelssohn and Babbitt, 1935, p. 329)

Replications: Rjabinin and Schubnikow G.N. Rjabinin and Lew Schubnikow also carried out measurements that were later taken as attempts to replicate Meiss- ner and Ochsenfeld’s (1933) experiments.295 In their paper, they start by pointing out that, until recently, it was assumed that the magnetic state of a superconductor could be calculated in terms of the Maxwell equations with inﬁnite conductivity (i.e. zero resistance). Recent unnamed experiments in Leiden on tin now provided good agreement, according to Rjabinin and Schubnikow, with work by Gorter (1933) on the thermodynamics of superconductors, which was based on the assumption that the superconducting and the non-superconducting state formed phases, in the thermodynamic sense, which could be diﬀerentiated in terms of their magnetic permeability:296 µ = 0 in the superconducting phase, µ = 1 in the non-superconducting

295 Rjabinin and Schubnikow themselves do not refer explicitly to Meissner and Ochsenfeld: they rather mention Gorter’s thermodynamic work (to be discussed later, see page 170). It were mostly others that saw these experiments as replications of Meissner and Ochsenfeld’s experiments. Fritz and Heinz London, for example, list them in a footnote concerning what they call “Meissner’s experiment” (1935a). And Fritz London also lists these experiments in a footnote concerning “an experiment that was first carried out by Meissner and Ochsenfeld, and which was repeated afterwards by different researchers” (London, 1937b, p. 10) (“une expériencequi fut d’abord réalisée par Meissner et Ochsenfeld, et répetéeensuite par plusieurs chercheurs”). 296 A thermodynamical phase is delineated by the stability of certain thermodynamical properties of a system. The most well-known phases are states of matter such as a system being a liquid, a gas or a solid. A change of phase occurs because of a change in properties external to the system: a liquid such as water, for example, can become solid because of a change in the temperature. What is significant about such a change of phase is that it is characterized by discontinuities in the specific thermodynamical properties whose stability makes up the state. Whereas the

157 Chapter 3. Experiment and Superconductivity phase (Rjabinin and Schubnikow, 1934, p. 286). This raised the question whether experiment would indicate that there are indeed two different phases, which would problematize the Maxwellian conception of superconductivity as a limiting case of ordinary conductivity. Gorter’s thermodynamical work was motivated in particular by two results: experimental measurements by Wander de Haas and J. Voogd (1931b) on the influence of the strength of the applied magnetic field on the disappearance of the superconducting state, “in which the extreme sharpness was demonstrated of the transitions, which occur if the temperature or the magnetic field [. . . ] is varied” (Gorter, 1933, p. 378); and the theoretical elaboration by Arend Joan Rutgers, which was published in the appendix of a paper by Paul Ehrenfest on thermodynamical phase transitions (1933), of an expression connecting the specific heat change during the superconducting transition with the critical magnetic field. What Gorter showed was that Rutger’s equation could be used to account for the results obtained by de Haas and Voogd, if one conceptualized the superconducting transition as a thermodynamical change of phase. On Gorter’s view, the state of a body in the superconducting phase was to be described in terms of three properties: the temperature T , the applied external magnetic field H and the body’s flux density B. Characterizing the phase in this way then provided Gorter with expressions for the first and second law of thermodynamics in terms of changes in the body’s specific heat, on the assumption that the transition between the superconducting and non-superconducting phase was conceptualized as a cycle (see figure 3.7): cooling under a constantly applied field (A → B); applying a magnetic field with a value a bit lower than the critical field value HC (B → C); increasing the temperature (C → D); and removing the applied field (D → A). One particular consequence of this thermodynamical treatment of superconductors, Gorter pointed out in his conclusion, was “that it is possible to describe the energetic phenomena connected with the persisting currents by assuming the existence of a susceptibility χ = −1/4πd if we have not to do with rings” (1933, p. 386), with d the density of the metal. Rjabinin and Schubnikow now decided to investigate experimentally “whether, indeed, two phases exist” (1934, p. 286). This would manifest itself in discontinuities during the superconducting transition in the properties whose stability, according to Gorter, made up the superconducting phase: the temperature, the applied field and the flux density. For this, they carried out two kinds of measurements: one on the change in a superconducting leaden rod’s flux density B with respect to sudden increases in the applied field H from H = 0 to H > HC ; and one on the magnetic flux density B within the spool that was used to apply the magnetic field H to the leaden rod, after the rod had been removed very quickly. On the Maxwellian conception of superconductors, they pointed out, one would expect B to remain the same (i.e. frozen in and equal to the field H0 applied before transition) until the critical threshold HC was reached, after which it would become equal to the applied field: B = H = HC (this characterization of the magnetic state of superconductors is depicted by the thick black line on figure 3.8). electrodynamical conception of superconductors sees the superconducting state as a limit case, and hence as continuous with, the normal conducting state, the thermodynamical conception entails that there is a discontinuity between the superconducting and the non-superconducting phase (Matricon and Waysand, 2003, p. 44; 48 – 49).

158 Experiment, Time and Theory

Figure 3.7: Gorter’s conceptualization of the superconducting transition as a thermodynamical cycle. Figure source: (Gorter, 1933, p. 380).

What their measurements showed, however, was that while at the critical threshold B would indeed become equal to HC , it was not the case that the magnetic flux remained equal in the superconducting body with increases in H below HC . Rather, they found that the flux would vary with sudden in- or decreases of the applied magnetic field (see the thin lines on figure 3.8). From the Maxwellian point of view this would seem strange, since on this view we would expect changes in the applied field to induce persistent currents that would compensate these changes in such a way that the magnetic flux would remain the same. As such, Rjabinin and Schubnikow concluded, their results provided evidence against the Maxwellian conception and in favour of Gorter’s thermodynamical conception:

Our experiments show that in the vicinity of [HC ] a sudden change occurs in B with increasing as well as decreasing field strength. These results do not agree with the former concept of a supraconductor, in which, when the field-strength is decreased, the induction should be maintained constant by means of induced persistent currents. The actual fact that a jump takes place in the induction in falling field strengths we are inclined to ascribe to the formation of a new phase B = 0. (Rjabinin and Schubnikow, 1934, p. 287)

De Haas and Casimir-Jonker’s Experiments As Meissner, Ochsenfeld and others discussed above had done, Wander de Haas and Josina Casimir-Jonker (1934) also investigated possible changes in the state of magnetization of a body during the superconducting transition through measurements of the magnetic field distribution. In contrast with the earlier experiments, however, their concern was not with the magnetic field distribution outside the superconducting body, but rather with the distribution on the inside. To measure this, de Haas and Casimir-Jonker inserted three bismuth wires into glass capillaries within a rod of white tin. All three capillaries would be parallel to the axis of the rod, and one of them would be in the rod’s center (see figure 3.9). They used bismuth wires, since their resistance offered a good instrument to measure the variation of the magnetic field:

159 Chapter 3. Experiment and Superconductivity

Figure 3.8: Rjabinin’s and Schubnikow’s depiction of how their obtained results (thin lines) compared with those expected on the basis of the perfect conductivity-conception (thick lines). The dotted line depicts the results obtained in their measurements on the leaden rod, while the full thin line depicts their measurements on the spool. Figure source: (Rjabinin and Schubnikow, 1934, p. 286).

It is known that, at liquid helium temperatures, bismuth shows a considerable change in resistance within a magnetic field; this property can be used to determine small field changes: from an observed change in resistance one can infer a corresponding change in field. (de Haas and Casimir-Jonker, 1934, p. 291)297

Figure 3.9: A cross-section of the white tin rod employed by de Haas and Casimir-Jonker, with the three bismuth wires (I, II, III) going in the direction of the page. Figure source: (de Haas and Casimir-Jonker, 1934, p. 292).

They would measure the resistance of bismuth wires at two diﬀerent temperatures: at 3.83K, which is a bit above TC for tin, and at 3.48K, which is just below TC . For both temperatures, they would then apply a magnetic ﬁeld H < HC with

297 Wismuth is an old name for bismuth. The original German goes as follows: “Bekanntlich zeigt Wismuth bei der Temperatur des flüssigenHeliums eine beträchtliche Widerstandsänderung im Magnetfeld; diese Eigenschaft kan man ausnützenum kleine Feldänderungenfestzustellen: aus einer beobachteten Widerstandsänderungkann man auf eine eintsprechende Feldänderung schliessen”.

160 Experiment, Time and Theory a direction perpendicular to the orientation of the wires (see figure 3.9). In the case of the measurements above TC , applying the magnetic field would not give rise to the superconducting state (these measurements are indicated by the dotted line on figure 3.10). They would then increase the magnetic field until it surpassed HC . Comparing the resistances measured during these two runs would then provide them with insight into how the material’s magnetic flux B changed during the transition from the superconducting to the non-superconducting state.

Figure 3.10: De Haas and Casimir-Jonker’s measurements of the resistance variation of bismuth. The dotted line gives the curve of their measurements of the resistance variation for T = 3.83K > TC . The other curves give the resistance variation of the three bismuth wires during a tin rod’s transition from the superconducting to the non-superconducting state. Figure source: (de Haas and Casimir-Jonker, 1934, p. 293).

These measurements showed three things, according to de Haas and Casimir- Jonker (see figure 3.10): first, up until a particular value, the resistance does not change at all; second, this value is higher for the wire in the middle of the rod; and third, the plotted curve of the resistance in the superconducting case differed significantly from the curve obtained in the case of a temperature just above TC (de Haas and Casimir-Jonker, 1934, p. 294). This indicated, according to de Haas and Casimir-Jonker, that, up until a specific value, the application of an external magnetic field gave rise to persistent currents that compensated the change in magnetic field in the interior of the superconductor, in such a way that no changes in the resistance were to be measured. When this magnetic field value was surpassed, however, the superconducting state would be destroyed, which entailed the disappearance of the persistent currents and the penetration of the magnetic field, giving rise to a strong resistance change. De Haas and Casimir-Jonker also carried out a

161 Chapter 3. Experiment and Superconductivity few measurements with the magnetic field parallel to the direction of the bismuth wires, which led to the same results as for a perpendicular field. At the end of their paper de Haas and Casimir-Jonker stated that the recent paper by Meissner and Ochsenfeld also prompted them to observe what happened when the material was not made superconducting by first cooling and then applying the magnetic field, but rather by first applying the magnetic field and then cooling. This suggested to them that there could indeed be a magnetic permeability zero in this case, although it primarily indicated that more measurements needed to be made:

Finally we have carried out some observations, during which the tin rod was cooled in a constant field. It seems to be the case, that in the surroundings of the outer bismuth-wires the field disappears out of the superconductor. For the middle wire, on the other hand, we found an increase of the field at the transition-point. Qualitatively, these findings are in accordance with the measurements of Meissner and Ochsenfeld (1933). These observations could indicate that the disappearance of the magnetic field out of a superconductor forms a complicated phenomenon; however, in general the measurements are not yet reliable enough. (de Haas and Casimir-Jonker, 1934, p. 296)298

De Haas, Voogd and Casimir-Jonker The third series of experiments on the list, by de Haas, Voogd and Casimir-Jonker (1934), concerned the influence of the direction of the applied magnetic field on the resistance for different temperatures. These were elaborations of earlier experiments by de Haas and Voogd (1931a), which concerned the magnetic behaviour of superconductors during the transition of a metal wire from the superconducting to the non-superconducting state.299. What prompted them to return to these experiments was an article by von Laue (1932), who attempted to provide a theoretical account of these results obtained earlier. These earlier experiments were generally taken to show two things. First, they showed that the superconducting transition displays hysteresis, which means here that the value of the applied magnetic field for which the resistance disappears is lower than the magnetic field value for which it reappears (de Haas and Voogd, 1931a, p. 63). De Haas and Voogd took this to indicate that the relation between resistance and applied magnetic field was more complex than that there would just be no resistance until the applied field reached the critical threshold, as the Maxwellian view entailed. Second, they showed that there was a difference in the point of reappearance of resistance depending on the orientation of the magnetic field with respect to the wire: for a magnetic field applied transversally, i.e. perpendicular to

298 The original German goes as follows: “Schliesslich haben wir einige Beobachtungen aus- geführt,bei denen der Zinndraht in einem konstanten Feld abgekühltwurde. Es scheint sich zu ergeben, dass in der Umgebung der äusserenBi-Drätchen das Feld aus dem Supraleiter verschwindet. Beim mittleren Drätchen hingegen wurde beim Sprungpunkt eine Zunahme des Feldes gefunden. Qualitativ sind diese Ergebnisse in Ubereinstimmung¨ mit den Messungen von Meissner und Ochsenfeld (1933). Diese Beobachtungen könnten eine Anzeige dafürsein, dass das Ver- schwinden des Magnetfeldes aus einem Supraleiter ein kompliziertes Phänomendarstellt; doch sind im allgemeinen die Messungen noch zu unverlässig”. 299 See (Dahl, 1992, p. 142 – 147) for a discussion of these experiments.

162 Experiment, Time and Theory the wire’s axis, the critical field value at which resistance would start to reappear would be approximately 0.6 times that for an applied field that was parallel to the wire. Measurements of the disappearance of resistance also showed that in the transition to the superconducting state with a transversally applied field, the point of disappearance of the resistance depended on the strength of the measuring current used, whereas this was not the case for the transition to the superconducting case with a longitudinally applied field (de Haas and Voogd, 1931a, p. 65). These observations about the relation between the direction of the applied magnetic field and the dis- and reappearance of the resistance suggested that the precise penetration depth of the magnetic field played an important role with regards to the point at which resistance would reappear:

In our opinion the principal point found is the characteristic difference between the longitudinal and the transverse disturbance. In further experiments we shall try to learn something more of the mechanism of magnetic disturbance (both longitudinal and transverse) in the wire. Hence we must find out how far in the different stages of the magnetic transition curves the magnetic field has intruded into the wire. (de Haas and Voogd, 1931a, p. 68)

Von Laue’s Analysis According to von Laue, these results indicated “that, in the case of the mentioned temperatures and for not too high field strengths, the metal behaves as a perfect conductor in the sense of Maxwellian theory” (1932).300 Von Laue argued for this by showing how, on this conception, we would expect the resistance to disappear for a transversally applied field at a critical field value that was approximately 0.5 times that of a parallel field, on the assumption that the strength of the measuring current was not of significance.301 This discrepancy between the measured ratio (0.6) and the predicted value (0.5), was not a problem, according to von Laue: it was possible that the measurements were not sensitive enough to detect an earlier disappearance of resistance for the transverse field, or maybe the wire was less uniform in shape than de Haas and Voogd had claimed, or maybe they hadn’t been accurate enough in determining the precise direction of the applied fields (von Laue, 1932, p. 795). If the experiments were carried out correctly, von Laue claimed, they would be in line with the 0.5 prediction for a Maxwellian conceptualization of superconductors as perfect conductors. Moreover, von Laue continued, this Maxwellian conceptualization could also account for the observed hysteresis. On this conception, approaching the superconducting state by lowering the applied field below HC while holding the temperature T < TC fixed will induce frozen in fields equal to the field applied before transition, and further variation of the applied magnetic field therefore could not influence the inner field anymore. But this state could also display other, different properties (von Laue does not specify which) that could render the relation between resistance and applied magnetic field more complex than assumed, in such a way that the point of disappearance could differ from the point of reappearance. This showed, according

300 The original German goes as follows: “daß sich das Metall bei den in Rede stehenden Tem- peraturen und nicht zu hohen Feldst¨arken als vollkommener Leiter im Sinne der Maxwellschen Theorie verh¨alt”. 301 For a discussion of von Laue’s analysis, see (Dahl, 1992, p. 167 – 169).

163 Chapter 3. Experiment and Superconductivity to von Laue (1932, p. 795), that the observed hysteresis was not necessarily a problem for the Maxwellian view. In a footnote, von Laue then suggested that this would be the most plausible way to investigate the observed hysteresis, since these frozen in ﬁelds were not just a theoretical hypothesis but rather experimentally established by Kamerlingh Onnes and Tuyn:302

G. Lippmann had already derived this and other consequences from the hypothesis of a perfect conductor. He shows, among other things, that a superconductor with a “frozen in” inner magnetic ﬁeld forms a permanent magnet. The well-known experiment by Kamerlingh Onnes and Tuyn easily proves in this sense the constancy of the magnetic moment. (von Laue, 1932, p. 795)303

De Haas and Colleagues Respond De Haas first replied to von Laue in his (1933) article, in which he presented an overview of earlier and new measurements by him, Voogd, and others on the influence of magnetic fields on resistance. He pointed out there that, in contrast to what von Laue had assumed, he believed that one could not ignore the influence of the measuring current (de Haas, 1933, p. 64). He also pointed out that at the time, he was carrying out measurements with Voogd on superconducting wires of different forms which, they claimed, had frozen in fields, in order to investigate whether the discrepancy between von Laue’s 0.5 prediction and their 0.6 measurement could be a consequence of the wire not being circular enough. In their (1934) article, de Haas, Voogd and now also Casimir-Jonker further discussed what these new measurements meant for von Laue’s analysis. They carried out, more specifically, measurements of the disappearance of resistance with a decreasing applied transverse magnetic field for different measuring current strengths. In line with the earlier experiments by de Haas and Voogd, these showed a clear influence of the measuring current on the disappearance of resistance (see figure 3.11): “The decreasing curve strongly depends on the current strength” (de Haas et al., 1934, p. 285).304 For these new measurements, they also ensured increased accuracy and a wire that was as circular as could be, in order to address von Laue’s two other possible explanations for the discrepancy between theory and observation. The ratio of the measured transverse and longitudinal field strengths at which resistance disappeared still showed a clear discrepancy with von Laue’s 0.5-ratio, and this was too big a difference to be explained by the geometry of the wire, as von Laue did (de Haas et al., 1934, p. 285).

302 I find von Laue’s claims about hysteresis rather unclear, and I have therefore tried to present them as literally as possible. Von Laue further elaborated his work on the magnetization of Maxwellian perfect conductors in an article together with Friedrich Möglich (1933), which was used by Meissner and Ochsenfeld (1933) and by Meissner and Heidenreich (1936) to calculate the permeability of the superconducting bodies employed in their experiments. Von Laue there does not, however, discuss the experiments by de Haas and Voogd anymore. 303 The original German goes as follows: “Schonn G. Lippmann hat diese wie andere Folgerungen aus der Hypothese des vollkommenen Leiters klar ausgesprochen. Er weist u. a. darauf hin, daß ein Supraleiter mit ‘eingefrorenem’ innerem Magnetfeld einen permanenten Magneten bildet. Der bekannte Versuch von Kamerlingh Onnes und Tuyn beweist in diesem Sinne einfach die Konstanz des magnetischen Momentes”. 304 The original German goes as follows: “Die abnehmende Kurve hängtsehr stark von der Strömstärke ab”.

164 Experiment, Time and Theory

Figure 3.11: De Haas, Voogd and Casimir-Jonker’s measurements of the eﬀect of the strength of the measurement current (ranging between 20 and 210mA) on the disappearance of resistance for a decreasing applied transverse magnetic ﬁeld. Figure source: (de Haas et al., 1934, p. 284).

In the final part of their paper, they then investigated the disappearance of resistance for wires that were made superconducting by first applying a transverse magnetic field, and then lowering the temperature while keeping the field constant. This showed that for such transitions as well, the point at which the resistance would disappear was similarly sensitive to the applied measuring current and the geometry of the wire, which suggested, according to de Haas, Voogd, and Casimir-Jonker, that there could not be any frozen in fields after the transition to the superconducting state.305 We would rather expect this, they concluded, if the magnetic field was expelled upon transition to the superconducting state, as had recently been shown in experiments by Meissner and Ochsenfeld (1933):

This analogy between the thermal and the magnetic transition figure is barely understandable from Laue’s point of view; at least not if one does not want to accept, that in the case of cooling in a constant magnetic field this field is expelled from the superconductor. Meissner and Ochsenfeld have now really found such a similar effect. (de Haas et al., 1934, p. 290)306

305 If there were frozen in fields, we would expect very different curves depending on whether we vary the temperature while the field remains constant or vice versa. This is not what was observed by de Haas, Voogd and Casimir-Jonker. As Dahl puts it: “according to the classical theory [. . . ], the behavior under this particular powering and cooling sequence [i.e. transition with the applied magnetic field held fixed] should be qualitatively different from that under the earlier sequence [where the temperature was held fixed]. Though preliminary, the resultant curve [. . . ] leaves little doubt that this in fact is not the case. The curve shows a strong resemblance to the magnetic transition curve at constant temperature, again exhibiting hysteresis between the descending and ascending branch and is reproducible only for increasing temperatures. ‘The character of the curve,’ reported de Haas, ‘develops as in the case of changing the field at constant temperature’.” (Dahl, 1992, p. 171). 306 The original German goes as follows: “Diese Analogie zwischen der thermischen und der magnetischen Ubergangsfigur¨ ist von dem Laue’schen Standpunkt aus kaum zu verstehen; wenn man wenigstens nicht annehmen will, dass bei Abkühlungin konstantem Magnetfeld dieses Feld

165 Chapter 3. Experiment and Superconductivity

Keesom and Kok

Before they published their (1934b) measurements of the specific heats of solids during the superconducting transition, Willem Keesom and Johannes Kok had already carried out earlier measurements of this kind within the broader program of low-temperature specific heat measurements. They refrained from publishing the superconductivity results, however, because for these measurements the determination of the resistance relied on the stability of the magnetic field, and the experimental results of Meissner and Ochsenfeld (1933) and de Haas and Casimir-Jonker (1934) “had shown that one must be cautious as to the appreciation of the value of the magnetic field in the neighbourhood of a supraconductor” (Keesom and Kok, 1934b, p. 503).307 They therefore decided to redo their specific heat measurements with a thermometer – a phosphorbronze wire in which they measured resistances – that was specifically calibrated within the superconducting region. This indicated to them that, in line with what they describe as Meissner and Ochsenfeld’s observation that upon transition to the superconducting state the lines of magnetic force are expelled, there is a pressing together of magnetic field lines outside the superconducting body (Keesom and Kok, 1934b, p. 505).308

Figure 3.12: Keesom and Kok’s results of the measurements of atomic heats for superconducting thallium when a constant magnetic ﬁeld of 33.6 gauss is applied. The dotted line represents the atomic heat of thallium when no external magnetic ﬁeld is applied. The temperature scale ranges from 1.6 to 2.4K. Figure source: (Keesom and Kok, 1934b, p. 506).

These new measurements now showed that when a body is rendered superconducting, and the temperature is then slowly increased, there will be a peak in the aus dem Supraleiter getrieben wird. Meissner und Ochsenfeld fanden nun wirklich einen ähnlichen Effekt”. 307 They did publish the low-temperature results that did not rely on the application of a magnetic field (Keesom and Kok, 1934a). 308 This pressing together can be seen on figure 3.5 on page 154, where, when the magnetic field is expelled from the superconducting state, there is an increase in lines of force in the area outside, close to the body’s surface.

166 Experiment, Time and Theory atomic heat curve at around 2.1K (see figure 3.12).309 This value was very close, Keesom and Kok point out, to the point found by de Haas and Voogd (1931b) for which, with the same applied magnetic field, the superconducting state would disappear. Keesom and Kok also carried out the same measurements with a stronger magnetic field. This led to a curve of the same form, i.e. with a peak in atomic heat at the point where, according to de Haas and Voogd’s (1931b) measurements, the superconducting state would disappear for this magnetic field strength, namely 1.9K (Keesom and Kok, 1934b, p. 506). As such, these experiments convinced Keesom and Kok that the disappearance of the superconducting state would go together with a sudden peak in the atomic heat. They also provided them with a formula for the change in a body’s atomic heat c during transition from the superconducting to the non-superconducting state, which included, among other things, an expression for the latent heat r supplied during the transition.310 Calculating r on the basis of their measurements then in turn provided them, they claimed, with a means to test experimentally whether the transition from the non-supraconductive state to the supraconductive state is a reversible process (Keesom and Kok, 1934b, p. 508). This question emerged out of Gorter’s (1933) thermodynamical treatment of the superconducting transition in terms of a cycle, which was discussed on page 158. For this cycle to be reversible, the net entropy of the total cycle would have to be zero. Keesom and Kok expressed the increase in entropy when the cycle passes the curve presented in figure 3.7, discussed on page 159, in terms of the following equation: r/T + σ, where σ is the entropy “being due to some possible irreversible process” (1934b, p. 509). For the cycle to be reversible, σ would thus have to be zero.311 Keesom and Kok’s data now showed, for transitions between the superconducting and non-superconducting state with a constant applied magnetic field, “that the process mentioned may be considered as reversible as far as thermodynamical consequences go, viz. that [. . . ] σ = 0” (Keesom and Kok, 1934b, p. 509). In this way, Keesom and Kok’s experiments provided evidence in favour of conceptualizing superconductors in terms of a thermodynamical phase, since they had evidence for a sudden discontinuity in the superconducting body’s atomic heat during the transition, and the latent heat they could obtain from their data was in line with Gorter’s thermodynamical treatment of the phenomenon.

Manipulability and the State of Magnetization Under the perfect conductivity-interpretation provided by Lorentz’s electron-theory of conduction in metals, we have seen on page 141, the data produced by Kamerlingh Onnes and Tuyn could be taken to provide evidence in favour of the existence of frozen in fields. Lorentz’s theory provided such an interpretation, in the sense that it offered an account of how the variations in the applied magnetic field would influence

309 A body’s atomic heat is its speciﬁc heat expressed as the calories per degree Kelvin for one mole of the substance. 310 Latent heat is “the quantity of heat that must be supplied to change the state of one unit of mass”, where with state is meant a thermodynamical phase (see footnote 296) (Matricon and Waysand, 2003, p. 51). 311 This would mean that the net entropy of the total cycle would be zero, since r/T for the transition at point A would be equal to −r/T for the opposite transition at the point C (see ﬁgure 3.7 on page 159).

167 Chapter 3. Experiment and Superconductivity the persistent currents induced on the superconducting body in such a way that the stationary state observed by Kamerlingh Onnes and Tuyn would come about. Given that, in this way, Lorentz’s account entailed the empirical regularities observed in the experiments, these experiments could then be taken as a confirmation of Lorentz’s electron-account of the existence of frozen in fields, as was done, for example, by von Laue (see the quote on page 164). The different experiments discussed in the present section showed, however, that there were issues with this perfect-conductivity interpretation. Meissner and Ochsenfeld’s parallel cylinders-experiment indicated that, contrary to what one would expect, no frozen in fields were present in the cylinders after their transition to the superconducting state. Rjabinin and Schubnikow found that the magnetic flux would not remain constant under variations in the applied magnetic field. De Haas, Voogd and Casimir-Jonker observed that for both the magnetic and the thermal transition, the point at which the resistance would disappear was sensible to the strength of the applied measuring current, which could not be explained by von Laue’s account. Keesom and Kok, finally, found that a superconductor’s atomic heat would display a discontinuity during the superconducting transition, which would be difficult to understand if the superconducting state was continuous with, in the sense of being a limit of, the normal conductivity state. These experiments were able to raise issues with the perfect conductivity conceptualization because they varied, in a significant sense, on the experimental procedure and set-up employed by Kamerlingh Onnes and Tuyn. Meissner and Ochsenfeld varied, for example, the way in which the superconducting state was, until then, normally brought about:

Evidently, the diamagnetic behaviour uncovered by Meissner and Ochsen- feld was fundamentally different from the diamagnetism of Lippmann for perfect (R = 0) conductivity. Indeed, that conception had suggested the von Laue effect, predicated on the cooling preceding application of the field – the invariable laboratory practice until 1933. (Dahl, 1992, p. 179; original emphasis)

Previously, superconductors were studied by first cooling, and then applying a magnetic field in order to bring about persistent currents. That such currents arose was then, following Lippmann’s theorem, taken as evidence in favour of the existence of frozen in fields, and it was assumed that proceeding in the opposite direction would provide the same result.312 Meissner and Ochsenfeld’s experiments indicated, however, that this was not necessarily the case. A second variation concerned the way in which the superconducting state was compared with the non-superconducting state. Kamerlingh Onnes and Tuyn carried out measurements at two temperatures: one just below TC and at 273K, and then compared the resistances measured at these two temperatures (see equation 3.1 on page 135). The experiments by Rjabinin and Schubnikow, de Haas and Casimir- Jonker together and with Voogd, and Keesom and Kok, on the other hand, all concerned measurements not only of the superconducting and non-superconducting state, but also of the transition, and this indicated that the superconducting state

312 Kamerlingh Onnes, for example, proceeded in this way in his (1921, p. 178 – 179) experiments on microresidual resistance and in his (1924, p. 255) experiments with Tuyn.

168 Experiment, Time and Theory was not as simple as the perfect conductivity-conception assumed (i.e., R = 0 and frozen in ﬁelds until HC is reached). A third variation concerned the measurement instruments used. In order to obtain information about the magnetic ﬂux, Kamerlingh Onnes and Tuyn had to rely on measurements of the resistivity of the persistent currents by means of bismuth wires (see footnote 264). According to Matricon and Waysand, however, this was a problematic way of proceeding:

The idea of frozen in flux inside the actual superconducting metal was [. . . ] only a myth, but one with a hard skin. It depended on measurements of the magnetic field inside the lead sphere, and these measurements were not easy. The method, which had been classic since the beginning of the century, was to put a small piece of bismuth wire at appropriate positions in the sphere. The resistivity of bismuth varies strongly in the presence of a magnetic field, and the variation is particularly large at low temperatures. For once in Leiden, the credo of Kamerlingh Onnes was obviously not followed.313 After the frozen flux had apparently been discovered, no one took the trouble to repeat the measurements.314 (Matricon and Waysand, 2003, p. 55)

By the time of the experiments discussed here, however, other ways of measuring the magnetic flux were used: Meissner and Ochsenfeld, and Rjabinin and Schubnikow, made use of a ballistic galvanometer, and while de Haas and Casimir-Jonker still used bismuth, they used it in such a way that they measured not only the flux at the surface, but inside the superconducting body as well (see figure 3.9 on page 160). In line with Brillouin’s analysis of Bloch’s impossibility-theorem, these experiments could thus be taken to indicate that there were issues with the perfect conductivity-conception. What was less clear, however, was how this was to be overcome. Some, such as Rjabinin and Schubnikow or Keesom and Kok took their experiments as providing evidence that the superconducting state had to be conceptualized as a thermodynamical phase with permeability zero. Meissner and Ochsenfeld, on the other hand, seemed to take their experiments to indicate that a further elaboration of the ferromagnetic analogy underlying the perfect conductivity-interpretation offered by the spontaneous current approach was required. Still others, such as Mendelssohn and Babbitt or de Haas and Casimir-Jonker, saw their experiments primarily as indications that the superconducting state was more complex than both the perfect conductivity conception and the zero permeability view assumed. What this now shows is that, contrary to what Hacking (see page 21) seems to believe, varying on an experimental manipulation will not in itself show that the effect brough about by the manipulation is robust or not. While the different experiments together could be taken to suggest that the frozen in fields brought

313 By this, Matricon and Waysand mean that if Kamerlingh Onnes’ adagium ‘Door Meten tot Weten’ (through measurement to knowledge, see footnote 244) had been properly followed, i.e. if the measurements of the magnetic flux by means of bismuth had been carried out at different points inside the superconducting body, it would have been realized soon enough that the magnetic flux inside the superconducting body was not in line with what one would expect on the basis of the perfect conductivity-conception. 314 Matricon and Waysand are not the only ones to argue this. Kostas Gavroglu as well states in his biography of Fritz London that “[t]his physical assumption was regarded as being so self-evident that there was no systematic experimental study of the predicted phenomenon” (1995, p. 112).

169 Chapter 3. Experiment and Superconductivity about following Lippmann’s theorem were maybe not as robust as assumed, they did not show that there were no frozen in fields. Some experiments suggested a state with zero permeability. Most rather indicated that the magnetic flux was lower than expected, but not zero. And they definitely did not show in themselves which conceptualization had to replace it, if one took the experiments to indicate that the frozen in fields were not robust, since, as we have seen in the previous paragraph, the results could be interpreted in all kinds of ways. As we will see now, it was only by introducing theory besides the experimental results that sense could be made of them, in such a way that it could later be claimed, by scientists such as Fritz London and by philosophers of science such as Cartwright, French, Ladyman, Suárezand Shomar (see the quotes on page 131), that Meissner and Ochsenfeld’s experiments showed that superconductors are diamagnetic.

3.6 Superconductors and Phenomenological The- ories

We have now had an overview of diﬀerent experiments that all in their own way raised questions about the experiments carried out by Kamerlingh Onnes and Tuyn and the claims connected to it. Our focus now will be on the way in which these experiments were translated into new conceptualizations of the phenomenon of superconductivity. We will start with Gorter and Casimir’s (1934) phenomenological account of its thermodynamical characteristics, after which we will turn to London and London’s (1935a) electrodynamical account based on Gorter and Casimir’s work. This will then allow us to evaluate and contextualize the claim by Fritz London with which we opened this chapter, that Meissner and Ochsenfeld’s experiments led to a revolution with regards to the way in which superconductors were conceptualized because they showed that superconductors are like diamagnets.

Gorter and Casimir’s Thermodynamic Account The experiments discussed above, Gorter and Casimir stated in the opening paragraph of their article, “gave rather unexpected results” (1934, p. 306). However, what still needed to be done with these results was to investigate “in how far they allow new conclusions concerning the nature of the supraconductive state, and in how far they have to be considered as merely secondary eﬀects” (1934, p. 307). Fol- lowing Gorter’s (1933) work (see page 158), Casimir and Gorter carried out such an analysis in thermodynamical terms, especially since Keesom and Kok’s (1934b) results indicated that such a treatment, which conceptualizes superconductivity as a distinct phase, was indeed feasible. Gorter’s work had shown, more speciﬁcally, the following:

Limiting himself to those supraconductive states, where the induction B equals 0, he showed that Rutgers’ equation is identical with the statement, that the second law of thermodynamics applies to the magnetic disturbance, in spite of the fact, that the dying out of the so called persisting currents seems at ﬁrst sight to be an irreversible phenomenon. (Gorter and Casimir, 1934, p. 308)

170 Experiment, Time and Theory

For those cases where B = 0, Gorter had suggested that disturbing the superconducting state by applying a magnetic field H > HC was a reversible phenomenon, since the net entropy, as we have seen in our discussion of Keesom and Kok’s experiments on page 167, was zero. What Meissner and Ochsenfeld’s (1933) and de Haas, Voogd and Casimir-Jonker’s (1934) experimental results now suggested, Gorter and Casimir continue, was that “in the supraconductive state B may always equal zero” (1934, p. 308). This then urges them to further elaborate Gorter’s (1933) thermodynamical approach, which conceptualized the superconducting phase, as we have seen, in terms of three properties: the temperature T , the applied magnetic field H and the internal magnetic flux B. One particular consequence of this elaboration, Gorter and Casimir pointed out, was that this suggested that the persistent currents are only to be found on the superconducting body’s surface, and that the case of a superconducting ring, where, as Lippmann (1919) had shown, we expect frozen in fields, had to be seen as an exception:

If we cool the body to a temperature below the normal transition point in a zero external field and then apply a field, which is not strong enough to disturb supraconductivity, we must expect such persistent currents to be induced on the surface of the body, that B remains zero at the inside of it. The same phenomenon can formally be described by assumming the magnetic susceptibility to be: χ = −1/4πd. If an isolated body has not the shape of a ring, we can completely describe its behaviour in a field by putting χ = −1/4πd, or B = 0 inside the body. If, however, we have to do with a supraconducting ring, we must add the condition, that the total magnetic flux through the ring must remain zero. It has been suggested previously [by Meissner and Ochsenfeld’s experiments with two parallel superconducting cylinders], that, if we start with a body in a magnetic field and then lower the temperature, the condition B = 0 will also be fulfilled in those parts of the body, which are in the supraconductive state. It is clear that, if we consider the possibility, that supraconductive rings have been formed, the total flux through such rings will have to remain constant; but will not necessarily be zero. (Gorter and Casimir, 1934, p. 309 – 310)

Gorter and Casimir did not expand on these remarks further, but rather turned to the elaboration of Gorter’s thermodynamical account for the specific case where, if we have a superconductor shaped like a needle, the magnetic field applied is in the direction of the body’s axis.315 Afterwards, Gorter and Casimir summarized their work as having shown that, on the assumption that B = 0, a treatment of superconductivity as a reversible transition between two thermodynamical phases characterized in terms of T, H, and B, is possible. This entailed that “whenever a part of a body becomes supraconductive, such persistent currents are started, that the external field will be screened off, in order that B = 0 inside the supraconductive part” (Gorter and Casimir, 1934, p. 318).

315 They turned to this speciﬁc case because it concerns the results of de Haas and Voogd’s (1931b) experiments, which motivated Gorter’s (1933) thermodynamical approach. The idea that the state B = 0 is the standard condition for superconducting bodies, and that the frozen in ﬁelds observed in the case of superconducting rings are rather the exception, was developed further by Fritz and Heinz London, as we will see shortly.

171 Chapter 3. Experiment and Superconductivity

As they pointed out themselves (Gorter and Casimir, 1934, p. 318), their whole account rests on the assumption B = 0. As a kind of conclusion, they then discussed in how far this assumption was justified by the different experiments. Meissner and Ochsenfeld’s (1933) experiment, they claimed, presented evidence in favour of it, and de Haas, Voogd and Casimir-Jonker’s (1934) results also suggested it. There were also, however, certain difficulties with the assumption, since the same experiments by Meissner and Ochsenfeld (1933)316 and the experiments by de Haas and Casimir- Jonker (1934) indicated that sometimes regions within a superconducting body could exist where B 6= 0. A second problem concerned the question when there is a gradual disturbance of the superconducting state by e.g. the transverse application of a magnetic field H > HC . In that case, we would expect that the superconducting region would retreat from the surface into the body’s interior. This, however, posed a problem for their conceptualization in terms of two phases, since “it seems better to imagine, that part of the supraconductor will be perforated or reduced to pieces, rather than to suppose that there will exist a sharp retiring boundary between the two phases”, which would entail that “the condition B = 0 may thus perhaps lose its rigour in the neighbourhood of the transition line” (Gorter and Casimir, 1934, p. 319 – 320). As such, Gorter and Casimir concluded, their assumption is probably not valid across the board, but it does have its merits:

Though certainly the assumption B = 0 cannot be considered as ri- gourously proved by all these measurements, this assumption oﬀers un- doubtedly the most simple and elegant way of explaining qualitatively the phenomena observed, with which it is never in contradiction. (Gorter and Casimir, 1934, p. 319)

Fritz and Heinz London’s Electromagnetic Account

The London & London Article Gorter and Casimir’s thermodynamical account entailed, we have seen, that the persistent currents would only emerge on the surface of a superconductor (see the quote on page 171). In fact, it was already shown earlier, in 1925 by Geertruida de Haas-Lorentz, that the current penetrates only in a very small layer, of about 10−6cm near the surface. De Haas-Lorentz’s work did not receive much attention, however, in contrast to the same results obtained by Richard Becker, G. Heller and Fritz Sauter (1933). They obtained, more specifically, a replacement for Ohm’s law for the case of superconductors. This law had to be replaced because it led to to an infinitely strong current in the case of infinite conductivity. This could be prevented, they reasoned, by taking into account the inertia of the electrons constituting the persistent currents. Working out this idea for the case of a rotating superconducting sphere then led them to the following

316 Gorter and Casimir indicate, following Meissner himself, that it is not completely clear how this is to be interpreted, since “it seemed, that in one case this phenomenon could be described by assuming the supraconductor to have a magnetic susceptibility −1/(4πd)(d being the density), but in another case (hollow leaden tube) the ﬁeld appeared not to diminish inside the tube” (Gorter and Casimir, 1934, p. 307). They do not mention the replications of the experiments by Mendelssohn and Babbitt and by Rjabinin and Schubnikow.

172 Experiment, Time and Theory equation, which was known as the acceleration equation:317

dJ h m i Λ = E; with Λ = (3.3) dt ne2 The London brothers took the equation as the starting point of their (1935a) article, because they saw it as an example of the commonly held belief that the superconducting currents can persist without being maintained by an electromagnetic field.318 This equation expresses that the current density J is proportional to the electric field E up to a certain factor Λ, in which e and m denote an electron’s charge and mass, and n the number of electrons per unit volume: as such, “it simply expresses the influence of the electric part of the Lorentz force319 on freely movable electrons” in a superconductor (London and London, 1935a, p. 71). The problem with this equation, however, was “that it implies more than is verified by experiment” and that it “implies a premature theory, the development of which has presented a hopelessly insoluble problem to mathematical physicists” (London and London, 1935a, p. 71). The London brothers showed this as follows. Taking the curl of equation (3.3) and applying Faraday’s law of induction 1 dH 320 ∇ × E = − c dt , provided them with the following equation: dJ 1 dH ∇ × Λ = − (3.4) dt c dt They then applied Ampère’slaw (∇H = (1/c)J, with the displacement current neglected):

dH 1 dH ∇ × ∇ × Λ = − (3.5) dt c2 dt This they reformulated in turn by means of Gauss’s law for magnetism, which tells us that ∇ · H = 0:

dH dH Λc2∇2 = (3.6) dt dt Integrating this equation with respect to time then gave the following expression for the magnetic ﬁeld H (where H0 denotes the applied magnetic ﬁeld at the time t = 0 before the transition):

2 2 Λc ∇ (H − H0) = H − H0. (3.7)

The solutions√ of equation (3.7) for the magnetic√ ﬁeld are given by the equation Λcx Λcx H = e + H0, where the exponentials e decrease very quickly with respect to

317 In their original article, Fritz and Heinz London use a different notation for the derivative with respect to time, namely J˙ . I have chosen to adapt this notation here for clarity and in line with the more contemporary literature. 318 As examples of this view being present in the debate, they refer not only to the work of Becker, Heller and Sauter (1933), but also to work by Werner Braunbek (1934) and by Heinz London himself (1934). See (Dahl, 1992, p. 174 – 175) for a historical discussion, and (Essénand Fiolhais, 2012, p. 166) for an intuitive illustration of how one obtains an infinitely strong current. 319 The Lorentz force, expressed in terms of the equation F = e(E + v × B), concerns the force exerted by an electromagnetic field on a charged particle. 320 Taking the curl of a vector field F, denoted as ∇ × F, means rotating this vector field by an infinitesimal amount.

173 Chapter 3. Experiment and Superconductivity the distance x from the material’s surface.321 This result was problematic, according to the London brothers, for the following reason:

The general solution means, therefore, that practically the original field persists for ever in the supraconductor. Only in a layer of the order 10−5cm below the surface all disturbances take place reversibly, provided the threshold value is not exceeded. The field H0 is to be regarded as “frozen in” and represents a permanent memory of the field which existed when the metal was last cooled below the transition temperature. Until recently the existence of “frozen in” magnetic fields in supraconductors was believed to be proved theoretically and experimentally. By Meissner’s experiment,322 however, it has been shown that this point of view cannot be maintained. It results clearly from the thermodynamic discussion of Gorter that at the transition to the supraconducting state any magnetic field which may have existed before in the conductor is pushed out of it so that experiments which seemed to show that magnetic fields are frozen in are to be explained by the existence of non-supraconducting inclusions, in which the magnetic lines of force are pressed together. (London and London, 1935a, p. 72 – 73)

The acceleration equation entailed that the changes in the superconducting state, which Fritz and Heinz London called disturbances, were reversible only in the small layer near the surface; the rest of the superconductor was still considered to be frozen in. This was a problem, because they took the work of Gorter and Casimir and the experiments of Meissner and Ochsenfeld to have shown that there are no such frozen in fields in the perfect superconducting state. The problem arose, according to the Londons (1935a, p. 73), because the acceleration equation is a differential equation. This entails a time-dependent current density (Schmalian, 2011, p. 49). Instead, if the value H0 was to be always zero within a superconductor, we should correct this in equation (3.7), and take that to be what the Londons call the fundamental law, not the time-dependent acceleration equation (3.3). Rewriting this new law by means of the Maxwell equations, in order to obtain an expression for the current density J, then led them to their alternative for the acceleration equation, which expresses J in terms of the applied magnetic field H:

1 ∇ × ΛJ = − H. (3.8) c The London brothers then compared their new equation with the acceleration equation. The main advantage of theirs was that it included what they called “Meissner’s eﬀect”, i.e. the expulsion of any magnetic ﬂux upon transition to the superconducting state characterized as B = 0 (1935a, p. 35); a possible disadvantage could be that it did not lead to the acceleration equation itself anymore, and hence we would not be able to say anything about the acceleration of the current density J, which

321 This is how the acceleration equation entails that the current, constituted by the electrons with which Λ is concerned, only penetrates into a small layer underneath the surface. 322 Here, Fritz and Heinz London refer to Meissner and Ochsenfeld’s original (1933) paper and further elaborations of their work, to de Haas and Casimir’s (1934) results on bismuth (see page 159), and to the replications of Meissner and Ochsenfeld’s experiments by Mendelssohn and Bab- bitt, and by Schubnikow and Rjabinin (see page 155).

174 Experiment, Time and Theory was required, as we have seen on page 173, because otherwise we would end up with an infinite current density. But this disadvantage was not a real problem, the Lon- dons claimed, since we can obtain equation (3.4) from the acceleration equation, by differentiating it with respect to time, and this equation, the Londons then showed, led to an expression linking J and the charge density ρ to the electric field E that was also satisfactory:

dJ Λ + c2∇ρ = E (3.9) dt In the following sections of their paper, London & London showed that their equations captured a few empirical thermodynamical regularities concerning superconductors, and how they could be applied by means of some examples.323 In the final section, they then indicated that there seems to be a formal similarity between their equations, reformulated in terms of the magnetic potential A and the electric potential φ,324 and formulas from Walter Gordon’s (1926) relativistic formulation of Schrödinger’swave mechanics for electric current and charge (London and London, 1935a, p. 86).325 Fritz and Heinz London then elaborated what this formal similarity could tell them about the lowest state of energy of the electrons constituting the persistent currents and about the application of a magnetic field to a superconducting body. If they were conceptualized, on this view, as free electrons, then applying a magnetic field would result in a very small diamagnetism, which they called Landau-Peierls diamagnetism.326 If, on the other hand, they were characterized as coupled by some kind of interaction, then a current could become possible given the application of a sufficiently weak magnetic field. Without stating it explicitly, the London brothers were thus investigating how their results related to Bloch’s impossibility- theorem, which, as we have seen on page 149, emerged because the lowest state of energy of a superconductor could not carry a current. And while this formal similarity, they indicated, did seem to carry some promise, at the time “these last

323 What the London brothers obtained was, first of all, an expression for Joule’s law for superconductors, which concerns the heat produced by a current (1935a, p. 78). 324 See footnote 214 of chapter 2 for a short explanation of these potentials. 325 As we have seen in footnote 274, Schrödingerformulated his wave mechanics in order to elaborate a formalism for the concept of matter waves proposed by de Broglie. De Broglie’s concept, however, was relativistic: as Helge Kragh puts it in his entry on relativistic quantum mechanics in the Compendium of Quantum Physics, “[a]ccording to de Broglie, quantum theory and special relativity theory were unified by the relativistic formula mc2 = hν = hc/λ, or λ = h/p (where λ is the wavelength associated with the momentum p of some particle)” (2009, p. 632). In his elaboration of de Broglie’s work, however, Schrödingerwas forced to use a non-relativistic approximation, which led many physicists to search for a relativistic formulation, one of whom was Walter Gordon. See Kragh’s entry for more historical background (2009, p. 632 – 637). 326 Both Lev Landau (1930) and Rudolf Peierls (1933) had proposed a quantum-theoretical account of diamagnetic metals, in which they elaborated an alternative for what Landau saw as the common assumption that the magnetic properties of electrons, except for their spin, are to be accounted for exclusively in terms of their binding to atoms. Landau by contrast conceptualized the diamagnetic properties of metals in terms of free electrons forming a gas, which provided him with “the famous result that the diamagnetic susceptibility of the gas in a weak field is exactly minus one-third of the Pauli spin susceptibility, rather than zero, as in the classical theory” (Hoddeson et al., 1992, p. 126). Peierls elaborated Landau’s work for the limit region of strong applied magnetic fields, i.e. applied magnetic fields with a strength near the treshold field value for the disturbance of diamagnetism (Hoddeson et al., 1992, p. 128).

175 Chapter 3. Experiment and Superconductivity remarks are to be taken as indicating roughly a programme which requires a detailed quantum mechanical investigation” (London and London, 1935a, p. 87). They then summarized their ﬁndings as follows:

In contrast to the customary conception that in a superconductor a current may persist without being maintained by an electric or magnetic field, the current is characterized as a kind of diamagnetic volume current, the existence of which is necessarily dependent upon the presence of a magnetic field. That magnetic field itself may be produced reciprocally by the current. (London and London, 1935a, p. 88)

The London Equations and Bloch’s Impossibility-Theorem In his (1935) presentation at the Royal Society symposium on superconductivity (see footnote 284), Fritz London further elaborated the program sketched at the end of the (1935a) paper with his brother. He no longer situated their work, however, within the context of the acceleration equation. What he was concerned with, as he stated in the opening paragraph, was rather that the phenomenon is normally interpreted as a limiting case of ordinary conductivity, i.e. as a conductor with perfect or infinite conductivity. This was a problem, according to Fritz London, since it led to the impossibility-result obtained by Bloch and generalized by Brillouin: on the assumption that a superconductor has to be modeled as a metal that can carry a perfect current without being maintained by any external field, it turns out that a theory of superconductivity is impossible, since according to Bloch’s own electron-theory of conduction, “the most stable state of any mechanism of electrons for very general reasons may very probably have no current” (London, 1935, p. 25). The Londons’ (1935a) work provided a way out of this situation, Fritz London argued. The perfect conductivity conception entailed that the magnetic flux inside a superconductor must be constant. Meissner and Ochsenfeld’s experiments had shown, however, that in ideal conditions – where he does not specify what these conditions are, except that non-ideal conditions include frozen in fields – there is zero magnetic flux inside a superconductor (London, 1935, p. 25). Hence, the cases where we do find frozen in fields, such as e.g. superconducting rings, should be seen as exceptions to the rule, rather than the general case. In the ideal case, superconductors should not be seen as perfect conductors, but rather as similar to diamagnetic metals, in line with the programme that was suggested by the formal similarity between the Londons’ equations and those for current and charge of Gor- don’s relativistic quantum theory. This diamagnetic conception would entail that it was only on the condition that a magnetic field is present that we would obtain a superconducting current, since, as we have seen in footnote 236, a diamagnetic material “loses its magnetization when the applied field is removed” (Keith and Quédec,1992, p. 364):

[A]ccording to Meissner’s experiment, it looks as though the transition from the non-supraconducting to the supraconducting phase in a magnetic ﬁeld is microscopically reversible, so far as the magnetic ﬂux can be considered as equal to zero in any volume element of the pure supraconducting phase, independently of the way in which the threshold curve has been passed. The magnetic behaviour of a supraconductor resembles that of a very strongly diamagnetic metal, namely, of such a one which

176 Experiment, Time and Theory

has a diamagnetic susceptibility χ = −1/4π or a permeability µ = 0. In a diamagnetic atom we have an example of a permanent current flowing in a system which is in its most stable state. The apparent contradiction to Bloch’s theorem is here avoided by the remark that Bloch’s theorem deals with a system without external electric or magnetic field. We see that in a magnetic field this theorem evidently does not hold. (London, 1935, p. 26)

On the account of superconductivity offered by the Londons’ equations (3.8) and (3.9), Fritz London argued, “[t]he supracurrent [. . . ] appears as a diamagnetic current which is maintained by a magnetic field” (1935, p. 26). In this way, their account promised a way to evade Bloch’s impossibility-result, if it could be shown that in the ideal conditions – i.e. when B = 0, as suggested by Meissner and Ochsenfeld’s experiments – the superconducting current maintained by a magnetic field indeed forms a stable minimal energy state. To elaborate an answer to this question, Fritz London turned to the issue of a superconducting ring, i.e. a circular surface S with a non-superconducting interior bounded by a closed curve C that is superconducting. In such cases, Lippmann had already shown, we do expect magnetic flux inside the ring, i.e. a frozen in field. The Maxwell equations give us an expression for the magnetic flux through S in terms of the energy of the current in the superconducting region, to which the London equations, Fritz London showed, could be applied. In this way, he obtained the permanent magnetization as predicted by Lippmann:

A magnetic flow which is once present in the hollow of the ring remains constant for any time, whatever perturbing external fields may be applied. The ring behaves like a permanent magnet. But, as it contains the magnetic energy of the flux, the ring is to be regarded as being in a metastable state. Only by a finite variation of the parameters of the system (i.e., by transgressing the treshold value) can it change into the absolutely stable state which contains no flux. (London, 1935, p. 29)

That the ring is a system in a metastable state, we have seen on page 150, means that the currents occur in a stable state that is different from the system’s lowest energy state. What the Londons’ equations showed was that the occurence of persistent currents in a superconducting ring could only occur because of the extra energy provided by the magnetic flux through the ring: it should not be seen as the system’s lowest energy state (Leggett, 1995, p. 918). In this way, Bloch’s impossibility-theorem could be sidestepped. As Brillouin (1935, p. 20) pointed out in his presentation at the Royal Society symposium, the theorem could only be overcome within the classical perfect conductivity approach by assuming that the current was metastable (see page 150). In the case of frozen in fields, as we have with superconducting rings, the current is indeed metastable. But, according to the Londons’ view of Meissner and Ochsenfeld’s experiments, these frozen in fields should not be seen as the normal condition of superconductors, but rather as the exception to the general case, which is the stable minimal energy state of a superconducting current maintained by an external magnetic field without any frozen in fields. Fritz London thus showed that Brillouin’s and Bloch’s argument was, in a sense, right: in the lowest energy state of a superconducting body there is indeed no

177 Chapter 3. Experiment and Superconductivity current, except when a magnetic field is applied. In this way, the Londons’ equations could offer an explanation not only for the currents in the stable minimal energy state, where there is no frozen in flux, but also for the special case of superconducting rings, where the current is metastable, in terms of the magnetic field of the frozen in flux. As such, Kamerlingh Onnes and Tuyn’s experiments on rings and hollow spheres and Meissner and Ochsenfeld’s hollow cylinder-experiments were not to be seen as paradigmatic or ideal cases of superconductivity, but rather as very specific exceptions to the general rule of B = 0: “[t]he persistence of the original magnetic fluxes should therefore not be regarded just as the elementary phenomenon but as a very complicated matter, due to the presence of several components or phases in a complicated microscopical interpenetration” (London, 1935, p. 25). This overcoming of Bloch’s impossibility-result relied, of course, on the assumption that what Fritz and Heinz London took to be the result of Meissner and Ochsen- feld’s experiments – that, in general, there is no magnetic flux inside a superconducting metal (B = 0) – was indeed the ideal condition. An argument for this assumption would have to be provided in terms of the physical mechanism responsible for the emergence of the superconducting state, i.e. the electrons that gave rise to conduction in metals. If it could be shown that, in a minimal energy state, they gave rise to a stable current, then this assumption could be taken as generally valid. We have seen that the Londons already started the elaboration of such a theory in their (1935a) article, where they investigated what kind of diamagnetism we would obtain, depending on whether we took the conduction electrons to be free or bound (see page 175). This was but the start of a theory, however, since, as Fritz London pointed out, “[t]he foundation of our macroscopical equations by the theory of electrons in metals has yet to be undertaken” (1935, p. 31). In the final part of his Royal Society lecture, Fritz London then tried to elaborate a bit more what these foundations would come down to, in line with the diamagnetic programme sketched at the end of their previous paper. Whereas in that paper, they only indicated that there were two possible options, depending on whether the electrons were free or bound, Fritz London argued here that the second option – “suppose the electrons to be coupled by some kind of interaction” (1935, p. 31; emphasis added) – could actually lead to a foundation for the London equations, by sketching how their accounts for both superconducting bodies in general and superconducting rings in particular would look like. He stressed, again, however, that this was only preliminary work for a future foundation of their theory (1935, p. 33), since, as the emphasized part in the statement above shows, what kind of interaction was responsible for the coupling of the electrons in such a way that the diamagnetism required for their equations could arise, was still unknown. Hence, at this point, the Londons had a programme for addressing Bloch’s impossibility- theorem, but not yet a completely satisfactory account yet, since the interaction was still unknown; and as we have seen on page 149, it was the repeated failure to find a fitting interaction that in the end led Bloch to formulate his impossibility-theorem.

The London Equations and Diamagnetism: 1935 The Londons’ elaboration of their account of superconductivity, and their claim that it would allow them to overcome Bloch’s impossibility-theorem, relied, as we have seen, on the assumption that Meissner and Ochsenfeld’s experiments indeed showcased superconductivity in its ideal state. In their (1935b) article, in which Fritz and Heinz London further elab-

178 Experiment, Time and Theory orated this diamagnetic view, they indicated, however that it was not yet completely sure whether the experiments could be taken to suggest B = 0 as a replacement for the perfect conductivity view:

While until now the flow of current with at the same time the collapse of the electric field strength is seen as the most characteristic trait of this state, we have now observed, that besides that also the magnetic induction inside the superconductor disappears, at least insofar as we can interpret these still very uncertain experimental findings in such an idealized form, as is suggested by the thermodynamical discussion of Gorter (1933) and Gorter and Casimir (1934). (London and London, 1935b, p. 341)327

If we take these experiments to be correct, the Londons pointed out, we could take their new equation (3.8), which links the current density J to the applied magnetic field H (discussed on page 174), to characterize a superconductor as a diamagnetic material of some kind. According to the theory of diamagnetism at the time, application of a magnetic field would, up to a certain point, not disturb the eigenfunction of the diamagnet’s atoms (see footnote 274 for the concept of eigenfunction). Simi- larly, for superconductors this would mean that the application of a magnetic field would bring about a current without disturbing the superconducting state. This led them to elaborate more thoroughly what they saw as the programme sketched by this similarity, namely to provide an electron-theory that could account for this fact that there is no real change in the superconducting state upon application of a magnetic field:328

A future electron-theoretical account will therefore apparently have to show something relatively easy, namely that with the arisal and ﬂow of a supercurrent, in fact practically nothing happens regarding the Ψ- function, that in fact Ψ in weak magnetic ﬁelds only experiences a disturbance of second or even higher degree.329 It has to show, on the ground

327 The first part of this sentence, concerning the presence of a flow of current and the collapse of the electric field strength, refers to Ohm’s law J = σE (see footnote 245), where σ denotes the material’s conductivity, which can also be expressed in terms of its resistivity η = 1/σ. Ohm’s law then becomes E = ηJ. The significant characteristic of superconductors, on this view, was then that we could have a current J even though its resistivity η, and hence also its electric field E, were zero. The original German goes as follows: “Währendbisher der Zusammenbruch der elektrischen Feldstärke bei gleichzeitig fliessendem Strome als das auffallendste Merkmal dieses Zustande angesehen wurde, haben wir jetzt erfahren, dass ausserdem die magnetische Induktion im Supraleiter verschwindet, wenigstens sofern wir den noch sehr unsicheren experimentellen Befund so auf seinen idealen Gehalt hin interpretieren dürfen,wie es durch die thermodynamische Diskussion durch Gorter (1933) und Gorter und Casimir (1934) nahegelegt wird”. 328 In his Royal Society lecture, Fritz London already made exactly the same claim (1935, p. 33). He there does not elaborate it further, however. 329 Elaborating their diamagnetic programme had provided Fritz London with the following quantum-mechanical formulation for the equation he had obtained with his brother for the current he ∗ ∗ e2 ∗ J (equation 3.8, discussed on page 174): J = 4πim (Ψ ∇Ψ − Ψ∇Ψ ) − mc ΨΨ A, where h denotes Planck’s quantum-constant, e denotes charge, i is the imaginary unit, Ψ∗ is the complex conjugate of the wave function Ψ, c refers to the velocity of light, m denotes the Planck mass, and A expresses the magnetic potential. That the wave function experiences only disturbances of second or higher order degree then means the following: “[W]ith the electrons coupled in such a way that an energy

179 Chapter 3. Experiment and Superconductivity

of which coupling the solidiﬁcation of the electron-eigenfunction against magnetic disturbances arises. (London and London, 1935b, p. 350)330

London and London pointed out that it was not yet clear how far this diamagnetic approach could take them, but that in any case “the analogy with a diamagnetic atom should not be taken too literally” (London and London, 1935b, p. 350 – 351).331 In the case of a diamagnet the application of an electric field disturbs its eigenfunction in a way that is proportional to the strength of the applied field. In the case of a superconductor, however, the Londons’ equation (3.9), which links current to electric field (discussed on page 175), entails that the application of an electric field should not disturb the eigenfunction. This indicated, more specifically, that the still unknown interaction responsible for the coupling of the electrons could not be the same as the one which occurs in the case of diamagnetism:

For the moment we do not know yet which coupling of electrons in a superconductor is responsible for the relative solidification of the eigenfunction against magnetic disturbances. It is in any case a coupling that is completely different from the nucleus-electron coupling present in the atomic field, and it is conceivable, that this as of yet unknown coupling also brings about a solidification of the electronwave-functions against electric disturbances. (London and London, 1935b, p. 351)332

Manipulability and the London Equations We have seen that the Londons arrived at their equations (3.8) and (3.9), discussed on page 174, on the basis of the assumption that, inside a metal rendered superconducting, the magnetic flux B = 0. They borrowed this assumption from Gorter and Casimir, and they took this assumption to be justified because of Meissner and Ochsenfeld’s experiments and the other experiments listed in section 3.5. This assumption entailed that the phenomenon of superconductivity should be conceptualized not in terms of frozen in fields presenting a memory of a magnetic field applied earlier, but rather as a reversible phenomenon. Filling in this assumption gap emerges and with a sufficiently weak magnetic field, the perturbation can be taken to be 2 proportional to the square, or higher, of the field: Ψ = Ψ0 + H Ψ1, where Ψ0 is the unperturbed wavefunction. Substituting this back in [the equation for J] the bracketed term gives a contribution which, being quadratic in H, can be neglected in comparison with the term containing A” (French and Ladyman, 1997, p. 387). 330 The original German goes as follows: “Eine künftigeelektronentheoretische Behandlung hat also anscheinend etwas relativ einfaches zu zeigen, nämlich dass beim Entstehen und Fliessen eines Suprastromes, was die Ψ-Funktion angeht, gerade praktisch nichts geschieht, dass nämlich Ψ in schwachen Magnetfeldern nur eine Störungzweiter oder noch höhererOrdnung erfährt.Es wird zu zeigen sein, auf Grund welcher Koppelung die Verfestigung der Elektroneneigenfunktionen gegen magnetische Störungenzustande kommt”. 331 The original German states “Betrachten wir nun die Gleichungen (3.9), so ist zu bemerken, dass die Analogie mit dem diamagnetischen Atom nicht zu wörtlich genommen werden kann”. 332 From the context, it is clear that the expression ‘the atomic field’ here refers to the diamagnetic atom. The original German goes as follows: “Nun wissen wir gegenwärtignoch nicht, auf Grund welcher Koppelung der Elektronen im Supraleiter das Zustandekommen der relativen Verfestigung der Eigenfunktion gegen magnetische Störungenberuht. Sie ist jedenfalls eine ganz andere Koppelung als die im Atomfeld vorhandene Kern-Elektronenkoppelung, und es ist denkbar, dass diese noch unbekannte Koppelung eine Verfestigung der Elektronenwellenfunktion in erster Näherungauch gegen elektrische Störungenzustande bringt”.

180 Experiment, Time and Theory in the acceleration equation (equation 3.3, discussed on page 173) then led them to their equations, which in turn suggested the similarity with diamagnetism by means of a formal analogy with Gordon’s equations. This in turn led them to their diamagnetic programme, which would allow them both to overcome Bloch’s impossibility-theorem and to account for the occurrence of frozen in fields in the case of superconducting rings, if a satisfactory coupling interaction could be found. The Londons’ equations and their diamagnetic programme entailed, more specifically, that in order for the superconducting state to arise, a magnetic field had to be present: see their equation (3.8), where the current density J depends on the applied field H, and the quote on page 176. In this way, their equations entailed a reconceptualization of the superconducting phenomenon, since before, it was assumed that the superconducting state would persist even if the complete applied field had been removed. This also entailed that the experimental inference characterizing the experiments carried out by Kamerlingh Onnes and Tuyn had to receive a different interpretation (this experimental inference and Lorentz’s perfect conductivity interpretation were discussed on page 142).

On the Londons’ view, lowering the temperature T below TC while applying a magnetic field (H < HC ) would bring the electrons in a state Ψ, which was still unspecified because it was not known yet which interaction could be responsible for the coupling of the electrons (see the quote on page 180). In line with their future electron-theoretical account that was to be developed on the basis of the diamagnetic programme (see the quote on page 179), such a state would not be disturbed by variations in the applied field (∆H). It would, however, have to give rise to persistent currents, which could be expressed in terms of the Londons’ equations for the current J (see footnote 329 for how the Londons expressed their equation for the current in terms of their diamagnetic programme). Applying this expression to the data obtained by Meissner and Ochsenfeld in their measurements of the external magnetic flux B in the parallel cylinders experiment would then entail that B = 0 in the pure superconducting state. Their programme also suggested to them that if it could be worked out, it would also be able to account for frozen in fields as an exception when superconducting rings are present. As such, applying it to the observations made by Kamerlingh Onnes and Tuyn would also provide them with the information that in those cases, there would be frozen in flux, which could, however, be weaker than the field strength H0 applied before the transition: 0 < B ≤ H0. In short, the Londons’ interpretation of the experimental manipulations carried out by Kamerlingh Onnes and Tuyn, and by Meissner and Ochsenfeld and others, can be represented as follows:333

[The Zero Permeability Interpretation]: c i i (Ψ) + (∆H) −→ Ψ −→ J −−−−→ (B = 0)&(0 < B ≤ H0) I(∞),B

What the discussion above has also shown is that, at the time, the Londons themselves were quite aware of the gaps and limitations of their approach. For one,

333 I claim here that this interpretation can also serve for the experimental manipulations carried out by others, even though their measurements were not always based on the persistent currents, since they proceeded in the same way. Meissner and Ochsenfeld and others also brought about the superconducting state by lowering the temperature, applying a magnetic ﬁeld and then varying it in order to obtain information about the properties they were interested in.

181 Chapter 3. Experiment and Superconductivity they explicitly acknowledged that it relied on taking Meissner and Ochsenfeld’s experiments as providing insight into the ‘ideal superconductor’, which could become problematic because these experimental findings were still very uncertain (see the quote on page 179). And as we have seen on page 167, the experimental findings were not completely in favour of the Londons’ reading of Meissner and Ochsenfeld’s experiment: some took it as established by experiment, others saw it as not generally valid or as not complex enough. And even Gorter and Casimir had to point out, near the end of their thermodynamical analysis based on the assumption that B = 0, that this assumption was not without problems (page 172). What this shows is that “the London brothers started off by making the Meissner effect a postulate of the theory” (Matricon and Waysand, 2003, p. 71). This postulation relied, moreover, on a very specific interpretation of Meissner and Ochsenfeld’s results, since it focused completely on the first part of these results – i.e. that the measurements on two parallel cylindrical superconductors indicated that B = 0 –, while ignoring the second part, namely that the measurements on a hollow cylindrical lead tube did not indicate a permeability of zero. This, together with new experiments by Heidenreich, led Meissner himself to raise questions about the Londons’ interpretation of his experiments in his (1935) presentation for the Royal Society Symposium (see footnote 284):

These experiments of Dr. Heidenreich confirm the statement of our first publication, namely that the hypothesis of a vanishing magnetic permeability does not enable one to describe the results of the experiments with hollow cylindrical tubes. The recent experiments also give rise, I believe, to doubts as to whether the hypothesis of Gorter and Casimir is valid for all experiments. Especially the diagrams, taken from the observations, lead, so far as can be seen now, to the conclusion that the normal component of the remaining field at almost all points of the inner and outer surface of the crystal tube differs from zero, a fact which seems to me not to be favourable to the general validity of the hypothesis of Gorter and Casimir and therefore also of the theory given by the Londons. (Meissner, 1935, p. 15; original emphasis)

As such, we have good reasons to follow Kostas Gavroglu and Yorgos Goudaroulis (1989, p. 126) in their evaluation of the Londons’ interpretation of Meissner and Ochsenfeld’s experiments as rather ad hoc, in the sense that it was formulated solely in order to account for their idealized postulate, i.e. B = 0. Moreover, at the time it was not even always noticed that the Londons presented a new interpretation of what a superconductor was. While A.H. Wilson, for example, presented their work in his (1936) review article as oﬀering the most promising way forward for the development of such a theory, he also saw it, at the time, as oﬀering “a purely formal theory [. . . ] which attempts to explain some of the properties of the superconducting phase, without troubling about the reasons for its existence” (1936, p. 269). A similar view was held by Gorter, at least if we can rely on the trustworthiness of his later recollections (1964), in which he describes his evaluation of the Londons’ work at the time as follows:

In 1935, F. and H. London proposed their well-known equation according to which the curl of the supercurrent density is proportional to the

182 Experiment, Time and Theory

local magnetic field. Though the elegance of the treatment was certainly recognized, I am afraid that its importance was underestimated somewhat in Holland. It was sometimes considered as a completion of Becker, Heller, and Sauter’s formalism by fixing the integration constant of the magnetic field according to the Meissner effect. (Gorter, 1964, p. 5 – 6)

As such, while the London brothers saw their equations as pointing towards a completely new conception of superconductivity, albeit still in a programmatic way, this view was not shared by everyone at the time. In order to understand how this changed over a few years, in such a way that Fritz London could describe his work with his brother as arising out of the revolution that was Meissner and Ochsenfeld’s diamagnetic result (see page 130), we need to turn to how Fritz London elaborated it afterwards, in response to new experiments. For this will show, again in line with Gavroglu and Goudaroulis, that it was through its later success that the meaning of the Londons’ diamagnetic programme became established:

[B]efore the invention of the new – but ad hoc – auxiliary hypotheses in the old programme, before the unfolding of the new programme, and before the discovery of the new facts indicating a progressive problemshift in the latter, the objective relevance of the Meissner-Ochsenfeld experiment was very limited. (Gavroglu and Goudaroulis, 1989, p. 126)

We will turn, more speciﬁcally, to investigations concerning the transition between the superconducting and the non-superconducting state, with special attention for how this transition from a ‘pure’ superconductor – what the London brothers would call the ideal case – to a non-superconductor was conceptualized.

3.7 Superconductors, Diamagnetism and Experi- ment

In what follows, we will first discuss experiments, carried out after the Londons’ early publications, which Fritz London listed in his (1937a) article (discussed on page 189) as evidence in favour of his diamagnetic conception of superconductors: de Haas and O.A. Guinau’s (1936) experiments on monocristalline tin spheres; experiments by Mendelssohn, Keeley and Moore (1934; 1936) on the behaviour of mercury during the superconducting transition; and David Shoenberg’s (1936) experiments on the state of magnetization of superconductors when an inhomogeneous field is applied. After this, we will turn, on page 189, to the way in which Fritz London employed these different experiments for the elaboration of his diamagnetic conception of superconductors (1936a; 1936b; 1937a).

De Haas and Guinau De Haas and Guinau’s measurements on the magnetization of tin spheres, they stated in the opening paragraph of their (1936, p. 182) paper, were a continuation of de Haas and Casimir-Jonker’s (1934) measurements on changes in the magnetic ﬁeld distribution inside superconducting bodies during the superconducting transition (discussed on page 159). Whereas the earlier experiments were carried out on a

183 Chapter 3. Experiment and Superconductivity tin cylinder (see figure 3.9 on page 160), these new experiments involved tin spheres, since these allowed for the calculation of what de Haas and Guinau called the factor of demagnetisation, whereas the cylinder did not.334 They measured, more specifically, the magnetic field strength H, both on the surface of the sphere and inside in a canal parallel to the direction of the applied field, and the magnetic flux B in a canal perpendicular to the field’s direction. As in the previous experiment, they used bismuth wires for these measurements, since their change of resistance offered a good indication of changes in the magnetic field (see the quote on page 160). De Haas and Guinau first measured the resistance of the wires when the body, at a constant temperature T < TC , was rendered superconducting by the application of a magnetic field H < HC (perpendicular to the direction of the wires), after which the field strength H was gradually increased until the body was no longer superconducting. These measurements showed no increase in resistance after the application of a magnetic field H < HC , which indicated that the magnetic flux remained zero, and that it stayed like this until the applied field strength was 24 gauss, which is equal to 2/3HC : then a change in resistance, and hence an increase in magnetic flux, was measured, which continued until an applied field value of 36 gauss (HC ) was reached, at which point the body was no longer superconducting, and the magnetic flux B became equal to the applied field strength H. There was thus no longer any expulsion of magnetic flux from the body. De Haas and Guinau took this as a confirmation of von Laue’s Maxwellian analysis of superconductivity (discussed on page 163):

M. v. Laue (1932) drew attention to the fact that the presence of a supraconductive body disturbs the distribution of the lines of force, after Maxwell’s field theory. Taking a supraconductive body as a perfect conductor in Maxwell’s theory, he stated that the normal component of dB/dt has to be zero, as well as B itself, if the initial value of B was zero. It follows thus, that a supraconductor will behave macroscopically from 335 the point of view of field theory as a magnetic body, for which µa = 0. This theory has been confirmed by a number of experiments.336 Its starting point was the different behaviour of a monocrystalline tin wire in a longitudinal and transversal magnetic field as determined by de Haas and Voogd (1931a). (de Haas and Guinau, 1936, p. 185)

Further measurements of B at a fixed temperature with increasing H, both inside and on the surface of the sphere, and even with moveable bismuth wires, all seemed to confirm the claim that de Haas and Guinau ascribe to von Laue, namely that the body’s initial permeability is zero, and that it starts to increase when H = 2/3HC . When the field applied was parallel to the direction of the wires, however, a different picture emerged. While the measurements of the change of resistance on the outside of the sphere are in line with those obtained earlier, the measurements inside the sphere show not a continuous increase of magnetic flux from 24 gauss on, but rather a sudden increase from B = 0 to B = HC , even though the applied field H < HC .

334 Demagnetisation is the process by which a body loses its magnetic ﬂux B. 335 µa denotes the magnetic ﬂux at point a, i.e. the center of the superconductor. 336 Here, de Haas and Guinau refer to (Meissner and Ochsenfeld, 1933; Rjabinin and Schubnikow, 1934; Mendelssohn and Babbitt, 1935).

184 Experiment, Time and Theory

The value of B then remains the same until H = HC , after which they again increase continuously as in the previous measurements. According to de Haas and Guinau, this meant that the whole body could only be conceptualized in Maxwellian terms as a perfectly diamagnetic body, if this state of diamagnetism was not brought about by microscopical currents penetrating into the superconducting body, but rather by a single current on the sphere’s surface (de Haas and Guinau, 1936, p. 188). Other measurements carried out with constant ﬁeld and increasing temperature led to similar results, which brought de Haas and Guinau to the following general picture of the magnetic ﬂux during the transition from the superconducting to the non-superconducting phase:

The whole phenomenon can now be described as follows: When a magnetic field is applied to the sphere, an induction current is formed on the surface of it. This gives a behaviour for the external field and for the magnetic induction as if the body were perfectly diamagnetic. This remains true until the equatorial field strength has reached a value HC . Then, in the image of Casimir and Gorter, this current breaks down into a number of smaller currents, only part of the sphere is supraconductive from here on. The regions which are still supraconductive are in the beginning still rather large, but diminish rapidly. At 31 gauss they are smaller than the diameter of the canal. At HC nothing of these regions is left, supraconductivity is entirely destroyed. (de Haas and Guinau, 1936, p. 188 – 189)

Fritz London and the Intermediate State Until recently, Fritz London pointed out in the introduction of his (1936b) article, superconductivity was conceptualized in such a way that only the pure superconducting state (i.e. E = 0,B = 0)337 and the thermal equilibrium phase between the pure and the non-supraconducting state could be treated theoretically. This was not sufficient, however, as he argued by means of the following considerations regarding a sphere’s transition from the superconducting to the non-superconducting state: when H = HC at the sphere’s equator, the superconductivity will disappear there, and the applied magnetic field will start to penetrate the sphere. There, however, the applied magnetic field will still be below HC , and hence the superconducting state would arise again there (London, 1936b, p. 450). In order to conceptualize this, Fritz London introduced the idea of an intermediate state, which he borrowed from Gorter and Casimir (see page 171). His idea was, more specifically, to conceptualize this state in terms of what he called superconducting layers and needles in the body, which could cross, overlap and lay next to non-superconducting regions in such a way that the body could have parts of both phases while at the same time having a correct macroscopical mean B-value. Fritz London stressed, however, that this proposal should not be seen as a correct picture of what goes on fundamentally in the intermediate regions of a body during the superconducting transition. It was probable, he claimed, that his layers and needles

337 That the electric ﬁeld was also taken to be zero follows from the perfect conductivity conception. According to this view, the material’s resistance R, and hence also its resistivity η (see footnote 233), is equal to zero. Ohm’s law, in the formulation E = ηJ (see the same footnote), then tells us that the electric ﬁeld should also be zero (see footnote 327).

185 Chapter 3. Experiment and Superconductivity would turn out incorrect. What was important, however, was that they enabled him to obtain correct results about the intermediate state.338 What is significant about Fritz London’s account of the intermediate state is that it allowed him to substantially reconceptualize the equations (3.8) and (3.9) he had obtained with his brother (discussed on page 174). This reconceptualization concerned two aspects of these equations: the way in which they related to a theory of superconductivity, and how they related to the frozen in fields. Let us first turn to its relation with theory. In his lecture to the Royal Society, Fritz London characterized his work with his brother as providing macroscopical equations that still lacked any account of how the phenomenon came about (see also 178): “[t]he theory of which I should like to speak deals only with the macroscopical interpretation of supraconductivity” (1935, p. 24). In his work on the intermediate state, however, Fritz London proposed to take their equations as offering a microscopical theory of this state:

The equations, which earlier, in their application to superconductors in the pure superconducting state, were denoted as “macroscopical” (and contrasted with molecular-theoretical), will now, when we assume their validity inside each layer, in view of the intended intermediate picture, be taken as microscopical. (London, 1936b, p. 452)339

On this view, the London equations were used as microscopical equations governing the emergence and disappearance of the layers and needles that made up Fritz London’s hypothetical account of the intermediate state. In the article, Fritz London then elaborated how superconducting regions could be characterized in terms of the mean field strengths of the electric and magnetic fields present (E¯, B¯). For the magnetic fields, he was able to show how they play a role in the emergence of the intermediate state, by expressing that state in terms of the equations he had obtained with his brother. In this sense, these equations could now be seen as microscopical. Yet, as Fritz London pointed out at the end of his article, how to obtain the same result for the mean value of the electric field strength was still an open question (1936b, p. 461 – 462). The second reconceptualization of the Londons’ equations concerned their relation with frozen in fields. The Londons earlier took their equations to form the ideal case, which was contrasted with the case involving frozen in rings. This case was an exception because, on the assumption that their diamagnetic programme could be carried out, these frozen in fields were the consequence of a metastable state, not of the stable minimal energy state (see pages 150 and 177). Here, however, the contrast was rather between the pure state – in which B = 0 holds – and the intermediate state. This change shows itself especially clearly in how Fritz London

338 As he puts it in the concluding remarks of the paper, “it cannot be excluded that the structural considerations presented here have no real meaning at all, and that they form nothing more than an imaginative construction” (London, 1936b, p. 462) (“Es ist nicht ausgeschlossen, dass diese Strukturvorstellungen gar keine reale Bedeutung haben und dass sie nur als eine gedankliche Konstruktion zu werten sind”). 339 The original German goes as follows: “Die Grundgleichungen, welche fr¨uhergelegentlich ihrer Anwendung auf den Supraleiter im reinsupraleitenden Zustande zuweilen als ‘makroskopisch’ (im Gegensatz zu molekulartheoretisch) bezeichnet wurden, werden wir jetzt, wenn wir ihre G¨ultigkeit innerhalb jeder einzelnen Schicht annehmen, im Hinblick auf die beabsichtigte Mittelbildung als mikroskopisch zu betrachten haben”.

186 Experiment, Time and Theory characterized the way in which the case of frozen in fields should be treated: in his Royal Society lecture, he had proclaimed that it was probably connected “with the presence of non-supraconducting inclusions” and that it was “due to the presence of several components or phases in a complicated microscopical interpenetration” (1935, p. 25); in his (1936b, p. 451) paper, however, these frozen in fields were no longer a consequence of the intermediate state, but were rather to be accounted for solely in terms of the pure superconducting state.340 As we have seen (footnote 338), Fritz London himself pointed out that this elaboration of a theory of the intermediate state could well turn out to be a mere imaginative construction, and that it should be judged primarily in terms of its predictions. In this respect, he claimed, his account seemed in good correspondence with the facts. Elaborating how, on his account, the magnetic flux B behaves on the in- and outside of a superconducting sphere led him to suspect that, if the applied field H was weaker than 2/3HC , the magnetic flux inside the sphere would be zero, and that once H increased, there would be an increase in B as well. Hence, de Haas and Guinau’s experiments, which they themselves took to provide evidence in favour of von Laue’s classical Maxwellian analysis of superconductors as perfect conductors (see the quote on page 184), could now also be seen as evidence in favour of the reformulation of the Londons’ account in terms of Fritz London’s intermediate state.

Further Experiments: Mendelssohn and Shoenberg Keeley, Mendelssohn and Moore on the Ideal Superconductor We have seen that Fritz and Heinz London characterized their assumption B = 0 as the ideal or pure superconducting state, i.e. the Meissner effect realized under ideal experimental circumstances. In his (1937b) lectures, Fritz London did not really specify what he took to be such circumstances, but he did refer to a short article by T.C. Keeley, Mendelssohn and J.R. Moore (1934). In this article, they presented results of new investigations of what they saw as the result of Mendelssohn’s and Babbitt’s (1934) paper (discussed on page 155), namely “that the magnetic induction in tin spheres, which were cooled in an external magnetic field until they became supraconductive, did not vanish entirely, but that part of the magnetic flux remained in the body” (Keeley et al., 1934, p. 773). Keeley, Mendelssohn and Moore described this as an observation of freezing in of magnetic lines of force, a result that, they claimed, was confirmed by the experiments by Rjabinin and Schubnikow (see page 157) and Keesom and Kok (see page 166). Keeley, Mendelssohn and Moore then discussed how they extended these measurements to other substances, which were all shaped as long cylindrical rods. These rods were wrapped in a copper wire coil, and after they were cooled below TC , an external field H < HC would be applied and switched off. The application of the magnetic field would render the body superconducting, and on the frozen in fields idea, as we have seen, the strength of these fields – i.e. the magnetic flux B – would depend on the strength of the applied field. These frozen in fields would induce a current in the coil, and they measured how strong the induced current was for different applied field strengths. This gave them a ratio of frozen in flux to a specific

340 The original German goes as follows: “Inbesondere ist das Ph¨anomendes permanenten Ringstromes nur mit Hilfe der urspr¨unglichen Formulierung der rein supraleitenden Phase zu erfassen”.

187 Chapter 3. Experiment and Superconductivity applied field strength, which was expressed in terms of percentages (see figure 3.13 for the percentages in the case of an applied field strength H a bit below HC ).

Figure 3.13: The percentages of frozen in ﬂux obtained by Keeley, Mendelssohn and Moore for the diﬀerent materials they studied. Figure source: (Keeley et al., 1934, p. 774).

The data showed, according to Keeley, Mendelssohn and Moore, that for what they called pure substances (i.e., Hg, Sn (single- and polycrystalline), and Pb), the percentage of frozen in flux was very low. Once a second element was added, however, the percentage increased significantly. This suggested, as Mendelssohn put it in a later paper discussing further experiments, that “very pure substances with undisturbed crystal lattices approximate most closely to the ‘ideal’ supraconductor in Gorter’s sense” (Mendelssohn, 1936, p. 559). More specifically, what the results obtained in these later experiments indicated, according to Mendelssohn, was that the width of the transition region – i.e. the region between the temperature at which the applied magnetic field starts to penetrate the superconducting material, and the temperature at which the superconducting state has totally disappeared – was much smaller for pure specimens than for impure ones, hence suggesting a way to investigate more thoroughly ideal superconductors (Mendelssohn, 1936, p. 565). Mendelssohn then carried out such investigations on a sample of mercury tran- sitioning from the normal state to the superconducting state. This indicated, he claimed, that two phenomena could occur during this transition: the occurrence of frozen in fields, which was due, according to Mendelssohn, to the geometrical shape of the specimen used in the experiments, which led to the formation of superconducting rings; and the gradual decrease of magnetic flux within the sample, which occurred in such a way that after a certain point the magnetic flux becomes zero (B = 0) (Mendelssohn, 1936, p. 567). This showed, according to Mendelssohn, that during the superconducting transition investigated, there were regions within the body which were already in the ideal state – i.e. in thermodynamical equilibrium with B = 0 –, but that this did not happen for the whole body at once. From this he concluded that “[t]here may possibly exist an intermediate state in which the electrical resistance is already very small, but not yet zero” (Mendelssohn, 1936, p. 569).

Shoenberg and Superconducting Rings and Spheres Meissner and Ochsen- feld’s discovery of zero permeability, according to David Shoenberg, raised doubts about the belief that the magnetic properties of superconductors could be obtained on the basis of Maxwellian electrodynamics alone. This gave rise to a new interest in experimentally investigating the state of magnetization, but most of these experiments, Shoenberg remarked, only investigated materials that were rendered superconducting by means of a uniform magnetic field. He therefore proposed to investigate the influence of an inhomogeneous applied field on a sphere of pure lead (Shoenberg, 1936, p. 712). The sphere would be suspended in a balance specifically designed for the purpose, which provided data about its magnetic susceptibility

188 Experiment, Time and Theory in terms of the way in which it was deflected by variations in the applied inhomogeneous field. Shoenberg would carry out measurements, more specifically, at a constant temperature and with an applied field strength that would first be increased from H = 0 to H > HC , and afterwards decreased again until H = 0 (1936, p. 714).

The values obtained from H = 0 to H = 2/3HC , according to Shoenberg, were in line with both the perfect conductivity view and the zero permeability view. At H = 2/3HC , there would be an abrupt increase, after which there would be a linear increase again in magnetic susceptibility until HC was reached. When the applied field was decreased again, the magnetic susceptibility would also decrease in a way that was very similar to that obtained by increasing the applied field. This is what the Meissner effect would make us expect, according to Shoenberg (1936, p. 716). When H = 0 was reached again, there was some remaining frozen in flux, which was, however, significantly smaller than we would expect on the perfect conductivity view. While these results provided a confirmation of the Meissner effect, according to Shoenberg (1936, p. 717), they were hard to reconcile with either the perfect conductor view or with a pure B = 0-state, since neither of them offer a good way to account for the magnetic susceptibility when the applied field was between 2/3HC and HC , i.e. the applied field range after the sudden increase in magnetic susceptibility. This entailed that the real issue was not how to conceptualize the pure superconducting state (i.e. with H < 2/3HC ), since the confirmation of the Meissner effect showed that this pure state could be characterized in terms of zero permeability. Rather, these results “[transfer] the difficulty of understanding the meaning of zero permeability to the difficulty of understanding the ‘intermediate’ state” (Shoenberg, 1936, p. 724).

The London Equations and Diamagnetism: 1937 Until recently, Fritz London claimed in the opening of his (1937a) article, the study of superconductivity was primarily concerned with how to account for the emergence of electrical conduction without any resistance. The aim was, more specifically, to find an electron-mechanism that could explain, for the enormous number of different electronic states possible in a superconducting body,341 “why in these states the motion of the electrons should not be damped, that is, why the electronic waves should not be dispersed” (London, 1937a, p. 793). The question was thus why the currents on a superconductor did not experience any resistance. This question became even more pressing because of Bloch’s electron-theory of conduction, which suggested that there was in fact no current possible in the most stable state of the electrons (London, 1937a, p. 793). This problem was overcome, according to Fritz London, by Meissner and Ochsen- feld’s discovery “that a supraconductor behaves not only like an ideal conductor, but in addition also like a very strongly diamagnetic metal” (1937a, p. 793). As such, we would expect the electrons to behave like the entities that make up diamagnetic materials, a suggestion that Fritz London then elaborated by investigating

341 These different electronic states correspond to “the infinite number of different currents possible in it [i.e. a superconducting body], different as regards direction and intensity” (London, 1937a, p. 793).

189 Chapter 3. Experiment and Superconductivity the properties of a diamagnetic atom. Such an entity, he claimed, can exhibit currents in its most stable state, in the presence of an applied magnetic field. It can do this because it displays the following two properties: “(a) its lowest state is not degenerate and belongs to the discontinuous spectrum. Its wave function is real.342 (b) In a weak magnetic field h, the wave function Ψ does not experience stronger perturbations than those proportional to the square of h or still higher powers of 2 h: Ψ = Ψ0 + h Ψ1, where Ψ0 is the wave function for h = 0” (London, 1937a, p. 794). Investigating these properties then enabled Fritz London to show that “in such a manner a diamagnetic atom in its one lowest state can show an infinite variety of different currents corresponding to the infinite variety of orientations and intensities of the applied magnetic fields, whereas its wave function does not show any appreciable reaction” (1937a, p. 794). This suggested that the electrons constituting the superconducting state were very much like a diamagnetic atom, since these as well can display an infinite variety of currents, and because their wave function as well should also not be disturbed (see the quote on page 179). Because of this similarity, Fritz London then proposed to “assume that in a simply connected supraconducting metal there may be one or several discrete electronic states of the same properties (a) and (b)” as a diamagnetic atom displays (1937a, p. 794). Elaborating this assumption then led him to the equation (3.8) he had elaborated with his brother, which linked the current density to the applied magnetic field (discussed on page 174). As such, the similarity with the diamagnetic atom could provide information about the emergence of the superconducting state. At the same time, Fritz London repeated that we should not take this for granted, since the electron-mechanism responsible for this emergence was still not available:

From our observations apropos of the diamagnetic atom, we may infer that in our model the notorious diﬃculties discussed above will not appear. Compared with the former conception of inﬁnite conductivity the assumptions (a) and (b) certainly signify an appreciable reduction of the mechanism which remains to be explained by the theory of electrons. On the other hand, (a) and (b) form, of course, in no way a necessary basis of [(3.8)], and it is quite possible that the future development of the molecular theory will replace them by a still more reduced basis. (London, 1937a, p. 795; original emphasis)

As such, whether or not superconductors could actually be conceptualized as diamagnets or as similar to them still depended on how an electron-account of superconductivity, which was still subject of future research (London, 1937a, p. 836) would look like. At the same time, however, this lack of an electron-theory of superconductivity was less of a problem than it was a few years earlier. There, we saw, the Londons’ diamagnetic programme depended on whether a ﬁtting interaction between the electrons could be found that could account for a stable current in the minimal energy state. Fritz London’s notion of the intermediate state, which conceptualized the superconducting state in terms of layers of super- and non-superconducting regions, allowed him to sidestep this issue:

342 In his entry on Degeneracy in the Compendium of Quantum Physics, Daniel M. Greenberger describes it as follows: “when there is more than one solution to the Schr¨odingerequation for a given energy, the energy level is said to be degenerate” (2009, p. 159).

190 Experiment, Time and Theory

At first sight it seems extraordinarily difficult to make such a microstructure of layers accessible to theoretical treatment. To do this it would be necessary to solve a very complicated boundary problem for which the shape of the boundaries has still to be determined, whilst even their number is not yet known. It is possible, however, to avoid this practically insoluble problem, if one abstains from determining that microstructure in detail and rather restricts oneself to considering the mean values of the field strengths taken over this microstructure of the phases. Actually it is these mean values of the fields which are above all the object of the experimenter. (London, 1937a, p. 835; original emphasis)

This intermediate state account had recently been confirmed, according to Fritz Lon- don (1937a, p. 835 – 836), by the experiments by de Haas and Guinau, Mendelssohn, Keeley and Moore, and by Shoenberg. As such, the Londons’ equations, which offered a microscopical account of the intermediate state (see the quote on page 186), could be used safely without having to worry about the underlying electron- mechanism. Moreover, the intermediate state could also account for why the pure superconducting state, B = 0, represented the ideal case. Fritz London showed this by filling in this condition B = 0 in the Maxwell equations, in their formulation for obtaining the mean values of the field strengths in the case of the intermediate state. In that case, “for B = 0 the pure supraconducting regions become unlimitedly large, which signifies that the description with the mean values B and H can no longer be legitimate and that one has now explicitly to apply the equations of the pure supraconducting state to the supraconductor as a whole” (London, 1937a, p. 835). The condition B = 0 is thus the ideal case in the sense that, according to the theory of the intermediate state, it informs us about those cases where there is absolutely no non-superconducting region within the body: then we have to apply the London equations of the pure superconducting state to the whole body. As such, Fritz London concluded, his intermediate state could account for both the pure superconducting state and the exceptions, i.e. those cases that display frozen in flux. And given that the microscopical equations governing it could be derived on the assumption of the similarity with the diamagnetic atom, it also offered a way forward for the investigation of the electron-mechanism supposedly underlying the superconducting state. In this way, their equations, obtained out of Meissner and Ochsenfeld’s diamagnetic result, had given rise to what the title of Fritz London’s (1937a, p. 793) article called ‘A New Conception of Supraconductivity’.

Manipulability and the Intermediate State We have seen that on Lorentz’s perfect conductivity interpretation of the experimental inference characterizing the manipulations carried out by Kamerlingh Onnes and Tuyn, the results were to be explained in terms of a stream of electrons Nev (see page 143). Bloch’s impossibility-theorem entailed, however, that it was unclear how the electrons could give rise to a stream that would display the properties that were taken to characterize the superconducting state, i.e. zero resistance and persistent currents maintaining frozen in ﬁelds. Experiments, we have seen, could pinpoint what the speciﬁc issues were with this interpretation, by varying on aspects of the experimental procedure of which it was

191 Chapter 3. Experiment and Superconductivity an interpretation (see page 167 for a discussion of how the experiments discussed in section 3.5 varied on Kamerlingh Onnes and Tuyn’s experiments). And they could, up to a certain point, indicate which alternatives were more plausible and which were not: de Haas, Voogd and Casimir-Jonker could argue, for example, that von Laue’s perfect conductivity interpretation of the experiments by de Haas and Voogd was not very plausible (discussed on page 165). What the different experiments discussed could not do, however, was provide an alternative interpretation, or indicate which one was correct: while some experimenters took their results to clearly favour one interpretation, other experiments were taken to point to another or to indicate that neither of the available interpretations would do. This was also the case for the zero permeability interpretation offered by the London brothers. It was only by turning the results of Meissner and Ochsenfeld’s parallel cylinders experiment into a postulate – the Meissner effect – that they could claim that these experiments and those that followed argued in favour of their zero permeability interpretation. This claim could, moreover, be disputed, since while their interpretation could make sense of some results, it could not account for others, as Meissner, for example, claimed about the Londons’ account of his hollow cylinder experiments (see page 182). The same can be said about Fritz London’s (1937a) work on the intermediate state. While he claims there that Meissner and Ochsenfeld discovered that superconductors behave like very strongly diamagnetic metals, that is not what Meissner and Ochsenfeld’s experiment provided, and it is not even what the Londons’ (1935a) interpretation of the experimental results entailed: as we have seen on page 175, their diamagnetic programme allowed for either weak Peierls-Landau diamagnetism or for a stronger diamagnetism, depending on how the electrons were conceptualized. Even Fritz London himself seemed to realize, further on in his (1937a) article, that the diamagnetic interpretation was not yet established: he had to assume that, just as diamagnetic atoms do, the electrons constituting the superconducting state also display the properties (a) and (b) (see page 189), and he had to admit that only an electron-theory of superconductivity could, in the end, tell us whether superconductors were (similar to) diamagnets (see the quote on page 190). However, this was not as pressing a problem for the Londons’ account anymore, since the intermediate state account developed by Fritz London, which he saw as offering a microscopical account of the behaviour described by the equations he developed with his brother, had been confirmed, he claimed, by more recent experiments. Here again we see the same pattern as with the experiments discussed in section 3.5. While these new experiments can be taken to indicate that there is such a thing as the intermediate state, they are less clear on how this state is to be conceptualized: de Haas and Guinau accounted for it in terms of von Laue’s perfect conductivity conception (see the quote on page 184); Mendelssohn, Keeley and Moore saw their results as indicating that there may possibly exist an intermediate state (see page 188); and Shoenberg took his results primarily to indicate that the real difficulty was with how to understand this intermediate state. As such, while the results obtained by these different experiments could be in line with Fritz London’s account of the intermediate state, they definitely did not provide a confirmation of it. What they did provide, however, was information about how a pure state of superconductivity could be distinguished from an impure or intermediate state: all

192 Experiment, Time and Theory three of them indicated that there was relatively little magnetic flux inside a superconducting body as long as the applied field was under 2/3HC . What enabled them to provide data that could be taken to support this claim, were further variations on how a superconductor’s state of magnetization was measured: de Haas and Guinau improved on the way in which bismuth wires could be attached to, and inserted in, a superconducting body; Mendelssohn, Keeley and Moore made use not only of pure metals but also of mixtures (see figure 3.13 on page 188); and Shoenberg employed inhomogeneous instead of uniform applied magnetic fields. Introducing these variations could then provide them with more information about how the pure superconducting state differed from the intermediate state during transition. While the results of these experiments should not be taken as an agument or decision in favour of Fritz London’s account of the intermediate state, his account could offer an interpretation of how the manipulations carried out in these experiments would give rise to the effect produced. In line with his claim that the actual object of the experimenter are the mean values of the field strengths (see the quote on page 191), this interpretation stated that lowering the temperature T below TC and applying a magnetic field (H < HC ) would give rise to an intermediate state (E¯&B¯). Varying the applied magnetic field (∆H) would then change the mean field strengths (E¯ 0&B¯ 0), which would entail a variation in the persistent currents that could be expressed in terms of the Londons’ equation for the current J (equation 3.8 on page 174). Applying this intermediate state account to the observations of persistent currents I(∞) by Kamerlingh Onnes and Tuyn, to the data obtained by Meissner and Ochsenfeld of the external magnetic flux B, or the data produced by de Haas and Guinau on the resistance R would then show them that all these displayed regularities that were to be expected on the intermediate state account: either zero permeability (B = 0) in pure superconducting regions or frozen in flux (0 < B ≤ H0) in regions characterized by superconducting rings. As such, we can represent Fritz London’s intermediate state interpretation of the experimental manipulations discussed in this chapter as follows:

[The Intermediate State Interpretation]: c 0 0 i i (E¯&B¯) + (∆H) −→ E¯ &B¯ −→ J −−−−−−→ (B = 0)&(0 < B ≤ H0) I(∞),B,R

3.8 Investigating the State of Magnetization

This chapter has shown that the experimental manipulations carried out by Kamer- lingh Onnes and Tuyn and Meissner and Ochsenfeld and others can be characterized in terms of the experimental inference discussed on page 142. This inference links the application of a magnetic field and the lowering of the temperature to the emergence of a superconducting state, which can in turn be manipulated by means of variations in the applied field, in such a way that the changes in the currents induced on the superconducting material can provide information about properties of the superconducting materials such as their microresidual resistance, their magnetic susceptibility or the invariance of the current distribution. This information in turn could be taken to provide information about their state of magnetization and frozen in flux.

193 Chapter 3. Experiment and Superconductivity

As in the previous chapter, we have seen here that, in order for such manipulations to provide information of this kind, the inferences that characterize them have to be interpreted. Such an interpretation is provided by a model of the electrons that are responsible for the superconducting state, and it provides an account of how the influence of the manipulation on these electrons is to be understood, and what kind of effect we can expect if these manipulations are carried out correctly. If this is the case, then these results can be seen as a validation of the model that offered the interpretation. Lorentz’s perfect conductivity interpretation, for example, allowed him to make sense of the data obtained by Kamerlingh Onnes and Tuyn, and the results of these experiments in turn could be taken as a validation of his perfect conductivity account. That such an interpretation is essential for obtaining information out of data produced by experimental manipulations is shown very clearly by Bloch’s attempts to formulate an account of superconductivity in terms of his quantum-mechanical electron-theory. Given that he could not find a causal mechanism responsible for the results produced in experiments such as those by Kamerlingh Onnes and Tuyn, he even started to doubt whether there was in fact a phenomenon for which a causal mechanism should be found. As he put it in the more radical formulation of his impossibility-theorem, ‘superconductivity is impossible’ (see the quote on page 149). Without an interpretation, Bloch began to doubt whether the data in fact provided information at all about any kind of phenomenon. Given this lack of a fitting interpretation, it was unclear how the data obtained in the experiments carried out at around the time of Bloch’s work on superconductivity, discussed in section 3.5, had to be understood. Most, except von Laue (see the quote on page 164), took them to indicate that there were some issues with the perfect conductivity conception. They could be taken to provide this information, because by varying on central aspects of the experimental set-up and procedure employed by Kamerlingh Onnes and Tuyn, they obtained results that seemed difficult to accommodate from the point of view of perfect conductivity (see page 168 for a discussion of the different variations). This indicated that the results produced by means of the original set-up and method were not as robust as assumed. As we have seen, it was less clear, however, what these new experiments said about how to proceed further. It was only through the London brothers’ elaboration of an electromagnetic phenomenology of Gorter and Casimir’s assumption B = 0 that a programme for the development of an alternative interpretation became available. According to this programme, it was only when a magnetic field was present that the electrons would give rise to a stream displaying the properties that the Londons ascribed to the superconducting state, i.e. zero permeability and the possible formation of superconducting rings. This was primarily a programme, since it lacked an underlying electron-mechanism that explained how the data produced in the experiments could come about. As such, this interpretation showed that Meissner and Ochsenfeld’s parallel cylinders experiments had worked properly, i.e. produced effects that were to be expected, on the assumption that a fitting interaction could be found. Through the development of his theory of the intermediate state, Fritz London argued, however, that this search for an electron-mechanism could be sidestepped, and in this way, he obtained an actual interpretation for the different experiments discussed here. On this interpretation, the influence of variations in the applied field

194 Experiment, Time and Theory was conceptualized not primarily in terms of the electrons constituting the persistent currents, but rather in terms of the mean field strength values, which in turn were taken to be responsible for the formation of new pure superconducting regions and superconducting rings. These would then be responsible for the different effects obtained in the different experiments, in such a way that the results obtained by Meissner and Ochsenfeld could be taken to be robust, i.e. to provide information about the properties of the pure superconducting state, and in such a way that the results obtained by Kamerlingh Onnes and Tuyn could also be seen as robust insofar as they were taken to concern only regions containing superconducting rings. As in the previous chapter, the historical discussion here thus shows that experimental manipulations have to be interpreted in order for the data produced by them to make sense. Such interpretations were, again, offered from particular theoretical standpoints. As such, this chapter can be taken as an illustration of Morrison’s claim that for manipulation to provide information about what is manipulated, theoretical information about what is supposedly manipulated is already required. It is difficult to state which information the experimental manipulations carried out by Kamerlingh Onnes and Tuyn or by Meissner and Ochsenfeld provided by themselves: it depends on how one interprets the experimental inference characterizing these manipulations. The information provided by experimental manipulations transforms over time. This transformation also provides an illustration of Arabatzis’ point that the causal claims obtained by means of manipulation are subject to conceptual change through changes in theory. What was brought about by lowering the temperature and applying a magnetic field depended on the interpretation used: a perfect conductor according to Lorentz, the intermediate state according to Fritz London. The way in which these theoretical changes occured also shows that neither French, Ladyman and Bueno nor Cartwright, Suárez,and Shomar correctly characterize Meissner and Ochsenfeld’s experiments (see page 131). Both sides take Meissner and Ochsenfeld’s experiments to provide some kind of direct insight into the pure superconducting state. Suárez et al. claimed that Meissner and Ochsen- feld’s experiments showed that superconductors are diamagnets. French et al., on the other hand, claimed that the experiments showed that superconductors are analogous to diamagnets. Neither reading fits Meissner and Ochsenfeld’s experiments, however, since, as Meissner and Ochsenfeld themselves pointed out, their two experiments together – parallel cylinders and hollow cylinders – provided results that were very difficult to combine in one representation (see the quote on page 154). Insofar as they could make sense of their own experimental results, Meissner and Ochsenfeld took them, moreover, to suggest not that they are (analogous to) diamagnets. They rather saw them as suggesting the further elaboration of the ferromagnetic analogy (see page 154). It was only if one accepted the Londons’ postulation of the Meissner effect that one could take Meissner and Ochsenfeld’s parallel cylinders experiment as evidence for the pure superconducting state displaying zero permeability. But there were reasons to doubt the generality of this postulate, as Meissner himself pointed out (see page 182). Even the London brothers themselves had to admit that their postulate was based on an idealization of uncertain experimental results. And, as Fritz London pointed out in his (1937a) paper on the intermediate state, the analogy between their account and the diamagnetic atom should not be taken as establishing that the

195 Chapter 3. Experiment and Superconductivity electrons constituting the superconducting state are in fact like diamagnetic atoms (see the quote on page 190). As such, neither philosophical reading of Meissner and Ochsenfeld’s experiments seems to hold: instead of the experiments showing that superconductors either are or are analogical to diamagnets, we rather have Fritz and Heinz London postulating that Meissner and Ochsenfeld discovered the Meissner effect, which entails that superconductors can be studied as diamagnetic materials of some kind. This now also provides an illustration of Massimi’s claim that a manipulation in itself does not necessarily provide insight into what was responsible for the results obtained. According to Meissner, it was the behaviour of electrons as the spontaneous current approach conceptualized them that had given rise to his data. For Fritz London, on the other hand, it was the behaviour of electrons as the diamagnetic programme characterized them. This at the same time also shows a difference with Massimi’s claim that it is theory that informs scientists about which entities are manipulated. Here, we rather see that it is by means of theoretical programmes that scientists try to provide an interpretation of the manipulations carried out in an experiment. Neither Meissner nor Fritz London relied on an established model or theory of superconducting electrons, but rather on programmes for the future elaboration of such a model. This is very similar to what we found in the previous chapter, where the data obtained by Kaufmann were not interpreted in terms of an established electron-model, but either in terms of the electromagnetic world view or the relativistic approach. This shows that the experimental manipulations carried out by Kamerlingh Onnes and Tuyn or by Meissner and Ochsenfeld should not be seen as establishing, by themselves, any information about superconductors or the electrons constituting them. And the information that they provide under a specific interpretation is not to be characterized as any kind of established factual information. Meissner and Ochsenfeld’s experiments did not show that superconductors are (analogous to) diamagnets, not even on the zero permeability interpetation. They rather indicated that the perfect conductivity conception was less plausible than assumed, and that an account of the electrons responsible for the emergence of the superconducting state had to take into account the application of the magnetic field. As such, on the zero permeability interpretation, what Meissner and Ochsenfeld’s experiments primarily did was delineate a space of possible electron-models, i.e. of models that could account for the data produced by the experimental manipulations carried out by Meissner and Ochsenfeld.

196 Chapter 4

Manipulation and an Epistemology of Exploration

4.1 Introduction

Scientific realists such as Putnam, we have seen in chapter 1, assumed that it is scientific theory that informs us about both the existence and the identity of unobservable entities. It was successful theory, more specifically, that we could take to be approximately true with respect to existence and identity, where this success was conceptualized in terms of a correspondence between the theory’s observation sentences and the observable world. In response to the arguments raised by Quine, van Fraassen and Laudan against this approach, Cartwright and Hacking presented their entity realism as an alternative, according to which the successful manipulation of an entity provides us with a good argument for its existence. A manipulation of an entity’s causal properties is taken to be successful if it brings about, in a reliable and robust way, an effect expected on the basis of the causal knowledge we have of the entity, i.e. what Hacking calls home truths. If we can manipulate in such a way, Cartwright and Hacking claimed, we have as good evidence of its existence as we can get. This evidence does not fall prey to the arguments raised against the standard realist position, since the home truths obtained are theory-independent, in the sense that they are not concerned with a theory of the entity’s identity (see, e.g., Cartwright’s claim, discussed on page 26, that the causal knowledge we obtain about the electron remains the same, whether we adhere to Bohr’s, Rutherford’s, or Lorentz’s electron-theory, or Hacking’s claim, discussed on page 21, that manipulation involves common lore, not common core). This theory-indendence of the home truths or capacity-claims obtained by means of manipulation was, however, disputed by Morrison, Massimi and Arabatzis. Mor- rison argued that the distinction between home truths and theory was not clear and not tenable, which raised the question why we should be realists with respect to the first but not the second. According to Massimi, in order to claim that bringing about a certain effect by means of a manipulation provides evidence for the existence of a particular entity, one needs to identify that entity as responsible for the effect, and not another one, and this involves a theory of the entity. Arabatzis, finally, argued that the causal knowledge expressed in the home truths obtained by means of experimental manipulations was equally well subject to theoretical change over time. As such, they claimed, if Hacking and Cartwright want to argue that ma-

197 Chapter 4. Manipulation and Exploration nipulation leads to the factual knowledge that the entity manipulated does indeed exist, we also need to ascribe theoretical beliefs about the entity’s identity to the scientists carrying out the manipulation. We then end up with the same issues that plague standard scientiﬁc realism about theories, as Massimi indicates very clearly in the quote on page 38 (see also the quote by Morrison on page 34). The argument by Massimi, Morrison and Arabatzis raises a valid point about the viability of the manipulability-idea for the development of a realist position. It also raises an epistemological question, however, which they do not really elaborate, but which is worth investigating. More can be said, I believe, about the epistemological aspects of manipulability than was done by Cartwright and Hacking. Cartwright and Hacking believed that manipulability in itself, i.e. without theory, provides scientists with established factual knowledge (Hacking’s home truths) of the causal properties of the entity manipulated. Given, however, that Morrison, Massimi and Arabatzis problematized these home truths, one may wonder how we are to understand the information about an entity’s properties obtained by means of manipulation. Hence, the following research question arises:

[Research Question]: How are we to characterize the information provided by experimental manipulations?

We have turned to a discussion of two historical episodes concerning experiments where the existence of the manipulated entities was not under discussion, in order to obtain more insight into what these experiments could teach us about the entities under study. These discussions have shown that manipulations carried out by scientists can be conceptualized in terms of experimental inferences. These link the supposedly established properties of the entity manipulated – e.g. its charge-to-mass ratio /µ0 or its zero resistance (R = 0) – to its more hypothetical properties, i.e. those properties that are the subject of the experimental investigation: the transverse mass m⊥ or the magnetic flux B. These discussions also showed that experimental manipulations, characterized in terms of such experimental inferences, do not lead in themselves to any factual knowledge about the properties investigated. In both cases, we found different and incompatible interpretations of the experimental inferences. For Kaufmann’s experimental inference (page 55), we have Abraham’s electromagnetic interpretation (page 56), Poincaré’srelativistic interpretation (page 66) and von Laue’s relativistic interpretation (page 123); and for Kamerlingh Onnes and Tuyn’s experimental inference (page 142), we have Lorentz’s perfect conductivity interpretation (page 143) and Fritz London offering both a zero permeability (page 181) and an intermediate state interpretation (page 193). This indicates that characterizing the knowledge obtained by means of manipulation in terms of factual information provided by the manipulation in itself, will not do. My aim in what follows is to elaborate an alternative characterization using work by Friedrich Steinle (1997; 2002) and Michela Massimi (2018; 2019) on exploration by means of experimentation and modeling.343 This work will allow me both to elaborate an alternative epistemology, which I will call an epistemology of exploration, in such a way that we can obtain a more adequate understanding of the information contained in the experimental inferences discussed in chapters

343 I will stick to Steinle’s and Massimi’s work on exploration here, since it is suﬃcient for the discussion. For a more general overview of exploratory experimentation and its history within philosophy of science, see Schickore (2016).

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2 and 3, and to pinpoint how, underlying the entity realist approach, there is still a standard scientiﬁc realist epistemology. This can then inform us about where the anthropology shared between both forms of realism needs to be adapted and corrected.

4.2 Exploration in Experimentation and Model- ing

4.2.1 Steinle and Exploratory Experimentation At first, it can seem quite strange to approach the experimental inferences discussed in the previous chapters in terms of exploration, since exploratory experimentation “is typically practiced in periods in which no theory or – even more fundamentally – no conceptual framework is readily available” (Steinle, 1997, p. S65). And exploratory modeling as well is primarily carried out “in domains that are still very much open-ended for scientific discovery” (Massimi, 2018, p. 338). The experimental inferences discussed in the previous chapters were formulated in a thoroughly theory-infused context. In the case of the Kaufmann experiments, we have Abra- ham’s and Lorentz’s electrodynamics, the theory of relativity and the work by Planck and Einstein on a theory of the quantum. In the superconductivity case, we have the Drude-Lorentz theory of the electron, Bloch’s quantum-mechanical electron-theory of conduction and Fritz London’s theory of the intermediate state. Still, we will see that the ‘epistemology of exploration’ offered by Steinle’s and Massimi’s work can offer a very insightful account of how to understand the information provided by experimental manipulation. Steinle elaborates his concept of exploratory experimentation by means of a contrast with what he calls theory-driven experimentation, which is what the standard philosophical view, as he calls it, takes to be the only epistemologically significant type of experimentation.344 According to this view, “[e]xperiments are done with a well-formed theory in mind, from the very first idea, via the specific design and the execution, to the evaluation” (Steinle, 1997, p. S69). Such theory-driven experimentation does not merely concern the testing of theories. It can equally well be concerned, for example, with measurements of a specific theoretical parameter. What is essential, however, to this kind of experimentation, is that it is theoretical considerations that drive scientists to carry out experiments. This entails that the experimental set-up used is quite rigid, because theory tells us exactly how to carry out the experiment in order to obtain the theoretical results searched after: “[l]ittle room is left for completely unpreconceived outcomes, the very design of the instrumental arrangement may exclude many of those” (Steinle, 1997, p. S70).345

344 Not all experiments that are not theory-driven would be exploratory: “[a]lthough exploratory experimentation is not theory-driven, it is not the counterpart of theory-driven experimentation. There may be various types of experimentation not driven by theory. Exploratory experimentation is but one of them, namely that one which has the goal of finding experimental rules and systems of those rules” (Steinle, 1997, p. S71). 345 The following experiment by Ampère,in which he tried to find experimental evidence for the attraction and repulsion between two electrical currents, provides a clear example of theory- driven experimentation according to Steinle: “Two spirals of wire were connected within the same electrical circuit and placed opposite one another. The first spiral was supported on a fixed stand,

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Exploratory experiments, on the other hand, are not carried out in order to accomplish particular theoretical aims. They are rather “driven by the elementary desire to obtain empirical regularities and to find out proper concepts and classifications by means of which those regularities can be formulated” (Steinle, 1997, p. 70). Because of this, this form of experimentation is characterized by very different methodological guidelines than theory-driven experimentation. Carrying out exploratory experiments involves, for example, varying a large number of parameters of the experimental set-up, or trying to obtain ‘simple’ or ‘elementary’ cases, which comes down to searching the minimal experimental conditions required for bringing about an empirical regularity (Steinle, 1997, p. S70). This requires, in contrast to the set-ups used in theory-driven experimentation, a large amount of flexibility in the experimental set-up: “[i]nstruments for exploratory work have to allow for a great range of variations, and likewise be open to a large variety of outcomes, even unexpected ones. The restrictions posed by the experimental arrangement must not be too confining” (Steinle, 2002, p. 422).346 The main difference with theory-driven experimentation, according to Steinle, is their epistemological context. While theory-driven experiments are carried out within a context of higly elaborate theory, exploratory experiments are carried out to elaborate concepts where there are none yet.347 These concepts are supposed to enable us to classify and categorize any empirical regularities we can find, but finding such a classification is quite a complex process, Steinle points out, since we do not have a way to test directly whether concepts are correct or not. It is because of the flexibility of the set-ups used that exploratory experiments offer a good way to investigate whether tentative conceptualizations are applicable to a field that has not been conceptualized yet, since slight changes in the set-up can immediately tell whether a particular conceptualization still holds. The epistemological significance of these kinds of experiments thus lies in that they allow for the development of a conceptualization and classification of a field of study: while the second could swing like a pendulum towards and against the first. The arrangement was designed explicitly to search for a specific effect: From the speculation that all magnetism might be made up of (hypothetical) circular electric currents within the mass of magnetic bodies, Ampère anticipated that two electrical currents, running in spirals, should attract or repel one another without the mediation of iron (i.e., without magnetic effects being involved)” (1997, p. S67). 346 Another experiment by Ampère,in which he searched for the effect of an electric wire on a magnetic needle, provides Steinle with an example of exploratory experimentation: “In a very early stage of his research, Ampèrepresented an experiment which he called the ‘astatic magnetic needle’ [. . . ]. A magnetic needle is supported such that it can rotate only in a plane perpendicular to the plane of the magnetic dip. Thus terrestrial magnetism cannot affect its motion, and the effect of an electric wire, supported by two variable posts, can be studied by itself. As a result of the experiment, Ampère formulated the general rule that the needle always swings into a position perpendicular to the direction of the wire” (1997, p. 66). This experiment is exploratory rather than theory-driven since its aim was not to search for proof that a specific effect exists, but rather to investigate whether there was a rule governing the behaviour of the needle in the presence of an electric wire. Because of this, the experimental set-up allowed for many variations with respect to the relative positions of the needle and the wire. 347 For an extensive overview of the philosophical discussion on concepts in scientific practice, see the edited volume by Uljana Feest and Steinle on this topic: Feest and Steinle (2012). For Steinle’s views on concepts, see his (2009) article and his chapter in this volume (2012, p. 105 – 125). Unfortunately, I cannot go into detail here on how we are to conceptualize a concept philosophically. I will rather stick to an intuitive conceptualization of concepts as offering a classification of objects and phenomena.

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The epistemic significance of such developments is immense. Concepts and classifications – the very language used to deal with a certain field – determine on a fundamental level the development of the thinking and acting within that field. Any more specific theory necessarily makes use of those concepts and classifications. In the process of forming and stabilizing the conceptual framework, decisions are made to which a whole subsequent development of more specific theories may be lastingly – and sometimes unconsciously – committed. (Steinle, 1997, p. S72)

What it means for a concept to be stable, according to Steinle, is that it allows us to formulate “stable and more or less general regularities on a phenomenological level, and thus enabling a reliable handling of instruments and apparatus” (2002, p. 423). Such a stability is always historically situated, in the sense that concepts can become destabilized, once it becomes apparent that they do not allow us to do what they are supposed to do anymore. In this way, concepts are subject to change, and such reconceptualizations often entail that “[o]nce [. . . ] a new language [. . . ] has been formed, it becomes diﬃcult to put oneself back in the previous state in which that language did not exist” (Steinle, 2002, p. 423).348

4.2.2 Massimi and Exploratory Modeling Massimi does not explicitly link her work on exploratory modeling (2018; 2019) with Steinle’s work on exploratory experimentation. Still, as we will see, it does pay off to discuss them together. This is not only because Massimi’s work will allow us to elaborate further the exploratory epistemology underlying Steinle’s notion of exploration, but also because in both historical episodes discussed, exploratory modeling and exploratory experimentation were often carried out in tandem. Massimi develops her notion of exploratory modeling in the context of a discussion of what she calls the ‘problem of inconsistent models’ (PIM), which is a problem that arises for those who are realists about models, i.e. those who take them to be (partially and approximately) true. The problem arises once one, as a realist, accepts both the claim that scientific models in some way are supposed to offer a representation of a target system, and the claim that there can be more than one model within scientific practice that represents a particular target system. For in that case, one ends up with the metaphysical problem that, if we have multiple models that successfully represent, a particular target system can display incompatible properties:

If diﬀerent models (partially and approximately true though they might be) veridically represent relevant properties of the target system and (here come’s PIM’s bite) these properties are both essential and inconsistent with one another, a problem of metaphysical inconsistency arises (i.e., model M1 delivers a partial, veridical representation of properties

348 Steinle illustrates very clearly how reconceptualizations can have this influence by means of the following quote from the microbiologist Ludwik Fleck: “if after years we were to look back upon a field we have worked in, we would no longer see or understand the difficulties present in that creative work. The actual course of development becomes rationalized and schematized. We project the results into our intentions; but how could it be any different? We can no longer express the previously incomplete thoughts with these now finished concepts” (Steinle, 2002, p. 423).

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a1, b1, c1, while model M2 delivers a partial veridical representation of properties a2, b2, c2, which are inconsistent with a1, b1, c1). (Massimi, 2018, p. 336)

What gives rise to this problem, Massimi then argues through an analysis of the argument that leads to this claim, is “the assumption that different models ascribe different essential properties to the same target system” (2018, p. 345), where essential properties are those “that ground the disposition of the target system to behave in certain ways in the right conditions” (2018, p. 337). While this is often used as an argument against realism about models, Massimi then argues that we can remain realists if we commit ourselves to an alternative characterization of how models represent. Models, on her view, do not provide us with factual knowledge of the essential properties of target systems, but rather with modal knowledge of what might be possible about the system. This leads her to characterize models as fulfill- ing an exploratory function, in the sense that they offer “an exercise in imagining, or to be more precise, physically conceiving something about the target system so as to deliver modal knowledge about what might be possible about the target system” (Massimi, 2018, p. 339).349 We can then be realists with respect to such exploratory models, according to Massimi, in the sense that they offer partially true representations of the possibilities of a target system. It is just that the states of affairs about which they are true involve possible entities, i.e. entities about which it is not known whether they are actual or fictional (Massimi, 2018, p. 349). On Massimi’s account, what exploratory modeling allows us to do is to investigate what is objectively possible for the hypothetical entity modeled, which provides us with knowledge of the “possibilities concerning the very existence of the model’s hypothetical target system” (2019, p. 7). Exploratory modeling is able to provide such knowledge because it is constrained by laws of nature that “fix [. . . ] the nomological boundaries within which inferences about the hypothetical target system can take place” (Massimi, 2019, p. 7). Ex- ploring these models then provides scientists with different “how-possible inferences: How could [the possibilities] x1,..., xz be possible, were [the properties] y1,..., yn 350 physically conceivedLB thus-and-so?” (Massimi, 2019, p. 8). Scientists can then track objective possibilities by means of a bootstrapped inference process, where at each stage, certain inferred possibilities are ruled out by means of new experimental data:

349 Massimi often calls such models perspectival models. She does not call them exploratory models per se, to emphasize that perspectival models perform more than the four exploratory functions that models, according to Axel Gelfert, can perform in scientific practice: “they may function as a starting point for future inquiry [. . . ], feature in proof-of-principle demonstrations [. . . ], generate potential explanations of observed (type of) phenomena [. . . ], or lead to assessments of the suitability of the target” (Massimi, 2018, p. 339). Since my aim here is to draw parallels between Steinle’s and Massimi’s work, I will stick to the term ‘exploratory modeling’. 350 On Massimi’s view, that something is physically conceivable comes down to the following: “p is physically conceivable for an epistemic subject S (or an epistemic community C) if S’s (or C’s) imagining that p not only complies with the state of knowledge and conceptual resources of S (or C) but it is also consistent with the laws of nature known by S (or C)” (Massimi, 2019, p. 3). The LB-subscript means that here she is concerned with law-bounded conceivability, one form of physical conceivability offered by exploratory modeling. Another form is what she calls law-driven conceivability, which is connected to the use of fictional, targetless models, i.e. models that are about entities known not to exist. Because this other kind of exploratory modeling is not of importance to what will follow, it will not be discussed here.

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As new pieces of experimental evidence e1,..., e3 are brought in, they reﬁne the how-possible inferences by excluding more and more of the live objective possibilities x1,..., xz. This is because new evidence gradually and increasingly constrains what is physically conceivableLB (i.e. the antecedents y1,..., yn of the how-possible inference). (Massimi, 2019, p. 9)

4.2.3 Uljana Feest and the Process of Stabilization

Steinle’s and Massimi’s conceptualizations of the epistemology of exploration concern different elements of scientific practice: while Steinle is concerned with experimentation, Massimi focuses on modeling. Still, neither is concerned solely with either experimentation or modeling: on Steinle’s view, exploratory experimentation goes hand in hand with the formation and stabilization of concepts; and on Mas- simi’s view, exploratory modeling is a process that is bootstrapped by means of experimental input. This indicates that an epistemology of exploration can, and possibly should, be formulated in such a way that it conceptualizes the exploratory process as involving links between experimentation and modeling.351 I will elaborate how such links could be understood by means of a discussion of Uljana Feest’s (2011) conceptualization of the process of stabilization. This will then provide an adequate starting point for developing an exploratory epistemology of manipulation. Feest (2011) is concerned with what she calls the stabilization of phenomena. Her aim is to bring together two closely related conceptions of phenomena. The first is Hacking’s, which was already discussed in section 1.4.3, and which emphasizes, according to Feest, “that a good deal of empirical work in the sciences consists on efforts to make phenomena observable” (2011, p. 59). The second is a conceptualization of phenomena offered by James Bogen and James Woodward (1988). They draw a distinction between what is directly observable in experiments, which is what they call data, and that which these data are supposed to be an instantiation of, i.e. a phenomenon. As Feest puts it, “scientists do not directly observe phenomena, but rather use data to gain evidence for claims about phenomena” (Feest, 2011, p. 59).352 At first, it could seem that these two conceptualizations of phenomena are in contradiction with each other, since, on Hacking’s view, phenomena are created and made observable in experiments, whereas on Bogen and Woodward’s view, phenomena are not observable but are rather inferred from that which is produced in an experiment, namely data. Bogen and Woodward themselves, for example,

351 This assumes, of course, that one can take scientific models to offer conceptualizations of some kind. Given the intuitive notion of concepts used here (see footnote 347), it does not seem implausible to say that scientists can use models to classify and organize the empirical regularities displayed by objects and phenomena. 352 In short, what scientists do when they try to identify a phenomenon in a data set, on Bogen and Woodward’s view, is draw a distinction within that data set between the data points that belong to a particular pattern, and those that are caused by quirks of the experimental set-up. We can then speak about the establishment of a phenomenon when we are dealing with a certain pattern that is invariant over different data sets, where these data sets are obtained by means of different, robust data production procedures. Scientific theories are in the business of providing explanations of these phenomena, in the sense that they specify the causal factors that are responsible for the production of the pattern.

203 Chapter 4. Manipulation and Exploration explicitly distinguish their view from Hacking’s in this way. As they put it in their original paper: In his Representing and Intervening, Ian Hacking introduces a notion of phenomena which is similar in a number of respects to our notion. But Hacking contends (pp. 227 – 232) that phenomena rarely occur in nature and that most phenomena studied by physicists are manufactured in the laboratory. While this is certainly true of some phenomena, such as a number of those created in very high energy particle accelerators, we claim below that is not correct as a general characterization of phenomena. These features which Hacking ascribes to phenomena are more characteristic of data. (Bogen and Woodward, 1988, p. 306) Feest argues, however, that there is in fact no contradiction, once we focus on what kind of work is required (in Hacking’s sense) for scientists to become convinced that they are dealing with a phenomenon (in Bogen and Woodward’s sense). This work is what she calls the process of stabilization. Stabilization, on Feest’s account, is a process that essentially involves two elements. The ﬁrst, which she calls the skill-aspect, is concerned with making an experiment work, i.e. ensuring that it reliably produces results. Besides the physical craftmanship required to get all the material parts operating together, this aspect also involves, she emphasizes, the ability to recognize that the experiment or instrument is indeed working, which means recognizing that the data produced by the experiment instantiate an empirical regularity. The second element, which she calls the validation-aspect, concerns the establishment of the empirical regularity as robust. This comes down to showing that a working experiment, i.e. one that is recognized as producing the empirical regularity, allows scientists to validate or refute claims about the phenomenon with which they take the experiment to be concerned (Feest, 2011, p. 59 – 61). While these two aspects need to be distinguished analytically, according to Feest,353 they necessarily operate in tandem in the stabilization of phenomena, as she argues by means of a discussion of the conceptual skill that is at play in both aspects of the stabilization process. This conceptual skill is the ability “to recognize that an experiment or instrument in fact works” (Feest, 2011, p. 62). Analyzing what this comes down to may indicate how Hacking’s notion of phenomena, which focuses on getting an experiment to work, can be reconciled with Bogen and Woodward’s account. This conceptual skill is required for both aspects in the sense that we need it to discern possible empirical regularites instantiated by data, as well as to validate

353 Feest illustrates why these two aspects need to be distinguished analytically by means of the following imaginary scenario regarding Caroline Herschel, an astronomer that was discussed by Hacking (1983, p. 180) because of her remarkable ability to identify and classify planets: “the practical knowledge required to run an experiment or to use an instrument has to be distinguished from the kinds of arguments required to back up the claim that the results of the experiments or instrument readings indeed indicate the type of thing the scientist takes it to be. For example, while Caroline Herschel may have been better than anybody else at using the light telescope to identify and classify a particular kind of structure, it is still conceivable that this structure might have turned out to be an artifact of the instrument rather than indicating a heavenly body, let alone a planet. This would have become apparent later, when different kinds of telescopes were used to replicate her findings. In such a case, we would still credit her with a particular kind of skill, while maintaining that her claim to have identified planets was not validated” (Feest, 2011, p. 60).

204 Experiment, Time and Theory claims about the phenomenon that we take these data to instantiate. We need to be convinced that an experiment is working in order to see that it produces empirical regularities and not just noise, and we need it in order to see that these empirical regularities can tell us something about the phenomenon that we are interested in. In order to better understand what role this conceptual skill plays exactly in the stabilization of phenomena, Feest then proposes to draw a distinction between two kinds of phenomena: on the one hand, what she calls surface phenomena, which are the empirical regularities that we can obtain from the data produced by a working experiment;354 and, on the other hand, what she calls hidden phenomena, which are more removed from these empirical regularities and which are closer to what Bogen and Woodward have in mind (Feest, 2011, p. 63).355 The stabilization of these kinds of phenomena would proceed more or less along the following lines:

To stabilize the ﬁrst type of phenomenon, then, would mean to identify some empirical data pattern and to provide evidence for its robustness. To stabilize the second type of phenomenon would mean to provide evidence for, and validate claims about, some regularity that is more removed from empirical data, though the evidence would presumably be provided by means of data. (Feest, 2011, p. 63)

Feest then points out that, to be able to recognize a particular set of data produced by an experiment as an instantiation of a specific empirical regularity, we rely on identification criteria provided by a hidden phenomenon: “in their search for criteria that determine the identity conditions of surface regularities, scientists assume that such identity conditions are determined by hidden phenomena that stand in a relevant explanatory relationship to the data that instantiate the surface regularities” (2011, p. 68).356 This raises the question, however, how scientists recognize that they are dealing with a particular hidden phenomenon that is supposedly causally responsible for, and hence determines the identification criteria of, the surface regularities. The problem, it seems, is that the only way to determine identification criteria for such hidden regularities is by abstracting them from the empirical regularities found in data sets which we take to be brought about by these phenomena. Yet this seems to render the process circular: to identify a surface phenomenon,

354 These phenomena could be seen as phenomena in Hacking’s sense, since Hacking, as Feest (2011, p. 63) points out, does not just take any observation produced by an experiment to form a phenomenon: what is observed should also form significant and repeatable regularities (see the quote in footnote 30). 355 Further on in her paper, Feest illustrates how she sees this distinction by means of a discussion of memory research: “Memory research provides us with a nice example of the distinction between surface phenomena and hidden phenomena, since in the literature we find references to phenomena like encoding and long-term memory, but also to phenomena like chunking effects or ceiling effects, where the latter are obviously very closely tied to particular experimentally generated data patterns, whereas the former are not” (2011, p. 67). 356 Feest illustrates this by means of a discussion of how the chunking effect is studied in memory research. This effect comes down to the fact that humans can remember more items when these are chunked, i.e. grouped together in meaningful wholes (Feest, 2011, p. 67). The identification of this effect in a particular set of data, she then claims, relies on identification criteria provided by a hidden memory phenomenon: “if the chunking effect is a memory phenomenon, its identity conditions are presumably determined by a brain process that is associated with memory (i.e., with a hidden memory phenomenon), where that process is causally responsible for all the data that instantiate the chunking effect” (Feest, 2011, p. 68).

205 Chapter 4. Manipulation and Exploration we rely on the criteria provided by a hidden phenomenon, but to know that we are dealing with a hidden phenomenon, we already need to recognize the empirical regularities that instantiate it. Feest argues that this is not necessarily a vicious circularity, since when we are able to show that a pattern obtained in a particular experiment is robust – i.e., that it is invariant under changes of the experimental set-up –, we have good reasons to believe that the pattern does instantiate a surface regularity and indicates the causal influence of a hidden phenomenon. It does entail, however, that surface phenomena and hidden phenomena are closely connected, in the sense that we already rely on the identification of a surface phenomenon in order to recognize a hidden phenomenon, and that this can, at the same time, change the way in which we classify the surface phenomenon.357 As such, Feest concludes, when scientists stabilize a phenomenon, what is stabilized is neither a surface nor a hidden phenomenon in isolation, but rather a fit between the two, and it is only by means of such a fit that we are able to recognize an experiment as working, in the sense of providing an instantiation of such a stable fit (2011, p. 66 – 67).

4.3 Stabilization, Exploration and Experimental Inferences

Exploratory experimentation, we have seen, is in the business of searching for empirical regularities, so as to inform the formulation and stabilization of concepts that offer a classification of the regularities discovered. Because of this, exploratory experiments involve an experimental set-up that is flexible in its materiality. The practice of exploratory experimentation can then be characterized as a search for a stable fit between the configurations of the experiment’s material set-up and a conceptualization that allows us to classify what we observe when the experimental set-up is running in a particular configuration. Exploratory experimentation can thus be understood as part of the process of stabilization that Feest discusses: in exploratory experimentation, we search for configurations of the experimental set- up that work, and this involves recognizing that a particular configuration produces data that can be conceptualized as an empirical regularity. The experiment can then be taken as having produced a surface phenomenon. Exploratory modeling, on the other hand, involves the search, constrained by certain laws of nature, for hypothetical models, such that these models can inform

357 Feest’s discussion of memory research illustrates this as follows: “It is quite conceivable that we use a specific chunking experiment under various different conditions, e.g. with subjects that have specific forms of brain damage with known functional impairments; or under conditions where the subjects are given other cognitive tasks to see how they affect their performance on the chunking task. Consider for example the scenario where an attention-demanding task greatly diminishes the subject’s chunking ability. This might leave scientists to suspect that chunking is really a phenomenon of attention, rather than memory. Or consider the scenario where patients with known memory impairments do well on some chunking tasks, but not on others. This might lead scientists to suspect that what was previously classified as one surface regularity is in fact a much more complex phenomenon, in that what were previously thought to be different indicators of the same hidden regularity are in fact indicators of different hidden regularities. These are both examples of how the surface regularity is instrumental in an investigation of a hidden regularity, which in turn may change the ways in which the surface regularity is classified” (Feest, 2011, p. 69 – 70).

206 Experiment, Time and Theory us about the objective possibilities of the model’s hypothetical target system. These models allow us to investigate, more specifically, how particular possibilities x1,..., xz could arise if we took certain other possibilities y1,..., yn, which are physically conceivable, for granted. We can then ensure that the obtained possibilities are objective by bootstrapping the different hypothetical models obtained by means of experimental input. In this way, we see how exploratory modeling can equally well be understood as part of Feest’s process of stabilization: we search for models that postulate hypothetical entities that could be responsible for the empirical regularities found in data produced in experiments, and this involves recognizing that the empirical regularities produced in these experiments can indeed be conceptualized as instantiations of these models.358 This suggests that Steinle’s exploratory experiments and Massimi’s exploratory models could be seen as two sides of the same coin, in the sense that what is stabilized when scientists obtain a certain successful conceptualization, is a stable fit between an exploratory model and exploratory experiments. On this view, seeing that an exploratory experiment works would mean that we have a hypothetical model that allows us to recognize an empirical regularity within the data produced by the experiment, i.e. it would provide us with a surface phenomenon. And this model would also inform us about what is objectively possible for the hypothetical entity that could be causally responsible for the effect produced, i.e. it would point towards particular hidden phenomena. Carrying out further experiments, by varying the set-up, could then provide more information about the robustness of the surface phenomenon, which in turn could lead us either to reconceptualize the hidden phenomena supposedly responsible for the surface regularities obtained, or to reconceptualize the way in which we identify empirical regularities. And carrying out further modeling, by elaborating the obtained models, by bootstrapping them with new empirical evidence or by trying to conceive alternative possibilities, could inform us about the viability and plausibility of the hidden phenomenon. This in turn could lead us in the direction of new experiments to investigate the robustness of the surface phenomenon, or to reconceptualize the empirical regularities identified by means of other (earlier or different) hypothetical models. As such, it seems that there are close connections to be drawn between the epistemology of exploration and Feest’s work on the process of stabilization, in the sense that Feest’s notion of a stable fit between surface and hidden phenomena can be understood as the result of exploratory experimentation and modeling working in tandem. Insofar as we can take a model to be concerned with the hidden phenomenon supposedly responsible for a surface regularity produced in an experiment, we should in fact expect them to work in tandem on Feest’s view, since surface phe-

358 While Massimi formulates her account of exploratory modeling in terms of laws of nature, I think that we should not put too much emphasis on it, in the sense of interpreting these as exceptionless true generalizations of any kind. Especially in ﬁelds where no real conceptualization is available yet, it seems to me that less well-established generalizations could also function as constraints in Massimi’s sense. I read Massimi in this sense since she herself often speaks in terms of ‘broad nomological constraints’ rather than laws of nature, and because she states that these constraints primarily function as “broad laws of nature so that theoretically pathological scenarios get discarded immediately” (Massimi, 2019, p. 8). In ﬁelds where no conceptualization is possible yet, the constraints used will probably be quite close to any empirical regularities already obtained, and hence there is no real worry that these would lead to theoretically pathological scenarios. Hence, I propose that we read Massimi’s claims about laws of nature in a rather relaxed way.

207 Chapter 4. Manipulation and Exploration nomena and hidden phenomena, she claims, stabilize each other. In what follows, I will argue that it is in terms of such stable fits that we have to understand how experimental manipulations, characterized in terms of experimental inferences, can be taken to provide information about what is supposedly manipulated. It is such a stable fit, more specifically, that provides scientists with a way to interpret these experimental inferences. And this information, I will then argue, should not be conceptualized in terms of factual knowledge about what is manipulated, but rather in terms of insight about what is conceivable and plausible. Successful experimental manipulations, on this view, delineate and constrain the space of possibilities for models of the target system that is supposedly manipulated. My starting point for the elaboration of this epistemology of exploration will be the experimental inferences and their interpretations that were discussed in the previous chapters. This wil lead me to a first formulation of this epistemology, which will then be elaborated further by means of a discussion of similarities and differences with the work of Steinle, Massimi and Feest. On the basis of this, I will then return to the research question that was raised at the end of chapter 1 in response to the work by Morrison, Massimi and Arabatzis. I will then conclude with some suggestions and remarks about what such an epistemology of exploration could entail for the anthropology underlying the realism-debate.

4.3.1 Exploration and the Electron’s Velocity-Dependent Mass The Electromagnetic Interpretation of Kaufmann’s Experiments Kaufmann’s first experiments, as the quote on page 45 shows, were carried out in order to obtain more insight into the velocity-dependency of the electron’s mass, a hypothesis proposed by Wien which had, until that time, not yet received any experimental investigation. This meant investigating whether the electron’s mass could be divided into a stable, mechanical part m (the electron’s real mass), and a velocity-dependent, electromagnetic part µe (its apparent mass). The best way to do this, according to Wien, was by using high-velocity electrons, since the contribution of the electromagnetic fields would be most noticeable there (see page 45). Kaufmann’s experimental set-up was very similar to those he had used earlier to measure the charge-to-mass ratio of cathode rays (Kaufmann, 1897; Kaufmann and Aschkinass, 1897; Kaufmann, 1898). The primary difference was that he now used Becquerel rays, because these were taken to consist of electrons that could attain velocities close to the speed of light. A second difference was that he would now deflect these electrons by applying electric (E) and magnetic (B) fields, in line with Kundt’s method of crossed spectra. In this way, he was able to distinguish the electrons with higher from those with lower velocities on his photographic plates: as we have seen on page 46, those with higher velocities would be deflected more, and would hence end up further away from the origin B(0, 0, 0). Kaufmann’s experimental set-up can thus be described as conceived in a theory- driven way, since he constructed it in order to investigate one particular theoretical hypothesis. This entailed that the set-up was rather rigid: the only variations that were possible concerned the strengths of the applied fields and the distance between the electron source and the photographic plate. After ensuring that even these variable factors were really fixed, Kaufmann would let the electrons travel over

208 Experiment, Time and Theory a specific distance while applying electromagnetic fields of a determined strength to them, in such a way that they would end up on a particular position on the photographic plate. He would measure the precise deflection y0 of the different spots obtained on the plate, fit all the points into a curve and determine its curvature ρ. These data showed him that the electron’s mass was in part velocity-dependent. These experimental manipulations, we have seen, could be characterized in terms of the following experimental inference (discussed on page 55):359

[Kaufmann’s Experimental Inference]: c i e µ + (E&B) −→ y0&ρ −→ µ0η

In order to make sense of the data he obtained – i.e., how the deflection y0 and the curvature ρ could inform him about the precise dependency of the electron’s e electromagnetic mass µ0η on the velocity given to it by the application of electromagnetic fields – Kaufmann had to rely on Searle’s model of the electron, which provided him with a way to calculate the energy of an electron, and to isolate the velocity-dependent part (see equations 2.6 and 2.7 on page 49). Abraham soon showed, however, that Searle’s model did not provide Kaufmann with what he was in fact after, namely the electron’s transverse mass (see page 50). The problem, Abraham showed, was that the electromagnetic mass should not be conceptualized in terms of the electron’s energy, but rather in terms of its electromagnetic momentum G. On the assumption that the electron’s velocity could be characterized in terms of quasi-stationary acceleration, this then led Abraham to the hypothesis that the electron’s mass could be completely accounted for in terms of its electromagnetic momentum. Applying Abraham’s electron-model to both Kaufmann’s earlier results and to results obtained by Kaufmann in new experiments then led both Kaufmann and Abraham to claim that the electron’s mass was completely electromagnetic in nature (see pages 52 and 53). What we see here is the emergence of a first stable fit. Kaufmann’s experiments were seen to be working, in the sense that the data could be taken to instantiate a certain empirical regularity – i.e. the velocity-dependence of the electron’s electromagnetic transverse mass as expressed by Abraham’s equation (2.9), discussed on page 51 – which was supposedly brought about in the way prescribed by Abra- ham’s electron model, i.e. in terms of the electromagnetic forces Fe exercised on the electron. This stable fit entailed a reconceptualization of the empirical regularities obtained by Kaufmann in his earlier experiments. As we have seen on page 52, it led him to dismiss certain of his earlier measurements as problematic. It also led him to reconceptualize the phenomena supposedly hidden under the empirical regularities obtained. While Searle’s model had led Kaufmann to claim that about one-third of the electron’s mass was brought about in an electromagnetic way (see the quote on page 49), Kaufmann and Abraham now took Kaufmann’s results to show that its mass was completely electromagnetic in nature. In short, Abraham’s electromagnetic electron-model provided the criteria to identify empirical regularities regarding the electron’s velocity-dependent transverse mass in Kaufmann’s data, and these empirical regularities in turn validated that this mass was completely electromagnetic in nature, in line with Abraham’s model.

359 How such an inference and its interpretation are to be read is explained in appendix A.

209 Chapter 4. Manipulation and Exploration

Hidden phenomenon and surface regularity thus stabilized each other. This stable ﬁt can be expressed in terms of what we called Abraham’s electromagnetic interpretation of Kaufmann’s experimental inference (discussed on page 56):

[Abraham’s Electromagnetic Interpretation]: c i e −dG i e i µ + (E&B) −→ quasi-stat. −→ F = dt −→ µ⊥ −−→ m+µe η y0,ρ 0⊥

As we have seen on page 56, what this interpretation provides is an account of what Kaufmann’s application of electric and magnetic fields to the electron does to its mass, according to Abraham’s model: it brings the electrons into quasi-stationary motion, which means that the force exercised on the electron by its self-induced fields (Fe) endows the electron with a specific electromagnetic momentum G, which will give it a transverse mass that can be captured in terms of Abraham’s equations for it (equation 2.9 on page 51). Applying this conceptualization to the data y0 and ρ obtained by Kaufmann then provided information about the precise part of the electron’s mass that was velocity-dependent. It showed, more specifically, that the electron’s mass was completely velocity-dependent. Kaufmann’s and Abraham’s conclusion that the electron’s mass is completely electromagnetic in nature depended on the assumption that the supposedly fixed properties of the set-up – i.e. E and B – were indeed properly fixed over an experimental run, and that the supposedly established property of the electron that was obtained – i.e. its low velocity charge-to-mass ratio /µ0 – was in line with what was known. Kaufmann argued that this was the case by providing the specifications of the instruments used to ensure the homogeneity, by checking the symmetry of the curves obtained on the photographic plates (see page 47), and by showing that his charge-to-mass ratio /µ0 was in line with the value obtained by Simon (1899) (see page 49). On the basis of this, Kaufmann could argue that his experiments had worked well and that the data produced could be taken to display empirical regularities and to validate claims about the electron’s dynamics. It was this stable fit between surface phenomenon and hidden phenomenon that then provided the empirical and theoretical constraints for the exploration of what was conceivable for the electron, a task that was carried out by Abraham. Since Kaufmann’s results indicated that the electron’s mass was completely determined by its electromagnetic momentum, this meant that its dynamics had to be completely electromagnetic in nature. Abraham’s modeling was thus, on the one hand, bootstrapped by the empirical regularity obtained from Kaufmann’s data, and on the other hand bound by the electromagnetic world view. This led him to claim, as we have seen on page 53, that it had to form a rigid body, that it did not really make a difference whether we were dealing with a volume charge distribution or a surface distribution, and that it could be either spherical or ellipsoidal (page 51), but that in the second case, stable motion was not possible in all directions (see page 54). Lorentz, as we have seen in section 2.3, also obtained expressions for the velocity- dependence of the mass of his ion, which he later identified with the electron. He originally developed these, however, not in response to Wien’s hypothesis, but in order to account for the results of the Michelson-Morley experiments. This meant that Lorentz’s search for a model was originally constrained not by the electromagnetic world view, but rather by the principle of relativity. This led him to a model according to which the electron’s shape had to be deformable. Elaborating

210 Experiment, Time and Theory his model further convinced him that it could be made completely electromagnetic in nature, while also being within the margins of error of Kaufmann’s results (see page 58). This suggested that the space of possible properties for the electron, which was bootstrapped by Kaufmann’s experimental evidence and bound by the constraints imposed by the electromagnetic world view, was larger than Abraham had thought. It allowed for at least two different hypothetical entities displaying different objective possibilities: while Abraham’s electron was rigid, Lorentz’s was deformable. Abraham therefore set out to investigate more thoroughly what was possible for the electron and what was not, by explicitly listing the foundational principles that were to constrain the theoretical study of the electron (see page 58). This led him to claim that while Lorentz’s electromagnetic electron was in principle conceivable under the constraints imposed by the electromagnetic world view, it was very implausible: first, because the two expressions for the electromagnetic momentum of Lorentz’s electron differed with a factor 1/3, and it was unclear how this could be accounted for purely in electromagnetic terms (see page 60); and second, because it was unclear whether a deformable electron such as Lorentz’s could perform force- free inertial motion in all directions (see the quote on page 61). In response to this, Poincaréintroduced his stresses, which provided a response to Abraham’s issues, but also implied that Lorentz’s electron was no longer completely electromagnetic in nature: it rather behaved, as Poincaréput it, as if it was completely electromagnetic (see footnote 110). This electron-model, discussed on page 66, offered the following interpretation of Kaufmann’s experimental inference:

[Poincar´e’sRelativistic Interpretationn]: c i −dG i i µ + (E&B) −→ relativistic motion −→ F = dt −→ µ⊥ −−→ m+µ η y0,ρ 0⊥

Poincaré’sinterpretation offered an alternative stable fit for Kaufmann’s (1901b; 1902; 1903) results. His electron-model provided identification criteria for empirical regularities, i.e. Lorentz’s equations for the velocity-dependence of mass µ⊥, that could be found in Kaufmann’s data. As such, these regularities could be seen as offering a validation of the claim that what was responsible for these regularities was the force F that influenced the electron’s electromagnetic momentum, i.e. the hidden phenomenon. The way in which Poincaréconstructed his model also shows that the space of possibilities for the electron was constrained by the stable fit provided by the electromagnetic interpretation of Kaufmann’s experimental inference: while the Lorentz-Poincaréelectron was no longer electromagnetic in nature, it still had to be constructed in such a way that its electromagnetic momentum was in line with the one that, according to the electromagnetic interpretation, was provided by Kaufmann’s experiments. Lorentz and Poincaréhad to construct their model in such a way that it could provide a response to the issues that were raised from the perspective of the electromagnetic world view, i.e. the stability-issue and the possibility of force-free inertial motion. As such, their electron behaved as if it was completely electromagnetic in nature. Kaufmann then decided, as we have seen in section 2.4, to carry out new experiments. Their purpose, however, had transformed. No longer were they primarily supposed to provide insight into the electron’s electromagnetic mass. The goal was now to provide an empirical decision between the electromagnetic world view, repre-

211 Chapter 4. Manipulation and Exploration sented by Abraham’s model and the Bucherer-Langevin electron, and the principle of relativity, represented by the Lorentz-Poincarémodel, which was also taken to cover Einstein’s derivation of formulae for the velocity-dependence of mass (see footnote 119). Even though the goal of his experiment had changed, Kaufmann did not alter his experimental set-up. He assumed that this decision could be obtained merely by improving the accuracy and the way in which he analyzed his data, which he now characterized in terms of his curve constants (see page 66). These curve constants were taken at the time to offer a direct way to compare the different theories, since they could be obtained directly from his apparatus constants (see the equations 2.20 on page 67), and because the different theories offered different predictions for them (see the equations 2.21 on page 67). As such, the decision came down to which theory offered the equation for the electron’s electromagnetic momentum that best captured the empirical regularities obtained in Kaufmann’s experimental set up. We thus see how, at this point, Kaufmann’s experiments were constructed in a way that Steinle would describe as completely theory-driven: there was a very specific theoretical question that was taken to require an answer, and the whole experimental set-up was fixed in such a way that the data produced could be taken to directly provide information about this question. The results were clearly in favour of the electromagnetic world view. The relativistic approach, as Kaufmann put it, could be seen as failed (see the quote on page 69). This entailed not only that Abraham’s model and the Bucherer-Langevin model were taken to be within the bounds of the physically plausible, whereas the Lorentz-Poincaré-Einsteinmodel was taken to be excluded (see Kaufmann’s conclusion on page 69). It equally well implied that it was the electromagnetic interpretation that constrained the space of possibilities for further explorations of the electron’s properties. The early relativistic responses to Kaufmann’s experimental results could not improve on this situation. Poincaréand Lorentz expressed their despair (see page 71), and while Einstein and Planck tried to argue that a relativistic account of the electron was possible, Kaufmann’s experiments had indicated that it was the electromagnetic world view that constrained the space of possibilities. Hence, Ehrenfest could always raise the stability-issue against their attempts. As long as Einstein and Planck did not specify which shape they ascribed to the electron and which forces held it together, in such a way that its momentum would be in line with Kaufmann’s results, a relativistic account of the electron was not considered to be very plausible. As such, Planck and Einstein could do nothing else than admit that these were issues for the theory of relativity. Einstein did this in his response to Ehrenfest (see the quotes on page 75 and page 77). Planck admitted in the discussion after his (1906b) presentation that his preference for the principle of relativity was a subjective one (see page 81). And Einstein had to admit in his (1907c) review article that Kaufmann’s results indicated that the foundations of the theory of relativity were possibly not in accordance with the facts (see page 82). It was only by means of new experiments that the space of possibilities could be opened up again. And while neither Bestelmeyer’s, Bucherer’s nor Hupka’s results should be seen as providing conclusive evidence in favour of the relativistic approach – each experiment could be criticized, which led Heil to claim that no real improvement in measuring the electron’s charge-to-mass ratio had been accomplished in more than five years (see the quote on page 91) –, they could be used by adherents of the relativistic approach to argue that Kaufmann’s measurements should not be

212 Experiment, Time and Theory seen as direct evidence for Abraham’s electron or for the electromagnetic world view. What these experiments allowed them to do, more specifically, was to argue that the link, embodied by his curve constants, between Kaufmann’s experimental apparatus and the electron’s electromagnetic momentum, in its role of arbiter between the different theories, was perhaps not as direct as Kaufmann and everybody else had assumed. These experiments did this by providing data displaying an empirical regularity that was not in line with Kaufmann’s regularity. In this way, they allowed the adherents of the relativistic approach to argue that the fit between Abraham’s electromagnetic electron and Kaufmann’s regularities was not a stable one. Other criteria for the identification of the electron’s velocity-dependence of mass as a surface phenomenon were required, and these criteria could be provided by the relativistic account of the electron. The way in which these experiments did this can be described as exploratory, in the sense that they changed particular aspects of the material set-up used by Kaufmann, in order to obtain a better insight into the electron’s charge-to-mass ratio and its velocity-dependent mass. Bestelmeyer used crossed fields instead of applied fields, which provided him with a velocity-filter (see page 82). Bucherer employed a cylindrical set-up, which allowed him to measure the stability of /µ0 over different velocities (see page 86). Hupka, finally, investigated the velocity-dependence of the discharge potential of cathode rays, which have a lower velocity than Becquerel rays, following Planck’s suggestion that such experiments would provide a clearer insight into the velocity-dependency of the kinetic potential (see page 80 for Planck’s proposal, footnote 137 for a similar suggestion by Einstein, and page 88 for Hupka’s experiments). I call these experiments exploratory, even though they were carried out with a specific theoretical question in mind, because they went against the experimental practice connected with Kaufmann’s experiments. Instead of trying to improve the accuracy, they varied elements of their experimental set-up. Their goal was thus not per se to obtain greater precision, but rather to investigate the robustness of the empirical regularities obtained by Kaufmann.360 In a sense, we can say that these experiments brought some flexibility in Kaufmann’s experimental set-up. The results obtained in these experiments now allowed some to argue that what Kaufmann had obtained were not real empirical regularities, because his set-up was possibly not as reliable as he had assumed. This was suggested by Planck in his (1906b) lecture, where he argued that the /µ0-value obtained by Kaufmann allowed for electrons with velocities higher than the velocity of light (see page 79). And as a result of Bestelmeyer’s experiments, Planck and Stark could also argue that there were possible problems with the constancy of the applied magnetic field E in Kaufmann’s set-up, which they took to be caused by radiation ionizing the remaining air in the experimental-set up (see page 84). In this way, the apparatus constants that served as the empirical foundation of Kaufmann’s curve constants, and hence of his way to evaluate the different theories involved, could be cast into doubt. This in turn allowed the adherents of the relativistic approach to argue, on the assumption that these later experiments had functioned properly, that the velocity-dependence of mass as a surface phenomenon had to be reclassified in line

360 As Bestelmeyer pointed out in the conclusion of his experiments, while he had constructed the apparatus with suﬃcient care, he had not obtained especially great accuracy, and still it was already clear that his results were not in line with Kaufmann’s (see the quote on page 83).

213 Chapter 4. Manipulation and Exploration with a relativistic account of the electron.

The Relativistic Interpretation of Kaufmann’s Experiments Insofar as some scientists took the results of Bestelmeyer, Bucherer and Hupka to destabilize the electromagnetic conceptualization of the electron’s mass offered by the fit between the regularities in Kaufmann’s data and Abraham’s electron-model, we would expect them to search for a new conceptualization that could make sense of these later results and others. We would expect this because, as Steinle points out (see page 201), a stable conceptualization is required in that it offers the language with which scientists approach a field of study. And we do indeed see that Planck, Einstein and von Laue embarked on a search for a relativistic conceptualization of the electron’s mass. Their starting point was not, however, a relativistic model of the electron, but rather the mass-energy equivalence that, Einstein had argued on the basis of a few specific cases, seemed to have general validity (see page 76). This entailed that this search could not be carried out solely in terms of the theory of relativity, since, as we have seen, the theory’s principles in themselves were only heuristic instruments that applied solely to rods, clocks and light signals (see page 74), and because in its formulation as a relativistic electrodynamics, it had its limitations (see page 76). Because of this, Planck and Einstein turned to the quantum. Already in his first papers on thermal radiation, in which he formulated his spectral distribution law suggesting that the energy emission and absorption of his oscillators could only be quantized in nature (expressed in terms of the formula E = hν), Planck indicated that there were certain connections between his law and the study of the electron. It led him, for example, to a value for the electric charge that was later experimentally confirmed (see footnote 166). And in his (1906c) lectures on the theory, he argued that the motion of his oscillators could be represented as straight motions of an electron (see the quote on page 97). However, it was his application of the principle of relativity and the principle of least action to the study of thermal radiation in motion, which led Planck to his general dynamics, that allowed him to really reconceptualize the workings of Kaufmann’s experiments. This reconceptualization targeted Abraham’s interpretation of the experiments and provided a programme for the elaboration of an alternative. What is significant is that this was done, in part, by redrawing the relations with Newtonian mechanics. Even though Abraham saw the electromagnetic world view as a replacement for the Newtonian mechanical approach to the foundations of physics, his electrodynamical account of the electron still relied on the Newtonian framework, in the sense that his conceptualization of the electron’s motion as quasi-stationary enabled him to characterize the electron’s electromagnetic momentum in terms of mass times acceleration, which allowed him to obtain its transverse mass (see page 50).361 What Planck did was reconceptualize the electron’s motion in terms of the relativistic mechanics he had obtained in his (1906a) article. On this view, force was not to be understood as the Newtonian mass times acceleration, but rather as the Newtonian rate of change of momentum, where the momentum was to be understood not in electromagnetic terms but in terms of the relativistic momentum (see equation 2.22 on page 73).

361 See also page 106 for the use Abraham made of Hertz’s mechanics.

214 Experiment, Time and Theory

In this way, Planck’s relativistic mechanics indicated how one of the two central elements in Abraham’s interpretation of the experimental inference characterizing Kaufmann’s experiments, the electron’s electromagnetic momentum, had to be reformulated in terms of its relativistic momentum.362 The question now was, however, how to reformulate the other central element of Abraham’s interpretation, the electron’s inertial mass. Planck addressed this question in terms of his general dynamics. This indicated that a body’s momentum not only depends on its velocity, but equally well on its temperature, expressed in terms of Gibb’s heat function R (see equation 2.30 on page 101). This led him to argue that a body’s inertial mass should not be characterized in terms of an absolute, unchangeable Newtonian constant, nor in terms of a distinction between real and apparent mass, but rather in terms of a body’s thermal energy (see page 98). In this way, Planck argued that the second element of Abraham’s interpretation, the velocity-dependence of an electron’s inertial mass, was merely an approximation of how such a body was to be characterized according to his general dynamics, namely in terms of its velocity, volume and temperature (see the quote on page 101).363 With regards to the first element of Abraham’s interpretation, the electron’s electromagnetic momentum, Planck’s general dynamics allowed him to argue that it was but one specific instance of his law of the inertia of energy. At the end of his (1908b) formulation of his general dynamics, we have seen, Planck suggested that a body in general had to be characterized as a supply of energy (see page 103). In his (1908a) development of his law of the inertia of energy, he then argued that whatever the source of this energy would be, when a body’s motion could be characterized in terms of the principle of relativity, a flow of energy would result, which could be represented as a vector that captured the body’s momentum (see the quote on page 104). This enabled him to argue that Abraham’s electromagnetic momentum was but a step in the progression towards his relativistic account of the conservation of momentum, his law of the inertia of energy (see the quote on page 103). It also enabled Planck to complete his redrawing of the relations with Newtonian mechanics, in the sense that he could now present Abraham’s electromagnetic momentum as an addition that disturbed the simplicity and generality of the mechanical concept of momentum, a disturbance that was then restored by Planck’s general dynamics (see page 106). In this way, Planck’s general dynamics provided a broad outline for a relativistic interpretation of Kaufmann’s experimental inference, i.e. for the stabilization of a fit between a surface and a hidden phenomenon that allows us to recognize that the experiments worked. I say ‘broad outline’ here, because Planck’s work was not directly concerned with the dynamics of the electron: it instead offered a framework for the elaboration of a dynamics of any kind of physical system. This outline was then concretized by Einstein’s work on the quantum and von Laue’s work on the electron, work that we could characterize as exploratory modeling bound by the

362 Planck already reconceptualized what was at stake in Kaufmann’s experiments in these terms in his (1906b) presentation, where he suggested that they in fact did not concern the velocity- dependence of mass but rather of momentum (see the quote on page 79). 363 And this mass depended not only on velocity, but equally well on pressure, volume and temperature, as he then shows by distinguishing four diﬀerent kinds of mass-dependencies: transverse, longitudinal isothermal-isochoric, longitudinal adiabatic-isochoric and longitudinal adiabatic-isobaric (see page 102).

215 Chapter 4. Manipulation and Exploration principle of relativity and the quantum-constraint E = hν.364 They investigated, more specifically, which model of the electron was physically conceivable under these constraints, where this search was now bootstrapped by experimental evidence concerning not only the electron, but equally well black-body radiation (see footnote 192 for the list of empirical facts that Einstein took to be unexplainable in terms of non-quantized radiation theories). This led Einstein, for example, to the claim that there existed a quantum-entity that was responsible for the transformation of matter into energy, and hence for the energy-mass equivalence (see page 110). In- vestigating how a theory concerning this entity would look like then led him to the equation h = 2/c (where denotes the electron’s charge), which he took to indicate that the same theory that was to account for the quantum-constitution of radiation would also lead to the electron’s constitution (see the quote on page 109). These explorations provided Einstein with four constraints that such a theory had to obey (see footnote 197). As such, he had obtained a space of physically conceivable models that provided the possible properties for a hypothetical phenomenon that would be responsible for both the electron and the quantum. This space was, according to Einstein, overseeable.365 And this hypothetical entity should equally well account, as he argues in his Naturforscherversammlung lecture (1909a), for the energy-mass equivalence he had derived from his theory of relativity (see page 111). While Einstein’s work can be seen as an exploration of what the physically conceivable possibilities were for a hidden phenomenon that was to account for the behaviour of the quantum and the electron and for the mass-energy equivalence, von Laue’s work could be seen as an exploration of how the theory of relativity could account for different empirical regularities (see page 114 for the list of phenomena that the theory should account for, according to von Laue). With regards to the experiments on the velocity-dependency of the electron’s mass, this came down, as he puts it in the quote on page 120, to the search for an account of the electron that could do justice primarily to the results obtained by Bucherer and Hupka, since Kaufmann’s experimental results were not accurate enough (see the quote on page 115). In order to obtain this, he required a model of the electron, just as Abraham, Kaufmann and Lorentz had needed one to make sense of Kaufmann’s results. As von Laue himself pointed out, however, he approached this issue in a different way than Abraham and Lorentz. While they took the electron’s electromagnetic momentum as their starting point, von Laue started from the electron’s total momentum required to keep it in equilibrium (see footnote 218). After calculating the total momentum and the electromagnetic momentum of an electron at rest, he could show, by means of the Minkowskian formalism, that when such an electron was put in a state of hyperbolic motion, it would behave as if it were a rigid body (see the quote on page 118). This then led him to the same expression for the electron’s electromagnetic momentum as that obtained by Abraham and Lorentz (see page 118). Its meaning, however, had changed on von Laue’s view: it was no longer to

364 Von Laue did not explicitly use the quantum-constraint E = hν, but given his reliance on the law of the inertia of energy and Planck’s general dynamics, which incorporated this constraint (see equation 2.31 on page 101, where Planck links his dynamical results to his quantum of action), his work was also in line with this constraint. 365 As Einstein puts it: “I have not yet succeeded in ﬁnding a system of equations fulﬁlling these conditions which would have looked to me suitable for the construction of the elementary electrical quantum and the light quanta. The variety of possibilities does not seem so great, however, for one to have to shrink from this task” (Einstein, 1909b, p. 193; Beck, 1989, p. 374).

216 Experiment, Time and Theory be equated with the electron’s total momentum, but was rather seen as a part contributed by the electron’s self-induced electromagnetic fields to the total momentum (see footnote 218). By means of this result, von Laue could then investigate whether the shape of the electron made any difference to its dynamics, which led him to the result, as we have seen on page 119, that it did not. The electron’s dynamics, expressed in terms of Planck’s law of the inertia of energy, remained the same when one conceived of it respectively as a point particle, a charged sphere or a charged body shapen by indeterminate stresses. The only difference between these conceptions concerned the possible sources of energy for the momentum, and in the case of the indeterminately shaped electron it was not possible to specify which different sources were responsible. But this was to be expected, since Planck’s characterization of the law of inertia of energy was indifferent to the specific source of energy that was responsible for the electron’s momentum conceived as a flow of energy. What we see here, again, is the emergence of another stable fit. This fit consists, on the one hand, of the velocity-dependency of the mass µ⊥ of any physical system as a surface regularity, and the total force F endowing it with a relativistic momentum p, as a hidden phenomenon. This stable fit entailed a reconceptualization of which experiments could be seen as working properly. While the data of Bucherer’s and Hupka’s experiments could be taken to instantiate this empirical regularity, Kauf- mann’s experiments suffered from insufficient accuracy (see the quote on page 115), and they could not provide what Kaufmann and Abraham were after, according to von Laue, namely a decision regarding the electron’s dynamical constitution (see the quote with which we opened chapter 2, page 42). This stable fit can be expressed in terms of the relativistic interpretation of the experimental inference characterizing the manipulations carried out by Kaufmann, Bestelmeyer, Bucherer and Hupka. This interpretation, we have seen on page 123, conceptualizes the electron in terms of the pressure p, and its energy E0, volume V 0 and stress tensor P0 in its rest frame. Applying electric and magnetic fields to such a system will bring it in hyperbolic motion, which means that it behaves as if it is a rigid body (see the quote on page 118). This means that the total force exercised on it can be conceptualized in terms of the relativistic momentum p, from which we can obtain an expression for the velocity-dependence of the system’s transverse mass µ⊥. Applying this expression to the data provided by Bucherer and Hupka then provided von Laue with information about the sources of energy (α + p) that played a role, in line with Planck’s law of the inertia of energy. As such, von Laue provided the following interpretation for Kaufmann’s experimental inference:

[von Laue’s Relativistic Interpretation]: 0 0 0 c i dp i i (p&E &V &P ) + (E&B) −→ hyperbolic motion −→ F = dt −→ µ⊥ −−→ (α+p)/c2 y0,ρ

This stable ﬁt was, again, brought about primarily through exploration. We have already seen that this holds for Einstein. Von Laue’s work as well can be characterized in terms of exploratory modeling. We see him investigating, bounded by the Minkowskian formulation of the theory of relativity, which shapes can be ascribed to an electron, and how we are to characterize its motion and constitution if we want to ensure that it remains in equilibrium. This at the same time also shows how the way in which the electron’s dynamics is to be explored has changed over time, as

217 Chapter 4. Manipulation and Exploration von Laue himself pointed out (see footnote 218). Abraham and Lorentz were guided by the belief that the electron’s dynamics had to be completely electromagnetic in nature, which was a consequence of the fact that the stable fit between Abraham’s electromagnetic electron and the empirical regularity for the velocity-dependency of mass it entailed, showed that Kaufmann’s experiments had worked. Von Laue was guided, however, by the belief that the electron’s dynamics had to be characterized in terms of Planck’s general dynamics, which was a consequence of the fact that the stable fit between his conceptualization of the electron as either a point particle with an arbitrary charge, or a charged sphere, or a charged body shapen by indeterminate stresses, and the empirical regularity for the velocity-dependence of mass it entailed, showed that Hupka’s and Bucherer’s experiments had worked. This exploratory modeling by von Laue even suggests that it could be possible that the electron’s mass is completely electromagnetic in nature (see page 120): the theory of relativity does not make any claims about this. This shows that the emergence of a new stable fit not only entails a reconceptualization of the field of study, but equally well of the way in which theories relate to each other. Before, the theory of relativity and Abraham’s electrodynamical theory were taken to be competitors with respect to Kaufmann’s experiments. Now, von Laue can present the theory of relativity as allowing for the incorporation of parts of the electrodynamical approach, just as Planck had been able to present Abraham’s electromagnetic momentum as a step towards his law of the inertia of energy (see page 106), and just as Einstein was able to turn Ehrenfest’s stability-issue into the aim of his future quantum-research (see the quote on page 109). In this way, the relativistic approach could present itself as the programme for the future, while the electromagnetic world view, as Helge Kragh (1999, p. 114) puts it, became a world view in decline.

4.3.2 Exploration and Superconductivity’s State of Magne- tization Superconductors as Perfect Conductors Kamerlingh Onnes and Tuyn’s experiments, we have seen, were originally carried out in order to obtain more insight into the microresidual resistance of superconducting materials, a hypothesis first proposed by Kamerlingh Onnes in his presentation at the Solvay conference (1921). This required them to carry out resistance measurements of the persistent currents I(∞) that would arise, in line with Lippmann’s theorem (see the quote on page 134), as a consequence of variations in the applied field (∆H) after the body had been made superconducing by lowering its temperature (T < TC ) and applying a magnetic field (H < HC ). As Kamerlingh Onnes himself pointed out (see footnote 250), this was common procedure in his laboratory at the time. Most investigations of the properties of superconducting bodies were carried out by manipulating the persistent currents brought about by the application of a magnetic field and measuring their resistance (see also footnote 264). In order to ensure that the values obtained were indeed informative, i.e. that they did in fact point towards an empirical regularity with regards to the microresidual resistance of different materials, Kamerlingh Onnes and Tuyn first had to acquire more insight into the invariability of the strength and direction of the persistent currents and of their distribution over a superconducting body. This led them to their experiments on a superconducting ring and hollow sphere, where the variation in

218 Experiment, Time and Theory the magnetic field was induced by rotating the superconducting object with respect to the fixed outer ring. They would then observe whether there were any variations over time in the superconductor’s position with respect to its suspension axis, which would be caused by variations in the ponderomotive forces exercised by the persistent currents on the superconducting material. If no variations were to be observed, it could be concluded that there were no variations in the strength or distribution of the persistent currents, and hence that their measurements of the microresidual resistance were reliable. As we have seen, neither in the case of the superconducting ring (see page 137) nor in the case of the superconducting hollow sphere (see page 138) were significant variations observed. These experiments were then taken to indicate that there was no change in the superconductor’s magnetic flux B. As we have seen on page 142, the manipulations carried out by Kamerlingh Onnes and Tuyn can be characterized in terms of the following experimental inference:

[Kamerlingh Onnes and Tuyn’s Experimental inference]: c i (T < TC &H < HC ) + (∆H) −→ I(∞) −→ B

On the basis of the secondary literature – especially Dahl (1992) – and given that Kamerlingh Onnes’ laboratory was, at the time, the only place where the conditions for superconductivity could be obtained (see footnote 241), and because Kamerlingh Onnes was quite involved in most of the experiments carried out there, I believe that we can take him on his word that the procedure sketched here was common procedure (see footnote 250). This suggests that many investigations in the field of superconductivity at the time can be characterized in terms of this experimental inference. The aim of these investigations would be to measure, and acquire insight into, the different electromagnetic and thermal properties of superconducting bodies by varying the strength of the applied field. Kamerlingh Onnes and Tuyn’s (1924) experiments present us with what Steinle would call a theory-driven way, since their set-up was quite rigid and they were constructed and carried out with a specific theoretical question in mind. If the characterization of the common experimental procedure presented in the previous paragraph is correct, moreover, we can claim that they were part of a practice of theory-driven experimentation. Following Kamerlingh Onnes’ adagium of through measurement to knowledge, many experiments carried out in the laboratory at the time were variations on the same experimental procedure, where what was varied either concerned the materials rendered superconducting – i.e. their shape or the material used – or through the improvement of technology – e.g. by being able to attain even lower temperatures.366 What drove this experimental practice, it seems, was the perfect conductivity conception, since it was Lippmann’s theorem that informed the experimental procedure (see footnotes 250 and 264).367

366 In their (1924) paper, for example, Kamerlingh Onnes and Tuyn point out that their experiments were only made possible because they had ﬁnally been able to construct a cryostat, i.e. a device in which samples could be kept at extremely low temperatures, that was transportable. This allowed them to carry out measurements at places that were calmer than the room where the liquid helium required for the low temperatures was produced. Before, they point out, it was often diﬃcult to obtain adequate measurements, since that required a place where the temperature changes would be only very minimal, and this was not always the case in the liquid helium workshop (Onnes and Tuyn, 1924, p. 254). 367 Casimir, for example, claimed that it was this experimental procedure that was responsible

219 Chapter 4. Manipulation and Exploration

Because it was assumed that when a metal was placed in an environment with a temperature T < TC and a magnetic field H < HC , its resistance would become almost zero, superconductors were taken to form perfect conductors, i.e. conductors that could be conceptualized in terms of Maxwell’s equations with resistance zero (R = 0). This meant that superconductors were mostly studied as a limiting case of normal conductors, as Lorentz did in his Solvay lecture (1924a). He there approached the subject in terms of his electron-theory of conduction, according to which a conducting metal was to be conceptualized as consisting of a crystal lattice of atoms and a collection of free electrons moving around it, which constituted a current (see the quote on page 139). Following Lippmann’s theorem, Lorentz argued, on the basis of this theory, that when a body was rendered superconducting, a variation in the applied magnetic field (∆H) would bring the electrons constituting the persistent currents in such a state of motion that they would induce a magnetic field that would cancel out these variations: C(α ± ∆H). On the basis of this, Lorentz could then obtain an expression for the strength of the currents (Nev) which, when applied to the observations of Kamerlingh Onnes and Tuyn, entailed that there would be a frozen in magnetic flux B that was equal in strength to the field H0 applied before the superconducting transition. As such, Lorentz’s perfect conductivity conception accounted for the functioning of Kamerlingh Onnes and Tuyn’s experiments in terms of the following interpretation of the experimental inference characterizing the manipulations carried out (this interpretation is discussed on page 143):

[The Perfect Conductivity Interpretation]: c i i (R = 0) + (∆H) −→ C(α ± ∆H) −→ Nev −−−→ B = H0 I(∞)

In this way, a first stable fit that could offer an interpretation of the experimental inference characterizing Kammerlingh Onnes and Tuyn’s experiment emerged. Lorentz proposed, more specifically, a hidden phenomenon – i.e. the motion of electrons experiencing zero resistance around a crystal lattice giving rise to currents that induce a magnetic field – that allowed him to identify an empirical regularity in the data provided by Kamerlingh Onnes and Tuyn’s experiments, namely the behaviour of the currents in response to variations in the magnetic field. In this way, Lorentz showed that the experiments had worked, while the experiments at the same time could be taken as a validation of his perfect conductivity account, which conceptualized superconductivity in terms of frozen in fields maintained by for the persistence of the frozen in fields superstition (see footnote 234): “That these superstitions could prevail so long may have had to do with peculiarities of the Dutch language. In Dutch ‘to measure’ is called ‘meten’ (messen in German) and to know is called ‘weten’ (wissen in German). Kamerlingh Onnes had created the slogan ‘Door meten tot weten’ (by measurements to knowledge); because it happens to rhyme in Dutch it was not easily forgotten. This slogan had in some way a very bad influence on physics at Leyden. Not that one should not carry out measurements, of course one should; but it caused people to concentrate on measurements rather than on observations. It is very fine to carry out measurements of a property if you know what you are going to measure, but before you know that a phenomenon exists at all, you cannot measure. So there was a tendency not to make observations that could lead to something new, but rather to take well- known properties like specific heat, vapour tension and electrical resistance and then carry out long series of measurements under well-defined conditions. And that is not always the best way to discover new effects” (Casimir, 1977, p. 174).

220 Experiment, Time and Theory the free electrons. Surface regularity and hidden phenomenon stabilized each other. On the basis of this view, Lorentz then explored which properties one could possibly ascribe to these free electrons, where this search was bootstrapped by Kamer- lingh Onnes and Tuyn’s results and earlier ones on conductors and superconductors, and constrained by his perfect conductivity conception. This led him to claim that there was really only one possibility with regards to the motions of the free electrons, if one wanted to account for Kamerlingh Onnes and Tuyn’s results: the electrons could not move around completely freely, but had to be imagined as moving through rigid paths, i.e. tubular filaments (see page 141). It soon turned out, however, that Lorentz’s hidden phenomenon could not provide what it was supposed to, since there were several empirical regularities – concerning e.g. the specific heats of metals, their different possible states of magnetization, and the computation of thermal and electrical conductivity (see page 143) – that could not be properly accounted for by his theory. This brought Sommerfeld, Bloch and others, to reformulate the theory into quantum-mechanical terms, which led them to the development of an electron-theory of metals that could account for the different regularities that escaped the earlier, classical theory. Just like the classical theory, this quantum-mechanical theory conceptualized conduction in terms of a gas of electrons moving through a metal. In contrast to Lorentz, however, who tried to conceptualize it purely in terms of the free electrons moving around the lattice (see footnote 261), Bloch conceptualized the electrons, characterized in terms of the four quantum-numbers, as situated in a force-field with the same periodicity as the lattice (see the quote on page 146). This allowed him to ascribe to all electrons involved a wave function from which he could calculate the contribution that was required for them to move freely through the lattice. This electron-theory of conduction could account for all known empirical regularities, according to Bloch, except for one: superconductivity (see page 147). In order to overcome this, Bloch turned to an analogy with ferromagnetism. Just as the application of a magnetic field to ferromagnetic materials aligns the spin vectors of the electrons in such a way that the material retains a magnetic moment after the applied field has been removed, the application of a magnetic field to a superconductor would somehow make the electrons interact in such a way that the material retains frozen in fields even after the applied field had been removed (see page 148). Making the analogy work required him to take into account the interaction between the electrons, something that he had not done in his earlier conduction theory (see page 146). The problem was, however, that he could not come up with a single interaction that would allow for the emergence of a current in a superconducting material. This brought Bloch to formulate his impossibility- theorem, which stated that every theory of superconductivity would be refuted or, in its more radical formulation, that superconductivity was impossible (see the quote on page 149). Bloch’s search for an interaction can be characterized in terms of exploratory modeling, constrained by the laws of Bloch’s electron-theory and the perfect conductivity conception. He engaged in a search, more specifically, for a physically conceivable model that would ascribe possible properties to the electron, in such a way that its behaviour could give rise to stable currents in the electron’s minimal energy state, and which hence could provide identification criteria for the empirical regularities associated with superconductors, i.e. their persistent currents. These

221 Chapter 4. Manipulation and Exploration regularities could thus be taken as empirical evidence that bootstrapped Bloch’s exploratory modeling. The problem was that no such hidden phenomenon, in Feest’s sense, could be found, and hence no stable fit could be obtained that would provide an interpretation of the experimental inference underlying experiments such as Kamerlingh Onnes and Tuyn’s. As such, in line with Bloch’s theorem, it seemed that superconductivity was in fact not physically conceivable, and hence that there were no objective possibilities to be ascribed to the hypothetical entities supposedly responsible for the phenomenon, i.e. the conduction electrons. Exploratory modeling had reached a dead end, in the sense that the modal knowledge it provided was that superconductivity was not possible. The discussion of Steinle’s, Massimi’s and Feest’s work suggested that there is a tight interconnection between exploratory modeling and exploratory experimentation, in the sense that the achievement of a stable fit could be understood as a result of the two working in tandem. The discussion of the experiments on the velocity- dependence of mass indicated that this is indeed possible. As long as Kaufmann’s experiments worked in tandem with Abraham’s electron, the field of study was conceptualized in terms of the stable fit of the electromagnetic world view. Once other experiments suggested, however, that the regularities identified by Kaufmann in his data by means of Abraham’s electron were maybe not as robust as he had thought, this domination became destabilized. It was not until an alternative account of the electron was developed by means of exploratory modeling, however, that a new stable fit, a relativistic one, could be achieved. Here in the superconductivity-case as well, we see that when exploratory modeling came to a halt, because of Bloch’s impossibility-theorem, the focus shifted from the development of a theory to new experiments. The first series of new experiments, carried out by Meissner, Ochsenfeld and Heidenreich (see page 152), Babbitt and Mendelssohn (page 155), and Schubnikow and Rjabinin (page 157), concerned the measurement of the state of magnetization of the region surrounding a body before and after the superconducting transition. Previously, Meissner and Ochsen- feld pointed out, it was believed that upon transition, any applied field H would be frozen in. Yet, their experiments called this into question, in a way replicated by later experiments of this kind: some experiments, such as Meissner and Ochsenfeld’s parallel cylinders experiment or the experiments by Rjabinin and Schubnikow, indicated that upon transition, a superconducting body’s magnetic permeability would become zero; others, such as Meissner and Ochsenfeld’s hollow cylinder-experiment or Babbitt and Mendelssohn’s sphere experiments, showed that while there was a certain increase in the magnetic field surrounding the superconductor, which indicated a decrease in the body’s permeability, there was no complete reduction to zero permeability. This led Meissner and Ochsenfeld to the conclusion that it was difficult to imagine how these results could be accommodated into a general representation of the superconducting phenomenon, since it rendered unclear how the magnetic flux density B related to the applied field H (see the quote on page 154). Mendelssohn and Babbitt arrived at a similar conclusion, namely that their results were in line neither with the old frozen in fields view nor with the zero permeability view, and that they indicated that zero permeability could only be obtained under special circumstances (see the quote on page 157). Only Rjabinin and Schubnikow took their experiments to argue clearly in favour of a phase with zero permeability (see the quote on page

222 Experiment, Time and Theory

159). As was the case with Bestelmeyer’s, Bucherer’s and Hupka’s experiments, we can call these experiments exploratory in the sense that they varied on particular aspects of the experimental set-up and procedure that was common practice at the time. A first aspect that was varied, if we follow Dahl (see the quote on page 168), was the way in which the superconducting state was brought about. Previously, standard laboratory practice was to bring it about by first cooling and then applying a field. This applied field would then bring about persistent currents, which was taken as evidence in favour of the existence of frozen in fields. It was then assumed that the same would arise when one proceeded in the opposite direction, by first applying a field and then cooling. One expected that the applied field would become frozen in too. What the experiments by Meissner and Ochsenfeld, Mendelssohn and Babbitt, and Rjabinin and Schubnikow suggested, however, was that this was not necessarily the case. A second, related variation of the experimental procedure, we have seen on page 168, can be discerned in the experiments by de Haas, Voogd and Casimir-Jonker on whether the direction of the applied field had an influence on the disappearance of the resistance (these were discussed on page 162). Kamerlingh Onnes and Tuyn, carried out measurements at only two different temperatures: a temperature T just below TC and the temperature 273K, i.e. zero degrees Celcius, and they then compared the values obtained at these two different temperatures (see equation 3.1 on page 135). What de Haas and colleagues did, by contrast, was measure how the resistance would differ when either the applied magnetic field or the temperature was kept constant and the other variable was increased in an almost continuous way (see figure 3.11 on page 165). This provided them with very detailed information about how the resistance could change during the superconducting transition, and contrary to what von Laue claimed (see page 163), they took these results to be difficult to reconcile with perfect conductivity (see the quote on page 165 as well as footnote 305). A third variation, as we have seen on page 169, concerned the way in which measurement instruments such as bismuth wires were used. While Kamerlingh Onnes and Tuyn attached these only to the surface (see the quote by Matricon and Waysand on page 169), de Haas and Casimir-Jonker inserted them into the superconducting rod they were experimenting on (see figure 3.9 on page 160). They compared measurements taken at temperatures just below and above TC , just like they had done with Voogd in their experiments on the influence of the direction of the applied field. As such, they were able to measure with great precision the way in which the resistance varied during the superconducting transition (see figure 3.10 on page 161), which showed that the resistance starts to reappear at different places at different moments. Their results, they suggested in their concluding remarks, seemed to be in line with those obtained by Meissner and Ochsenfeld, but they primarily indicated that the disappearance of the magnetic flux was a complex phenomenon, and that more measurements were required in order to obtain reliable information (see the quote on page 162).

Superconductivity and B = 0 We thus see how exploratory experimentation suggested that, contrary to what was expected, after the transition to the superconducting state, the magnetic ﬂux in-

223 Chapter 4. Manipulation and Exploration side the superconducting material would not be equal to the applied field strength H. Some experiments indicated that upon transition, the material’s permeability became zero. Others, however, primarily indicated that it was difficult to provide a simple and general characterization of a superconductor’s state of magnetization. As such, we end up with a situation that is very similar to the one that arose as a consequence of Bestelmeyer’s, Bucherer’s and Hupka’s experiments. The experiments by themselves should not be seen as establishing in any way how superconductors had to be conceptualized. They could be used, however, by scientists such as the London brothers to raise issues with the robustness of the patterns identified in the data of experiments such as those by Kamerlingh Onnes and Tuyn, since the experimental set-up and the procedure employed in these experiments were maybe not as reliable as assumed. In short, there was no stable conceptualization of these experimental results on offer. This situation differs from the velocity-dependence case, where a programme was already available for elaborating an alternative conceptualization, namely the relativistic approach. In the superconductivity case, no such programme was available, since Bloch’s impossibility-theorem made it clear that the most promising candidate, the quantum-mechanical electron-theory of conduction, could not offer such an alternative conceptualization. And while Gorter’s thermodynamical account, based on the assumption B = 0 (see page 158), was in line with the results of the experiments by Rjabinin and Schubnikow (see the quote on page 159) and Keesom and Kok (see page 167), it did not fit, for example, with the results of Meissner and Ochsenfeld’s hollow cylinders experiment (see page 154) or with those of Mendelssohn and Bab- bitt (see page 156). As such, it was unclear how the study of superconductivity was to proceed on the basis of these results. Because of this, Gorter and Casimir and the London brothers did not turn to the development of a theory of the hidden phenomena responsible for superconductivity, but rather to the development of a phenomenological theory, i.e. of a description that allowed them to adequately classify what they took to be the known empirical regularities. This reconceptualization was achieved primarily through the work of the Lon- don brothers. They took the assumption B = 0 – which they saw as an empirical regularity, because of Meissner and Ochsenfeld’s experiment, and which they called the Meissner effect (see page 174) – from Gorter and Casimir, who had shown that it could be used to characterize the superconducting transition as a reversible cycle between two distinct phases (see pages 158 and 170). What the London brothers did was turn it into a representation of the pure superconducting state. This move – described by Matricon and Waysand (2003, p. 71) as turning the result of Meissner and Ochsenfeld’s parallel cylinders-result into a postulate – was rather bold, given that there were many experimental results that indicated that this assumption did not have general validity. Meissner argued, for example, that it could not accommodate the other experimental results he had obtained with Ochsenfeld and which were confirmed by Heidenreich, namely those of the hollow cylinder-experiments (see page 182). Mendelssohn and Babbitt took their experiments to indicate that this assumption only held under very specific circumstances (see the quote on page 157). Even Gorter and Casimir themselves stated, in the conclusion of their (1934) article, that while the assumption B = 0 definitely offered the most simple and elegant way to represent the superconducting phase, it could also lose its rigour with regards to the superconducting transition (see page 171).

224 Experiment, Time and Theory

By postulating B = 0 as an empirical regularity, it could act as a bootstrap on the London brothers’ investigation of how to conceptualize the empirical regularities which they took to belong to the domain of superconductivity. The investigation of a first regularity, the penetration depth of the superconducting currents as it was provided by the acceleration equation, then led them to their phenomenological account of the electrodynamics of superconductors, i.e. their equations (3.8) and (3.9) (discussed on page 174), which, as they showed then, could also cover thermodynamical regularities such as e.g. Joule’s law (see footnote 323). In the final part of their first paper, London and London reflected on what their phenomenological account could imply for the study of the hidden phenomena responsible for the emergence of the empirical regularities captured by their equations. They thus embarked on an exploration of which properties one could possibly ascribe to the electrons constituting the superconducting currents, and this search was both bootstrapped by the empirical regularities obtained and bounded by the analogy with Gordon’s relativistic formulation of Schrödinger’swave mechanics (see footnote 325). They investigated, more specifically, how the electrons were to be conceptualized: as free electrons, which led them to a form of weak diamagnetism which they called Landau-Peierls diamagnetism (see footnote 326), or as electrons coupled by some kind of interaction, which led them to the suggestion that a superconducting current could arise in case a magnetic field was present (see page 175). In this way, the London brothers’ search for an adequate conceptualization of what they took to be surface phenomena led them to a complete reconceptualization of the superconducting state. Whereas previously, the superconducting state was assumed to persist even when the applied magnetic field was removed, on their view the presence of a magnetic field was a necessary condition. And as Fritz Lon- don argued in his Royal Society lecture, this conceptualization suggested a way to overcome the impossibility-theorem raised by Bloch, at least if the interaction responsible for the coupling of the electrons could be specified (see page 178). As such, it also put them on the way towards the development of an account of the hidden phenomena underlying these surface regularities, i.e. their diamagnetic programme. These hidden phenomena, Fritz argued, would also be able to account for why the experimental results of Kamerlingh Onnes and Tuyn and of Meissner’s hollow cylinder-experiments had to be recognized as exceptions to the pure superconducting state (B = 0) brought about in Meissner’s two cylinders-experiment, namely because they involved superconducting rings. As such, it was through exploratory modeling, bootstrapped by their postulated Meissner effect and bound by their diamagnetic programme, that Fritz and Heinz London were put on the way towards a stable fit between surface regularities and a hidden phenomenon. This modeling was a search for a state Ψ of the electrons that, when the temperature was lowered (T < TC ) and an external magnetic field was applied (H < HC ), would remain undisturbed under variations of the applied field ∆H, in line with their characterization of a future electron-theory of superconductivity (see the quote on page 179), but which at the same time could carry a current J, in line with the Londons’ equations. As such, the London brothers were searching for a stable fit between a hidden phenomenon and the empirical regularities obtained: the ideal superconducting state B = 0 obtained by Meissner and Ochsenfeld in their measurements of the magnetic flux B outside the superconducting material and the

225 Chapter 4. Manipulation and Exploration

exception-state 0 < B ≤ H0 obtained by Kamerlingh Onnes and Tuyn in their measurements of the persistent currents I(∞). This programme for a stable ﬁt can be expressed in terms of the zero permeability interpretation oﬀered by Heinz and Fritz London of the experimental inference characterizing experiments such as as those of Kamerlingh Onnes and Tuyn (this interpretation is discussed on page 181):

[The Zero Permeability Interpretation]: c i i (Ψ) + (∆H) −→ Ψ −→ J −−−−→ (B = 0)&(0 < B ≤ H0) I(∞),B

Such an interpretation would show to the London brothers that Meissner and Ochsen- feld’s parallel cylinders experiments had worked, in the sense that it would allow them to recognize that the data produced by these experiments displayed an empirical regularity (the pure superconducting state B = 0) that validated their claims about what they took to be responsible for this regularity, i.e. the diamagnetic state Ψ. And it would show them that Kamerlingh Onnes and Tuyn’s experiments had worked, in the sense that it would allow them to recognize that the data produced by these experiments also displayed an empirical regularity (the exception state of frozen in fields) that validated their claims about the hidden phenomenon supposedly responsible for this regularity, i.e. the electrons in the state Ψ circulating in superconducting rings. If this programme could be accomplished, a stable fit would thus be obtained, in the sense that the surface regularities and the hidden phenomenon would stabilize each other. That the Londons saw themselves as on the way towards such a stable fit, does not mean, however, that others also saw it in this way. Both elements of their stable fit, i.e. the surface regularities and the hidden phenomena, were critized by others. Meissner, as we have seen on page 182, argued that they could not account for the empirical regularities obtained in the hollow cylinder-experiments, which raised issues with the general validity of their B = 0 assumption. A.H. Wilson claimed that, at the time, their equations formed a purely formal contribution to the debate, which did not say anything about how the phenomenon came about, i.e. about the underlying hidden phenomenon (see page 182). Gorter, finally, claimed that the Londons’ account was often seen as just a reformulation of the acceleration equation, rather than as a complete reconceptualization of the phenomenon of superconductivity (see the quote on page 182). Even the London brothers themselves, at this point, had to admit that their work only offered a programme for the elaboration of a stable fit. The Meissner effect, they pointed out, only formed an idealization out of empirical results that were still uncertain (see the quote on page 179), and the diamagnetic programme also seemed to have its limitations, since it suggested an eigenfunction that, upon application of an electric field, would be disturbed, whereas this should not be the case for superconductors (see page 180). The problem was that it was still not clear which interaction was responsible for the coupling of the electrons required to allow for the emergence of a stable current in a minimal energy state (see the quote on page 180). It was only after further exploratory experimentation and modeling that a stable fit of some kind could eventually be obtained. These new experiments were all very similar to the previous ones – they all attempted to investigate further the state of magnetization during the superconducting transition –, but they also varied, on spe-

226 Experiment, Time and Theory cific aspects, with these earlier experiments. De Haas and Guinau further improved on how bismuth wires could be inserted in and attached to the superconducting body (see page 183). Mendelssohn, Keeley and Moore investigated not only pure materials but also mixtures (see figure 3.13 on page 188). Shoenberg, finally, investigated whether applying inhomogeneous fields would make a difference (see page 188). Because of these variations, the way in which these experiments related to those of Meissner and Ochsenfeld also changed. While earlier experiments were still concerned with whether it was indeed possible to speak about a state B = 0 for a superconducting material, these new experiments all took this state as a real possibility, and their concern was rather with how this ideal or pure state was to be delineated. What is significant, however, is that the different scientists often still expressed their results in terms of frozen in fields and perfect conductivity: see e.g. de Haas and Guinau’s conceptualization of their results in terms of von Laue’s analysis of perfect conductors (page 184), Keely, Mendelssohn and Moore’s characterization of Gorter’s position in terms of a remaining frozen in flux (page 187), or Shoen- berg’s claim that his experiments showed that “a small magnetization (conveniently referred to as the ‘frozen in moment’) is left in zero field” (1936, p. 716) (discussed on page 188). This showed that while they took the ideal state B = 0 to be a real possibility, their experiments also indicated that even for very pure superconducting materials, it was still necessary to speak about frozen in fields. As Mendelssohn put it, “[t]he experimental realization of ‘ideal’ conditions which enable this question to be decided [i.e. to determine what counted as the ‘ideal’ state], however, encounters considerable difficulties” (1936, p. 565). As such, these experiments could be seen as exploring how robust the patterns were that one could identify in the data obtained by means of the pure state B = 0 conceptualization. To obtain a stable fit, the previous discussions have suggested, exploratory experimentation and modeling have to work in tandem. This is what we see here as well when we compare Fritz London’s two papers in which he elaborates his theory of the intermediate state. In his (1936b) article (discussed on page 185), he still took it to be solely a reasoning tool that would probably turn out incorrect (see footnote 338). Bound by the equations he had obtained earlier with his brother, and constrained by the results obtained by de Haas and Guinau, this allowed him to investigate specifically how to characterize the role of the magnetic field in the emergence of the intermediate state (he could not specify the role of the electric field at that time yet, see page 186). In his (1937a) paper, on the other hand, he no longer presented the intermediate state as merely hypothetical, but rather as an elementary phenomenon that could account not only for the results obtained by Kamerlingh Onnes and Tuyn, and Meissner and Ochsenfeld, but also for those obtained by de Haas and Guinau, Mendelssohn, Keeley and Moore, and Shoenberg. What Fritz London now presented was an account of the hidden phenomenon that was responsible for these empirical regularities, i.e. the intermediate state. He was now no longer concerned with investigating the question how to characterize the role of the electric and magnetic fields in the production of these empirical regularities. He had obtained such an account, since he could now claim that the emergence of the superconducting state could be accounted for completely in terms of the mean values of the field strengths E¯, B¯ (see the quote on page 191). As such, Fritz London had obtained a stable fit: the

227 Chapter 4. Manipulation and Exploration intermediate state as a hidden phenomenon could account for the empirical regularities obtained in different experiments, and these regularities in turn validated his account of the intermediate state. This stable fit differed, however, from the one obtained with his brother, i.e. their diamagnetic programme. This change shows itself, first of all, in how Fritz London reconceptualized their equations (3.8) and (3.9) (discussed on page 174): whereas in their original papers these only provided a macroscopical characterization of the pure and ideal superconducting state B = 0, now they were to be seen as offering a microscopical account of the intermediate state (see the quote on page 186). It was this intermediate state that was to account, more specifically, for both the Meissner effect (B = 0) and the emergence of frozen in fields because of the formation of superconducting rings. This shows that this new hidden phenomenon of the intermediate state also entailed a reconceptualization of some empirical regularities: whereas earlier the Meissner effect was to be seen as the standard superconducting state and superconducting rings as the exception, now both were secondary to the intermediate state. In this way, it also entailed an explanation for why B = 0 was to be seen as the ideal case: this state followed as a limiting case of the mean value field equations that governed the intermediate state (see page 191). Moreover, this intermediate state also entailed a reconceptualization of the diamagnetic programme. Previously, the success or failure of the programme depended on whether or not a coupling interaction for the electrons could be found. Now, this question of how the microstructure responsible for superconductivity looked like could be avoided, by making use of the mean values of the field strengths (see the quote on page 191). As such, this stable fit was no longer a programme, as the Lon- don brothers’ diamagnetic conception had been: its viability no longer depended on finding a fitting electron-account to account for the empirical regularities.368 Rather, whatever the precise electron-interaction that would be responsible for the coupling, it would give rise, according to Fritz London, to the mean field values that govern the emergence of the intermediate state. In this way, Fritz London had obtained an actual hidden phenomenon that stabilized the empirical regularities making up the phenomenon of superconductivity, and which in turn validated his intermediate state account. As we have seen on page 193, this stable fit can be expressed in terms of the following interpretation of the experimental manipulations carried out by Kamerlingh Onnes and Tuyn, Meissner and Ochsenfeld and others:

[The Intermediate State Interpretation]: c 0 0 i i (E¯&B¯) + (∆H) −→ E¯ &B¯ −→ J −−−−−−→ (B = 0)&(0 < B ≤ H0) I(∞),B,R

On this interpretation, lowering the temperature and applying a magnetic field brings the electrons, via an unspecified interaction, into the intermediate state (E¯, B¯). Variations in the magnetic field change the mean field values, and this

368 This does not mean that the emergence of the superconducting state is no longer conceptualized in terms of electrons. As Fritz London pointed out in the concluding paragraph of his article, his theory of the intermediate state was to guide research on how an electron-model of superconductivity was to be constructed: “The next stage will have to be the development of the electronic basis of this theory. One might presume that the new aspect here presented of supraconductivity may also give an indication for the construction of a molecular model of the supraconductor” (1937a, p. 836).

228 Experiment, Time and Theory will bring about changes in the persistent currents, which can be characterized in terms of the Londons’ equations (J). Applying these equations in turn to the data obtained in the different experiments – Kamerlingh Onnes and Tuyn’s observations on persistent currents I(∞), Meissner and Ochsenfeld’s measurements of the external magnetic flux B, de Haas and Guinau’s measurements of the resistance R, etc. – , then allowed the London brothers to show that these displayed different empirical regularities, depending on the state of the body: zero permeability (B = 0) for pure superconducting regions, and frozen in fields (0 < B ≤ H0) for regions that formed superconducting rings.

4.3.3 Manipulability, Exploration and Stabilization The historical discussions in chapters 2 and 3 have shown that the experimental manipulations discussed can be characterized in terms of experimental inferences. These inferences link a manipulation, i.e. an interaction between an entity endowed with certain supposedly established properties and an experimental set-up with supposedly fixed characteristics, to an effect that scientists can take to provide information. These experimental inferences are thus very similar to Hacking’s home truths or Cartwright’s capacity-claims, in that they concern a causal link between manipulation and effect. The discussions have also shown that contrary to what Hacking and Cartwright claim, these causal links in themselves do not yet provide any kind of knowledge about the entity supposedly manipulated. The manipulations carried out by Kauf- mann indicated to him that the electron’s mass was indeed velocity-dependent, but to say that these manipulations provided causal information about this property of the electron, in the sense of knowledge about how the application of electric and magnetic fields influences this mass exactly, the experimental inference characterizing the manipulation had to be interpreted. Such an interpretation is offered by a model of the entity manipulated, and it provides a detailed account of how the influence of the manipulation on the entity is to be conceptualized. It tells scientists how the manipulation, and thus the functioning of the experiment, is to be understood. In this way, an interpretation provides criteria for evaluating whether an experimental manipulation has worked, which is the case if the expected effect is indeed brought about. If this is the case, then the experimental results can at the same time be seen as a validation of the claims that the interpretation makes about the entity manipulated. As such, we see how interpretations of experimental inferences are to be understood in terms of Feest’s notion of a stable fit between the empirical regularities recognized in the data and the entities or processes supposedly responsible for these empirical regularities. An interpretation can allow scientists to recognize that an experimental manipulation has worked in the sense that it supplies a hidden phenomenon that provides them with identification criteria for empirical regularities which, if they are found in a data set, validate the interpretation’s account of the hidden phenomena. A successful interpretation thus consists of surface regularities and hidden phenomena stabilizing each other. This shows, as the historical discussions in the previous chapters have illustrated, that an interpretation of an experimental inference is in fact a dynamical process, since a stable fit can always be destabilized by new experiments or alternative ac-

229 Chapter 4. Manipulation and Exploration counts of the hidden phenomena. As Feest puts it, “neither surface regularities nor hidden regularities can be stabilized individually” (2011, p. 70). They stabilize each other, and when one of the two is problematized, the whole fit is destabilized. When this happens, scientists will search for a way to restore stability, but there is often no clear idea about how this is to be done. Some scientists may argue that the old fit has in fact not been destabilized, because the new experiments did not function properly, or because the alternative account of the hidden phenomenon does not fit with other regularities. Or they may try to find ways to incorporate these new results or some aspects of the alternative account into the existing stable fit. Others may argue that the new experiments show that the old experiments were not reliable, and that the empirical regularities they produced are therefore not robust. Or they may claim that the alternative model shows why the old account of the hidden phenomenon cannot be correct or is only an approximation or an exception. Because these interpretations are such dynamical processes, the information provided by an experimental manipulation can change over time. This was seen in both historical cases, where what the data provided by specific experiments were taken to show changed over time, as a consequence of changes in the stable fit that was used to interpret the manipulations producing these data. This shows, contra Hack- ing and Cartwright, that the information provided by experimental manipulation should not be characterized in terms of factual, established and theory-independent knowledge of the causal properties of the entity manipulated. In order to obtain information about the causal properties of the entity, an interpretation is required, and given that a model of the entity manipulated is required for the construction of such an interpretation, this information is not theory-independent. It is not established either, since given that the stable fit underlying the interpretation can be destabilized, the information provided is subject to such changes as well. This leaves us with the characterization of this information as factual. The historical cases discussed have already indicated that this characterization is problematic as well, since all experiments discussed allowed for multiple, incompatible claims about the properties of the entities manipulated. Kaufmann’s (1906b) results could be taken to allow for both a rigid electron dynamics (Abraham) and a deformable electron dynamics (Bucherer-Langevin). And Meissner and Ochsenfeld’s (1933) results allowed for both a perfect conductivity view with frozen in fields, and a zero permeability view without such fields. This indicates that an experimental manipulation, insofar as it can be taken to have functioned properly according to a particular interpretation, provides not factual but modal knowledge of which possibilities are conceivable for the entity manipulated. By this, I mean that the experimental results inform us about the boundaries for acceptable accounts of the entity, which are those accounts that are in line with the results obtained in the experiment. This space of conceivable possibilities can then be explored further by means of both experimentation and modeling. Such exploration can also, however, destabilize the fit underlying an interpretation of the experimental manipulations, by indicating that the surface phenomena obtained are not robust or by showing that the hidden phenomenon is problematic. As such, the space of possibilities delineated by experimental results is dynamical because the stable fit offering an interpretation of these results is. This characterization of the information provided by means of successful experimental manipulation, in terms of a space of conceivable possibilities shapen and

230 Experiment, Time and Theory constrained by a stable fit, can be clarified as follows. We have seen that an experimental inference links a manipulation, i.e. an interaction between an entity and an experimental set-up, to an effect. Interpreting this inference then means that the effect is analysed in terms of the manipulation endowing the entity with a specific kind of behaviour, which leads the entity to interact again with the set-up in such a way that the effect will be produced. Thus, applying electric and magnetic fields to Becquerel rays deflects the electrons constituting these rays. An interpretation such as the electromagnetic one tells us that this deflection is to be understood in terms of quasi-stationary acceleration, and that this will bring the electrons to hit the photographic plate in such a way that they will give rise to dots with a specific deflection y0 that form a curve with a specific curvature ρ. The relativistic interpretation, on the other hand, tells us that this deflection endows the electron with relativistic motion, which, according to this interpretation, will make the electrons hit the photographic plate in such a way that we end with a different deflection and a curve with a different curvature. As such, an interpretation analyses the causal chain that is the experimental inference in terms of two interactions between entity and set-up: a cause-interaction and an effect-interaction. On the assumption that the cause-interaction has worked as supposed – i.e., that the properties of the set-up are properly fixed, that the entity manipulated is indeed endowed with the established properties that the interpretation ascribes to it, and that these interact as supposed –, the interpretation then makes us expect that the effect-interaction will also work as supposed. If this is indeed the case, the results can be taken to validate this interpretation, but equally well each other interpretation that tells us how, given the correct cause-interaction, we would end up with the same effect-interaction. In this way, experimental results cannot be taken to establish factual knowledge about the entity manipulated, but rather modal knowledge about what is conceivable with regards to the entity manipulated. What the previous paragraph also shows is that this modal knowledge produced by an interpretation of a particular experimental inference is conditional on the proper functioning of the cause-interaction. If it is shown either that the properties of the set-up are not as fixed as assumed, or that the supposedly established properties of the entity are not as established as assumed, then it can be argued that the experiment is not functioning reliably, and hence that the regularities obtained are perhaps not robust. In that case, the experimental results no longer constrain and shape what is conceivable with respect to the entity manipulated, since it is not clear anymore whether we should be looking for an interpretation that links the experimental manipulation to the effect observed in the disputed experiments. Such a shift in what is conceivable is clearly observed in the Kaufmann case. Planck there argued that the charge-to-mass ratio /µ0 ascribed by Kaufmann to the electron was problematic (see page 79). He also claimed, with Stark, that the electric fields employed in Kaufmann’s experimental set-up were maybe not as stable as Kaufmann had assumed (see page 84). Given that Bestelmeyer had obtained a different empirical regularity than Kaufmann, Planck was then able to argue that Kaufmann’s results should not be seen as excluding the relativistic account of the electron as a possibility. Hence, the space of conceivable possibilities was opened up again, by raising doubts about the supposedly fixed properties of the set-up and the supposedly established properties of the electron.

231 Chapter 4. Manipulation and Exploration

Something similar took place in the superconductivity case. Bloch’s impossibility- theorem raised doubts about whether superconductivity had to be conceptualized in terms of an electron-theory of conduction (see page 149). The experiments by Meissner and Ochsenfeld and others then raised issues with whether Kamerlingh Onnes and Tuyn’s set-up had functioned properly, since investigating further specific aspects of their set-up and methodology brought them to results that were different from those one would expect on the perfect conductivity conception (see page 167 for a discussion of how they varied on Kamerlingh Onnes and Tuyn’s experiments). In this way, Gorter and Casimir and Fritz and Heinz London could argue that Kamerlingh Onnes and Tuyn’s experiments should not be seen as excluding superconductors without frozen in fields. Hence, again the space of conceivable possibilities was opened up by raising doubts about the supposedly fixed properties of the experiments and the supposedly established properties of the electron. What drives such shifts in the space of conceivable possibilities is exploratory modeling and experimentation. Exploratory modeling can show that alternative accounts of the entity’s role in the cause-interaction and effect-interaction are also conceivable, or that an account of the entity is not that plausible after all. Ex- ploratory experimentation can show, by varying certain aspects of the set-up of previous experiments, that the set-up is possibly not as reliable as assumed, since the regularities obtained in the previous experiments are not reproducible. Insofar as the previous sections have shown that the shifts between different interpretations were driven by exploratory modeling and experimentation, we can thus say that these concepts are not only applicable to fields where there is no conceptualization on offer yet, as Massimi and especially Steinle presented them,369 but equally well to fields where there is already a conceptualization present, such as the electromagnetic interpretation or the perfect conductivity interpretation. At the same time, the cases of exploratory experimentation and modeling discussed also differed in certain respects from the way in which Steinle and Massimi conceptualized

369 That Steinle presented exploratory experimentation in this way should be clear. As he puts it, “[i]t typically takes place in those periods of scientific development in which – for whatever reasons – no well-formed theory or even no conceptual framework is available or regarded as reliable” (1997, p. S70). That Massimi presented exploratory modeling in this way could be disputed. On the one hand, she explicitly states that this practice is bounded by laws of nature, which suggests that there is already a theoretical framework available. In her discussion of a case of exploratory modeling, on the other hand, she makes it clear that the laws that bind it should not be seen as already offering a theoretical conceptualization of what is to be modeled, but rather only as offering minimal boundaries within which particular hypothetical entities can then be conceptualized (see also her characterization of these laws as fixing nomological boundaries, discussed on page 202): “Over past decades, scientific efforts to find new particles, whose existence (if proved) would force physics to go beyond the Standard Model, have increasingly resorted to a variety of model-independent searches. By ‘model-independent,’ high-energy physicists usually mean ‘Standard-Model-independent’ searches, that is, searches that bracket as much as possible assumptions about the Standard Model so as not to compromise the possibility of detecting new entities whose physical features are not accurately described or represented by the Standard Model. Perspectival models are widely used in model-independent searches in Beyond Standard Model (BSM) physics because they cut across traditional philosophical distinctions between data models and theoretical models. Although data enter in perspectival modeling by fixing, for example, the exclusion regions for relevant events under study; perspectival models are not a sheer description or representation of the data. Perspectival models are not theoretical models either, because they are designed to be model-independent (i.e., as independent as possible from the Standard Model).” (Massimi, 2018, p. 349 – 350). For Massimi’s use of the term ‘perspectival model’ as an alternative for what I have called here ‘exploratory models’, see footnote 349.

232 Experiment, Time and Theory them. In what follows, I will discuss some of these differences, in order to further elaborate an account of the epistemology of exploration in such fields where there is already a conceptualization present. A first difference concerns Steinle’s claim that exploratory experimentation pro- ceeds mainly by means of the flexibility of certain aspects of a particular experimental set-up. None of the experiments discussed in the previous chapters displayed such flexibility. All were characterized by a rather rigid set-up, designed to investigate specific theoretical questions. Still, I have argued, we can speak about exploratory experimentation in both cases, if we conceptualize it not in terms of particular experiments, but rather in terms of variations on an experimental practice that was present at the time. Bestelmeyer’s, Bucherer’s and Hupka’s experiments could be seen as exploratory experiments, I argued on page 213, because they varied on Kauf- mann’s experimental practice of constantly trying to improve accuracy. Meissner and Ochsenfeld’s experiments and those carried out by de Haas, Voogd and Casimir- Jonker could also be seen as exploratory experimentation, I claimed on page 222, because they varied on different aspects of the way in which experiments such as those by Kamerlingh Onnes and Tuyn were carried out (see footnotes 250 and 367 for illustrations of this practice). A second difference concerns Steinle’s claim that successful exploratory experimentation can lead scientists to a new or better conceptualization of the field studied. However, none of the experiments discussed in the previous chapters was able to provide such a new conceptualization in itself. What the experiments I called exploratory accomplished, was rather that they enabled certain scientists to argue that the previous experiments were perhaps not so reliable as assumed, and that the empirical regularities provided by these earlier experiments were therefore not robust. Bestelmeyer’s, Bucherer’s or Hupka’s experiments should not be seen as establishing that the electron’s velocity-dependence of mass had to be conceptualized in relativistic terms, since each of them could, and was, criticized in turn. Meissner and Ochsenfeld’s parallel cylinders experiments or those by Rjabinin and Schubnikow or Keesom and Kok did not establish that the state of magnetization of superconductors should be conceptualized in terms of zero permeability either, since the hollow cylinders experiment by Meissner and Ochsenfeld, the experiments by Mendelssohn and Babbitt and those by de Haas and Casimir-Jonker suggested that the phenomenon fitted neither the perfect conductivity view nor the zero permeability view. Neither should the experiments by de Haas and Guinau, Mendelssohn, Keeley and Moore, and Shoenberg be seen as indicating that the intermediate state should be conceptualized in terms of Fritz London’s account: Shoenberg, for example, saw his experiments as primarily pointing out the difficulty of understanding this state (see page 189). The source of these differences, I believe, is that in the cases I have studied, there was already a conceptualization of the field, in the form of an interpretation supported by a stable fit, present. Because this stable fit provides an account of what a working experiment is, carrying out a new experiment that varies on significant aspects of such a working experiment cannot just show that this older working experiment does not work. It can always be argued that the newer experiments in fact did not work, because their results are not in line with what one would expect from a working experiment such as the older one. This shows that when there is already a conceptualization present, it will inform

233 Chapter 4. Manipulation and Exploration the way in which scientists act within a particular field of study, in line with what Steinle claimed in the quote on page 200. Such a conceptualization, we have seen, informs scientists about which experiments can be seen as functioning properly, and as such, it also provides examples of how future experiments can and should be carried out. Thus, since Kaufmann took his earlier experiments to have worked well, he continued working with an improved version of them. And because Kamerlingh Onnes had been very successful with his common laboratory practice (see footnote 250), he continued using it, with improved technology and various different materials. A third difference concerns Massimi’s claim that exploratory modeling bootstrapped by experimental evidence leads to knowledge of objective possibilities. We can raise the question whether the possibilities obtained by means of the examples of exploratory modeling discussed are best characterized in terms of objectivity. In the Kaufmann case, for example, this could entail that exploratory modeling bounded by the electromagnetic world view and bootstrapped by Kaufmann’s experimental results, as was done by Abraham and Ehrenfest, would have ruled out a relativistic electron as objectively impossible or not physically conceivable. This seems to go against the fact that Lorentz and Poincarécould construct a relativistic model of the electron that, while not in line with Kaufmann’s results, still remained an objective possibility, in the sense that it could be tested, evaluated and compared with other electron-models. Because of this, I propose that in what follows, experimental evidence bootstraps exploratory modeling not with respect to what is objectively possible, but rather with respect to what is plausible within the range of physically conceiveable objective possibilities. Thus, while Kaufmann’s experimental results did not completely rule out the possibility of a relativistic electron, they did indicate that it was less plausible, since it had to be adapted quite drastically to bring it in line with Kauf- mann’s experimental results (see the quote on page 69, where Kaufmann suggests how this could be done, but also claims that nobody would like to go that way). On this view, when there is already a conceptualization of the field of study present, in the sense of a stable fit providing a hidden phenomenon that can account for why certain experiments are taken to work, certain models or theories concerning the hidden phenomenon will be seen as more plausible than others, because they are more in line with the empirical regularities that are obtained in these properly functioning experiments. New experimental results, which are not in line with the earlier experiments that were taken to function properly, can allow scientists in favour of the less plausible models to argue that the old experimental results are not that reliable, and that the plausibility hierarchy is therefore not valid. In this way, models that are not in line with particular experimental results are not objectively impossible when these results are taken to bootstrap exploratory modeling, and they can even help in overturning which physically conceivable objectively possible models are seen as most plausible. A fourth difference concerns Massimi’s claim that it is laws of nature that are to act as constraints on what is physically conceivable. In neither of the two cases discussed was exploratory modeling bound solely by what we would call laws of nature. In the Kaufmann case, exploratory modeling was equally bounded by either the electromagnetic world view or the relativistic approach, and in the superconductivity case, it was constrained by either the perfect conductivity conception or the

234 Experiment, Time and Theory

B = 0 postulate as well. This does not mean that laws of nature did not play a role, but besides them, other factors also acted as constraints on exploratory modeling. What is responsible for this difference, again, is that in the cases discussed we are dealing with fields where there is already a conceptualization present. This conceptualization informs and shapes the way in which scientists approach new findings in the domain. Those who take the conceptualization to be applicable will try to explore how to model these new findings in terms of the hidden phenomena that can account, according to the stable fit present, for already established surface phenomena within the domain. This shows, again in line with Steinle’s claim on page 200, that when there is already a conceptualization present, it will inform and influence the way in which scientists think and reason when they try to elaborate existing models or conceive alternative ones. This is because the stable fit underlying this conceptualization validates the hidden phenomenon that is part of the fit, and as such, it provides scientists with an example of how phenomena in the field are to be approached. As such, in fields where there is already a conceptualization present, in the form of a stable fit, this conceptualization will shape and influence the way in which experimentation and modeling are carried out. The stable fit indicates to scientists which experiments have functioned properly and which hidden phenomena one can take as validated, and in this way, it shapes and influences how they are to reason and act in the future. As such, the information that, according to a particular stable fit, is provided by an experimental manipulation is always historically situated, in the sense that it is interpreted and evaluated by reference to earlier experiments and in terms of its promise for the future. This now also means that if a stable fit is replaced by an alternative one, the past and future of the information provided by an experimental manipulation will change as well. This is to be expected, since, as Steinle pointed out by means of the quote from Fleck (see footnote 348), after conceptual change has taken place, scientists will also reconceptualize what happened in the past. This can be seen, for example, in Planck’s work on the law of the inertia of energy, where he redraws the way in which Abraham’s elaboration of the notion of electromagnetic momentum relates to the past and the future. Whereas Abraham saw his notion as offering an alternative that could replace the Newtonian past in such a way that it would lead to a future electromagnetic world view, Planck reconceptualized it as an addition to the mechanical notion of momentum that formed a step on the progression toward the theory of relativity. In this way, Planck could not only reconceptualize the past but also the future, in the sense that his progression allowed him to present the theory of relativity as the best way to further elaborate the foundations of physics. Hence, a stable fit will influence and shape the way in which scientists construct what Staley calls the research histories of their investigations, i.e. the “accounts of the past [. . . ] that scientists offer in key papers and review studies[, which] play a substantive role in shaping understandings of new theory” (Staley, 2008a, p. 294; emphasis added).

4.3.4 Exploration and the Realist Anthropology The standard scientiﬁc realist position, we have seen in section 1.3.1, relied on a conceptualization of scientiﬁc success in terms of a historically stable correspondence

235 Chapter 4. Manipulation and Exploration between representations and reality. Quine, van Fraassen and Laudan problematized, however, each element of this realist hypothesis, as we have seen in section 1.3.5, by arguing that observation in itself could only provide us with a historically variable connection between multiple, incompatible theories and that which is observable for us. And, Hacking argued, we could not expect to improve on this situation as long as we stuck with such a spectator-theory of knowledge: if all we have is observation to distinguish true from false, then we will never be able to distinguish true from false beyond the observable, since we cannot go outside observation to check whether what we observe is correct or mere appearance (see the quote on page 6). Cartwright and Hacking therefore proposed their manipulability-idea as an alternative epistemology that could sidestep this issue. Experimental manipulations provide us with theory-independent knowledge of the causal properties of an entity under investigation, and if we can then use this knowledge to manipulate the entity to bring about a specific effect, we have as good evidence as we can get for the existence of this entity. Cartwright and Hacking thus conceptualize success in terms of a connection between theory-independent home truths and created effects that is stable over time, in the sense that they are stabilized in a process of self-vindication (see the quote on page 32). This theory-independence of these home truths was disputed, however, by Mor- rison, Massimi and Arabatzis, which led them to argue that in the end, Cartwright’s and Hacking’s realism falls back into standard scientific realism (see the quotes by Morrison on page 34 and by Massimi on page 38). This raised the question how we could characterize the information provided by manipulation, if not in terms of theory-independent home truths. On the basis of the study of two historical episodes, I argued that this information had to be characterized in terms of an epistemology of exploration. On this view, experimental manipulations can be taken to provide modal knowledge of the plausibility of different accounts of what goes on in the experimental set-up. In order to obtain such information, however, an interpretation of the experimental manipulation is required, i.e. a conceptualization provided by a model of the entity that tells us how the manipulation influences the entity in such a way that it will bring about a certain effect. Elaborating this epistemology also showed that the information provided by an experimental manipulation can shift over time, since further exploration can indicate that what was taken to be a stable fit was not so stable after all. And when exploratory modeling and experimentation work in tandem, in the sense that a new model suggests a way to make sense of newly obtained data, such exploration can also give rise to a programme for the elaboration of a new stable fit. This exploratory epistemology of manipulation was elaborated, however, by putting to the side the realism-issue that Cartwright and Hacking wanted to address. Neither case discussed concerned the establishment of the existence of an entity by means of manipulation, or disputes about the existence of the entity manipulated. The reason for this was that it was the realism-issue that brought Hacking and Cart- wright to claim that the causal knowledge obtained by means of manipulation was factual, established and theory-independent: only in this way could they argue that a historically stable correspondence between reality and representation was possible that would not fall prey to the arguments raised against the standard scientific

236 Experiment, Time and Theory realist position. As such, putting aside the realism-issue opened up the space for an exploration of a diﬀerent conceptualization of the epistemology of manipulation. It also entails, however, that the realism-issue still needs to be addressed in some sense, since, according to Hacking, this issue is closely connected with epistemology:

I have just run together claims about reality and claims about what we know. My realism about entities implies both that a satisfactory theoretical entity would be one that existed (and was not merely a handy intellectual tool). That is a claim about entities and reality. It also implies that we actually know, or have good reason to believe in, at least some such entities in present science. That is a claim about knowledge. I run knowledge and reality together because the whole issue would be idle if we did not now have some entities that some of us think really do exist. If we were talking about some future scientiﬁc utopia I would withdraw from the discussion. (Hacking, 1983, p. 28)

I will not use the historical cases discussed to formulate an argument either in favour or contra the existence of the electron, since they do not allow for this: in neither of them was the electron’s existence at issue. As Hacking points out, however, the realism-issue comprises more than just the question whether or not the electron exists: a realist position offers a programme that touches on the whole of philosophy of science (see footnote 26). As a sort of final, tentative investigation, I will therefore reflect on what the epistemology of exploration would have to say about the realist programme underlying the manipulability-idea, i.e. what Hacking would call its anthropology (see section 1.2). The discussion above shows that Hacking and Cartwright still operate within the framework of the anthropology underlying Putnam’s realist strategy (see the quote on page 7). Where the standard scientific realist takes successful theory to establish truth, Cartwright and Hacking take successful manipulation to establish existence. This is why the theory-dependence of home truths brings Morrison, Massimi and Arabatzis to argue that entity realism falls back into standard scientific realism. While they conceptualize success differently – as a correspondence either between theory and observation or between home truths and the creation of an effect –, their account of how scientists establish and recognize success is the same: either observation in itself or manipulation on its own can establish belief in truth or existence. This suggests that Cartwright’s and Hacking’s realism could fall prey to the same issue that, according to Hacking, led to the realism-impasse, namely the impossibility of the spectator-theory of knowledge to go beyond observation. Experimentation on its own, according to Hacking and Cartwright, can establish existence, if the manipulations carried out are successful (see e.g. the claim by Hacking, discussed on page 20, that it is manipulation that allows us to distinguish the real from the artefactual, or the quote by Cartwright on page 28, where she assumes that we can just recognize that a particular experimental set-up constitutes a nomological machine that produces empirical regularities). But the same problem then arises for the manipulation-epistemology, since how can we ever ascertain that our manipulations are indeed successful in the sense that Cartwright and Hacking require, if all we can rely on are these manipulations? Here, Cartwright and Hacking would argue that this is established empirically, by varying

237 Chapter 4. Manipulation and Exploration on the experimental set-up in order to show the robustness of the results obtained, or by empirically investigating the functioning of the set-up (see pages 21 and 28). But this would mean that one would carry out further manipulations to investigate whether the original manipulation was successful. This does not solve the problem, since the same question can be raised again: how are we to ascertain the success of these new manipulations if all we can rely on are manipulations? The problem is not that we will in fact never arrive at successful manipulation. Rather, the issue is that such success cannot be recognized solely on the basis of the same or further manipulations. Manipulation in itself cannot show that it was successful, since, as Heil points out in his discussion of Hupka’s experiments, each experiment can be criticized and disputed (see the quote on page 91). That there is always this possibility shows that our standards for the success of an experimental manipulation lie elsewhere. We need external standards or identification criteria to recognize that an experimental manipulation has worked. Such identification criteria, I have argued in the previous sections, are provided by what Feest calls a stable fit: it is on the basis of an existing stable fit between empirical regularities and a hidden phenomenon that scientists will be able to evaluate whether a new manipulation has functioned or not. This stable fit conception entails, we have seen, that the information provided by an experimental manipulation is always historically situated. It can change over time, and at each moment in time it has a certain past, i.e. earlier experiments taken to have provided the same information, and a future, i.e. what the information shows to be most plausible to investigate next. With changes in the stable fit, not only the information provided by this manipulation will be reconceptualized, but also its past and its future. Insofar as we can take such stable fits to allow scientists to recognize that an experimental manipulation has worked, this shows that there is a crucial element missing in the anthropology underlying both Putnam’s scientific realism and Cart- wright’s and Hacking’s entity realism: time. It is on the basis of a stable fit between a hidden phenomenon and experimental results obtained earlier that scientists can make sense of the experimental manipulations they are carrying out, i.e. evaluate whether they are working or not. It is on the basis of such a stable fit between a hidden phenomenon and earlier results that their modeling can be evaluated as either plausible or not. Finally, it is on the basis of such a stable fit, we have seen, that scientists can have a guide for how to proceed into the future, since it shapes and influences how they think and act. As such, in order to understand, on the realist anthropology, how scientists recognize that their theories or experiments are successful, we have to introduce temporal dimensions. It is the past that shapes the contemporary standards of success and the vision for the future. This entails that humans, according to this anthropology, interact not only with their environment, but also with their past, in the sense that they constantly conceptualize and reconceptualize how their current interactions relate to previous interactions, in such a way as to make sense of them and to understand what they will bring for the future. The realist hypothesis constructed by Hacking and Cartwright on the basis of their anthropology of manipulation, concerned the historical stability of a connection between home truths and created effects. Cartwright and Hacking took this historical stability to concern the robustness of causal claims under theory change.

238 Experiment, Time and Theory

Adding temporal dimensions to the anthropology changes, however, how we are to understand this historical stability. It becomes a process of reconceptualizing earlier results in light of a new stable fit, in such a way that a continuity is created with parts of earlier work, while other parts are forgotten. Von Laue, for example, reconceptualized the manipulations carried out by Kauf- mann: they had to be seen as endowing the electron with hyperbolic motion (see his interpretation on page 123), instead of quasi-stationary acceleration, as Abraham had done (see his interpretation on page 56). In this way, von Laue could create a continuity with Kaufmann’s results: they showed, even though they were not completely accurate, that there was a velocity-dependence of mass (see the quote on page 115). It also allowed him to reject other aspects of those experiments: his reconceptualization of quasi-stationary motion in terms of hyperbolic motion allowed him to argue that such experiments should not be taken as providing insight into the electron’s dynamics (see the quote on page 42 with which we opened chapter 2). In this way, the stable fit underlying von Laue’s relativistic interpretation of Kaufmann’s experimental manipulations entailed a reconceptualization of what was seen as historically stable. The same is observed in the superconductivity case. Fritz London reconceptualized the manipulations carried out by Kamerlingh Onnes and Tuyn: lowering the temperature and applying a magnetic field had to be seen as bringing the electrons in a state governed by the mean field strengths (see his interpretation on page 193) rather than by zero resistance, as Lorentz had done (see his interpretation on page 143). In this way, Fritz London could create a continuity with Kamerlingh Onnes and Tuyn’s results: they showed that frozen in fields could occur. At the same time, it also allowed him to reject other aspects of the experiments: his reconceptualization of perfect conductors in terms of the intermediate state allowed him to argue that they should not be taken to provide any insight into the pure, ideal superconducting state (see the quote on page 130 with which we opened chapter 3). In this way, the stable fit underlying Fritz London’s intermediate state interpretation entailed a reconceptualization of what was historically stable. As such, historical stabilization should not be seen as a process of self-vindication between established home truths and created phenomena, as Hacking argues (see the quote on page 32). Rather, it is a process of reconceptualizing earlier experimental manipulations on the basis of what one takes to be a stable fit between surface regularities and hidden phenomena, and this is a constant process, since a stable fit itself is a dynamical process. The historical stability of the connection between representation and reality is therefore not something that is established, but rather something that is constantly made and remade: it is an activity that involves the constant drawing and redrawing of what counts as the past, in order to bring it in line with the present so as to have an idea of what the future will bring.

239

Conclusion

Everyone knows that an experiment has little chance of succeeding when someone is watching.

The Cold Wars Jean Matricon and Georges Waysand

Summary

The aim of this dissertation has been to investigate and reﬂect upon the following research question:

[Research Question]: How are we to characterize the information provided by experimental manipulations?

This question arose out of the attempts by Cartwright and Hacking to overcome the impasse that the realism-debate, according to them, was in (see chapter 1). This impasse emerged, according to Hacking, out of the spectator-theory of knowledge underlying realist proposals such as Putnam’s: if all we can rely on in order to distinguish true from false is observation, then we shall never be able to distinguish truth from falsity beyond the observable, since we cannot go outside observation to check whether what we observe is correct or mere appearance (see the quote on page 6). What was responsible for this spectator-theory, as we have seen by means of a discussion of the different arguments raised against the realist position, was its representation-focused anthropology: Quine, van Fraassen and Laudan all argued, in their own way, that if we characterize scientists as human beings that are in the business of constructing representations whose success is evaluated in terms of observation, we cannot expect science to establish what the realist is after, namely a historically stable connection between representations and reality. Instead, they argued, all we can expect is to end up with historically variable connections between multiple, incompatible representations and that which we can observe. Cartwright and Hacking argued that this impasse could be overcome by replacing observation with manipulation. Successful manipulation, they claimed, can provide us with causal knowledge. If this knowledge allows us to bring about a particular effect, we have as good evidence as we can get for the existence of the entity that, according to these causal claims, is responsible for the produced effect. This causal knowledge can serve as a basis for a viable realist position, according to Hacking and Cartwright, because it is theory-independent: while we can have multiple, incompatible and empirically equivalent representations of the entity, once we know that we can manipulate it in specific ways, we are justified in taking it to exist.

241 Chapter 4. Manipulation and Exploration

The problem, however, as Morrison, Massimi and Arabatzis pointed out, was that it seemed difficult to ascribe theory-independence to this causal knowledge in the way that was required to render it a viable realist position. Contrary to what Hacking and Cartwright assumed, they argued, successful manipulation should not be seen as leading to a historically stable connection between causal claims and created effects. If one wanted to remain a realist, according to Morrison, Massimi and Arabatzis, then the manipulability-idea would make one end up as a standard scientific realist. While Morrison, Massimi and Arabatzis thus showed that the epistemology underlying the manipulability-idea was problematic insofar as it was supposed to enable the formulation of a realist position, they left open the question how the epistemology of manipulation could be conceptualized. In this way, we ended up with the research question formulated above. I then investigated this research question by means of two historical episodes. These concerned experimental manipulations that were seen, for a while, as successfully providing specific information about the properties of an entity that was manipulated, but which were reconceptualized over time. These kinds of experimental manipulations seem well-suited to investigate my research question: by tracking the factors that were responsible for why a certain manipulation was, at a certain time, taken to be successful, and then investigating what was responsible for the reconceptualization of this success, more insight could be obtained in how we are to characterize the epistemological contribution of experimental manipulations to information about a theoretical entity under investigation. Chapter 2 was concerned with experiments on the velocity-dependence of the electron’s mass. Kaufmann’s experiments on the electrons constituting Becquerel rays, which were the first to systematically investigate this property of the electron, were long taken to provide insight into the electron’s dynamics. They were taken to show, more specifically, that the electron’s mass had to be completely electromagnetic in nature, since Kaufmann’s experimental results validated the electromagnetic interpretation of the experimental manipulations offered by Abraham’s electron-model, which was completely electromagnetic in nature. Later experiments by Bestelmeyer, Bucherer and Hupka raised issues, however, regarding the reliability of Kaufmann’s experiments, and provided results that were more in line with the relativistic expression for the velocity-dependence of mass. Elaborating a relativistic account of the electron fitting these equations then led von Laue to the claim that experiments such as Kaufmann’s should not be taken to provide any insight into the electron’s dynamics. Independently of how one conceptualized their constitution, one would end up with the same dynamics, namely Planck’s law of the inertia of energy. Chapter 3 was concerned with experiments on the state of magnetization of superconductors. Kamerlingh Onnes and Tuyn’s experiments on a superconducting ring and a superconducting hollow sphere, which were originally concerned with a superconductor’s microresidual resistance and the invariability of the strength and distribution of the persistent currents, were long taken to show that superconductors were perfect conductors. They were taken to indicate, more specifically, that once a body had been rendered superconducting, it would display a frozen in magnetic flux, since the experimental results obtained by Kamerlingh Onnes and Tuyn validated the perfect conductivity conception of the experimental manipulations provided by Lorentz’s electron-model of electrical conduction, which essentially relied on frozen in

242 Experiment, Time and Theory

fields. Later experiments by Meissner and Ochsenfeld and many others raised issues, however, with the generality of the conclusion that was drawn from Kamerlingh Onnes and Tuyn’s experiments, since these later experiments suggested that there were sometimes no frozen in fields to be found, and at other times frozen in fields that were weaker than the field applied before transition. On the basis of these experimental results, Fritz and Heinz London then elaborated an account of the superconducting state according to which the results obtained by Kamerlingh Onnes and Tuyn were an exception rather than the rule: in the pure superconducting state, there was no frozen in flux to be found. These historical discussions showed that neither the earlier experiments, now taken to be unsuccessful, nor the later ones, could, on their own, be taken to provide any kind of causal knowledge as Cartwright and Hacking conceptualized it. While the later experiments were able to raise doubts about the causal claims regarding the entity provided by the earlier experiments, they were in turn also open to criticism, and their results were not always unambiguous. This raised the question how we could conceptualize these experiments as providing information about the properties under investigation. The historical cases allowed the development of a response to this question, I argued, because they showed that scientists that took particular experiments to provide such information relied on what I called interpretations of the experimental inferences that characterize the manipulations carried out. An experimental inference characterizes an experimental manipulation, we have seen, insofar as it offers a causal chain linking the manipulation of an entity by means of an experimental set-up to the production of an effect that scientists could take to be informative about the entity manipulated.370 In order to provide specific information about the entity’s properties, however, an inference has to be interpreted. Such an interpretation, which is provided by a model of the entity manipulated, offers a conceptualization of how the manipulation interacts with the properties that the model ascribes to the entity, in such a way that this interaction will produce a particular effect. If the effect is then to be found in the data produced by an actual manipulation, the interpretation can be taken to show that the experiment has functioned properly, while the data can be seen as a validation of the model that provided the interpretation. Finally, chapter 4 offered an elaboration of how this interplay between experimental inferences and interpretations was to be understood in the light of what the two historical episodes suggested, namely that the information provided by an experimental manipulation could shift over time. This was done by means of the work of Steinle, Massimi and Feest. The relation between inference and interpretation, I argued, could be understood in terms of Feest’s concept of a stable fit between surface phenomena, i.e. empirical regularities found in a data set, and hidden phenomena, i.e. entities or processes that are supposedly causally responsible for the production of these empirical regularities. According to Feest, neither surface regularities nor hidden phenomena are ever stabilized in isolation. They rather stabilize each other, in the sense that we rely on a hidden phenomenon in order to identify surface regularities, while at the same time a hidden phenomenon can only be identified through empirical regularities. Applied to the interplay between inference and interpretation, this gives rise to

370 See the appendix A for a short overview of the diﬀerent inferences and interpretations discussed.

243 Chapter 4. Manipulation and Exploration the following picture. A model offering an interpretation of an experimental inference can be seen as providing a hidden phenomenon that, when manipulated, will bring about a particular surface phenomenon. When an experimental manipulation brings about this surface phenomenon, the interpretation can be taken to offer an explanation, in terms of the hidden phenomenon, for why the manipulation provided what was obtained. At the same time, the surface regularity obtained can be seen as a validation of the claims made by the model about the hidden phenomenon. In sections 4.3.1 and 4.3.2, I then argued that it was indeed possible to conceptualize the experimental inferences and interpretations obtained in chapters 2 and 3 in these terms. This picture indicates, I have argued, that the information provided by experimental manipulations has to be conceptualized not in terms of factual knowledge, but rather in terms of modal knowledge. That a particular model offers a stable fit for the interpretation of experimental manipulations does not mean that the results of these manipulations show this model to be correct. Other models of the hypothetical phenomenon under study can perfectly well offer alternative stable fits. If this is the case, further experiments or further modeling are to provide information about the plausibility of the different models with respect to each other and to the results obtained. In this way, experimental manipulations can provide insight into the space of possibilities for models of the hypothetical target system. At the same time, a stable fit between supposedly established experimental results and a particular model can also delineate the space of possibilities, in the sense that it can constrain the way in which further experimentation and modeling will be carried out. Thus, the stable fit between Kaufmann’s results and Abraham’s electromagnetic model put a constraint on the modeling carried out by Lorentz and Poincaré:it had to be in line with the electron’s electromagnetic momentum that was supposedly uncovered by Kaufmann’s experiments. And the stable fit between Kamerlingh Onnes and Tuyn’s results and Lorentz’s electron-model put a constraint on the way in which theories of superconductivity were to be constructed: they had to conceptualize them in terms of perfect conductivity. Conceptualizing interpretations and inferences in terms of stable fits can also account for the transformations in the information provided by experimental manipulations that were discussed in the historical episodes. Given that a stable fit comes down to a surface phenomenon and a hidden phenomenon stabilizing each other, whenever one of the two elements becomes problematized, the fit will be destabilized, and scientists will begin searching for ways to restore stabilization or to find an alternative stabilization. This search can be characterized, I argued, in terms of an epistemology of exploration, which I developed on the basis of Steinle’s work on exploratory experimentation and Massimi’s work on exploratory modeling. By varying on relevant characteristics of the experimental set-up or procedure employed to bring about a surface phenomenon, scientists can investigate the robustness of the surface regularities already obtained. Proceeding in this way can show that the set-up employed in the earlier experiments is perhaps not as reliable as assumed, which can then be taken as an indication that the phenomenon investigated should be characterized by different surface regularities than thought. If it is then possible, by means of exploratory modeling, to conceive of an alternative hypothetical model that can account for the empirical regularities discerned in the new experiments, it can be said that a programme for an alternative stable fit has been obtained.

244 Experiment, Time and Theory

In fields where there is already a stable fit present, as was the case in the two historical episodes discussed, such a programme can only emerge when exploratory experimentation and modeling work in tandem. As long as there are only certain experiments that produce regularities that are not in line with the surface regularities belonging to the ruling stable fit, but no model providing an alternative hidden phenomenon for these new regularities, it can always be argued on the basis of the existing fit that these experiments are problematic. On the other hand, as long as there is only an alternative for the model belonging to the stable fit, but no surface phenomena that are in line with this alternative model, it can always be argued on the basis of the fit that this hypothetical model is problematic, since it is not in line with what is observed. Only when exploratory modeling and experimentation work in tandem in such a way that they can reinforce each other, can an alternative stable fit be worked out. When such an alternative stable fit has been developed, the boundaries of what is plausible, according to the information provided by a particular manipulation, can shift. Experimental results that were taken earlier to indicate that the original stable fit was very plausible, can now be seen as validating the alternative stable fit. In this way, we can understand how the information provided by an experimental manipulation can change over time. As such, an alternative stable fit entails a reconceptualization of the past. It also entails a reconceptualization of the future, since it will guide scientists in a new and different direction. This shows that scientists interact not only with their environment, but also with their past. Past experimental results will be interpreted in the light of a present stable fit, and as such they offer guidelines and standards of success for studying and evaluating new and unexpected results. When the present stable fit breaks down and a new one emerges, past experimental results, and hence also the guidelines and standards of success for the future, will be reconceptualized. This entails that what counts as a successful manipulation, in the entity realist’s sense of a historically stable connection between causal knowledge and an effect created in the laboratory, is itself subject to historical change. As such, we are brought to the final claim of the previous chapter, namely that temporal dimensions have to be added to the anthropology shared by both the standard realist and the entity realist. Neither a passive observation nor a manipulation in itself can show to a scientist that it is successful, in the sense that the realist requires: this judgment is rather based on earlier scientific results, and it is something that can change over time. On the basis of this result, the following tentative response to the research question can be formulated:

The information provided by experimental manipulations can be characterized as modal knowledge about the plausibility of a model of the entity manipulated. Such knowledge is obtained by means of an interpretation, guided by the model, of the experimental inference characterizing the manipulation and the eﬀect produced in terms of experimental results obtained earlier. This knowledge is historically situated in that the way in which the information shapes and constrains the space of plausibility can shift over time.

245 Chapter 4. Manipulation and Exploration

Remarks and Further Comments

I opened this conclusion by stating that the research presented in this dissertation concerned an investigation of and reflection upon the research question, and I characterized my response as a tentative one. By this I mean that the characterization of the epistemology of the experimental manipulations discussed in the previous chapters should not be seen as any kind of definite answer. I expect, and even hope, that further research will shed new light on, and reconceptualize, the way in which I discussed the historical episodes. How could I wish for anything else, if my own research suggests that research is always exploratory and subject to transformations over time? Reflecting upon my own trajectory towards the current results suggests that what I have been doing as well could be characterized in terms of an exploration for a stable fit between regularities that I tried to identify in the historical data and a hidden philosophical phenomenon that would allow me to make sense of them.371 And just as a stable fit is supposed to offer guidance to scientists in their thinking and acting, in this final section I would like to outline a few questions that, I think, would be worth further exploration. Whether or not such further exploration will reinforce or destabilize the stable fit that I have tried to elaborate here, only time can tell. I will start with a few possible criticisms that could be raised against the work I have presented here, and try to argue how these criticisms could either be addressed or turned into questions for further research. A first remark would be that in my discussions of my historical cases, I have not done justice to the way in which the manipulability-idea should be applied according to Cartwright and Hacking. For my concern has been with how manipulation can provide information about the electron, whereas if we follow the idea properly, in terms of Hacking’s slogan ‘if you can spray them then they are real’, it should be applied to the entities that are used by Kaufmann and Kamerlingh Onnes and Tuyn to manipulate the electron, i.e. electric and magnetic fields and temperature. If the research question is concerned with the epistemology of manipulation, my discussion should have been about the knowledge that Kaufmann and Kamerlingh Onnes and Tuyn had about the causal properties of their experimental set-up. A first reply to this remark is that Hacking’s and Cartwright’s epistemology of manipulation should also concern the electron in the historical episodes discussed, since successful experimental manipulations, on their view, provide us not only with the conviction that the entity used to carry out a manipulation exists, but also with further insight into the causal properties of the more hypothetical entity that is manipulated. It is by means of manipulations that we can obtain home truths about the entity under investigation, in such a way that over time, we can be able to manipulate it in turn, and hence become convinced of its existence. As such, I could say that this criticism I raised is not a real criticism. But that would be an easy way out, since there seems to be a more significant point underlying the issue raised. My characterization of the information provided by experimental manipulations as historically situated, the remark would go, does not apply to the knowledge that Kaufmann and Kamerlingh Onnes and Tuyn had about the properties of the experimental set-up they used. They did have stable

371 In line with Steinle’s quotation of Fleck (see footnote 348), we should of course expect these reﬂections to be conceptualized in terms of my current investigations of stable ﬁts.

246 Experiment, Time and Theory knowledge about the entities they used, i.e. electric and magnetic fields and temperature. This would entail that, contrary to the starting point of my investigation, it would be possible to drawn a distinction between home truths and theoretical claims: home truths are those truths that we use to construct and manipulate experimental set-ups and instruments, and even though the theories about the entities used in this construction and manipulation could change over time, the causal knowledge used remains stable over time. But this remark would go against what we have observed in the case studies. The set-ups used by Kaufmann and Kamerlingh Onnes and Tuyn were taken to be reliable at the time because the results they produced were in line with earlier experiments and with Abraham’s and Lorentz’s interpretation of their functioning. Once experiments such as those by Bestelmeyer or by Meissner and Ochsenfeld raised questions about the surface regularities obtained by Kaufmann and Kamer- lingh Onnes and Tuyn, scientists also started to reconceptualize the functioning of the experimental set-up. Kaufmann thought that he had correctly applied electromagnetic fields, but Bestelmeyer’s results allowed Planck and Starck to question the homogeneity of the electric field applied, and in this way opened up a whole discussion about ionization of the remaining air. And Kamerlingh Onnes and Tuyn thought they had correctly used bismuth in their measurements, but de Haas and Casimir-Jonker’s results raised doubts about this, and in this way brought about new investigations by de Haas and Guinau concerning the resistance of superconductors. This shows that the knowledge about the properties of the entities used to construct and manipulate the set-up is only historically stable insofar as there is a stable fit present: once this fit becomes problematized, the functioning of the experiment can be questioned and reconceptualized as well. This brings us to a second, related remark. The manipulability-idea, it could be argued, should not be applied to experiments such as Kaufmann’s, since these were explicitly carried out in order to investigate a theoretical question regarding the identity of a hypothetical entity. The idea is rather primarily concerned with what one could call engineering experiments, i.e. experiments that attempt to investigate the causal properties of a hypothetical entity by manipulating it in many different ways. One can reply to this by pointing to Kamerlingh Onnes and Tuyn’s experimental practice, which could be characterized as a kind of engineering practice: without much theory about superconductors, they attempted to measure and investigate as much properties of superconductors as possible. Still, we have seen, this practice as well was shapen and constrained by a particular fit, namely the perfect conductivity conception (see footnote 367 for Casimir’s account of how this conception influenced the experimental practice in Leiden). As such, even in such experiments which we could call engineering experiments, experimental manipulation can only be taken to provide any kind of information if a stable fit is present. The fits on which such engineering experiments rely are probably much more stable than the fit on which e.g. Kaufmann’s experiments relied, but a fit is still required. This brings us to a third possible remark, concerning my identification of stable fits in the historical cases discussed and the account I have developed on the basis of it. In this dissertation, both historical episodes have been analysed in terms of different stable fits that were opposed to each other and which replaced each other in time. In the velocity-dependence case, there was first the electromagnetic interpretation of Kaufmann’s experiments, which was then replaced by von Laue’s

247 Chapter 4. Manipulation and Exploration relativistic interpretation. In the superconductivity case, there was first the perfect conductivity interpretation, which was then overcome by the zero permeability and the intermediate state interpretations. One could argue, however, that the historical cases should not be conceptualized in terms of such absolute distinctions. In both historical episodes, one can also find scientists that seemed to believe that there was no opposition between the two interpretations that I contrast. Ehrenfest, for example, seems to offer an example in the velocity-dependence case: while he was a strong critic of the relativistic interpretation from the point of view of the electromagnetic approach, as we have seen in section 2.5, he also worked on the development of the relativistic interpretation, since he showed by means of the Minkowskian formalism that a rigid body was, strictly speaking, not possible from a relativistic point of view (see footnote 216). In the superconductivity case, we have the example of de Haas: together with Voogd and Casimir-Jonker, he claimed that their experiments on the influence of the direction of the applied magnetic field provided an argument against von Laue’s perfect conductivity interpretation (see the quote on page 165), but he also saw the results he had obtained with Guinau as evidence in favour of von Laue’s view (see the quote on page 184). This is a valid point to be raised with respect to the historical discussions and my development of an epistemology of exploration on the basis of it. I would like to see it, however, not primarily as a criticism, but rather as an invitation for further historical and philosophical research. My research has focused on how one interpretation overcame the other, and because of this, I conceptualized my philosophical account of the way in which interpretations shifted in terms of those figures that are taken, both in the primary and in the secondary literature, to be clearly on one side. As such, further research on the role of figures that were more in the middle would be more than welcome. What is also required is further research on how the adherents of the old interpretation, e.g. Abraham in the velocity-dependence case or von Laue in the superconductivity-case, fared after this interpretation had been replaced. Abraham (1909; 1910), for example, continued working on his electromagnetic interpretation, and used it to engage with the work of Einstein and Minkowski on relativistic electrodynamics. And von Laue published a handbook on the theory of superconductivity which aimed, as he puts it in the opening sentence of his introduction, “for the clarification of the insights on superconductivity, through the expansion of Maxwellian electrodynamics to the field of superconductivity on the basis of ideas developed by Fritz London in 1935 and later” (1947, p. 1).372 I have not had the time to incorporate these claims into the historical narratives in chapters 2 and 3, and further investigation could therefore destabilize or extend the conceptualization of the epistemology of experimental manipulations that I have offered here, in such a way that a more refined or different understanding of such epistemological transformations can emerge. In this way, we arrive at a final possible remark with respect to my conceptualization of the transformations discussed, namely that it only concerns epistemological factors, and leaves other factors, such as social or cultural ones, to the side. Thus, the fact that the relativistic interpretation was able to overcome the electromagnetic interpretation should not be conceptualized purely in terms of how different scientists

372 The original German goes as follows: “Diese Schrift strebt die Klärungder Anschauungen über Supraleitung an, und zwar durch Ausdehnung der Maxwellschen Elektrodynamik auf die Supraleiter nach Ideen, welche Fritz London 1935 und späterangegeben hat”.

248 Experiment, Time and Theory used the theory of relativity to address, defuse and overcome the challenges raised by the electromagnetic world view. It should equally well be concerned, for example, with the fact that Planck became a central figure in the scientific community at the time, as professor at the Friedrich-Wilhelms-Universitätin Berlin, as editor of the Annalen and as president of the German Physical Society (Heilbron, 1986, p. 35), while Abraham, a former PhD student of Planck, was without a permanent position during the whole period discussed.373 And in the superconductivity-case, the conceptualization offered should equally well be concerned with the fact that much of German science came to a halt near the end of the period discussed because of the rise of National Socialism: Heinz London’s PhD defense in 1934, for example, was “one of the last by a Jew in Germany before the war” (Matricon and Waysand, 2003, p. 70). To this, I would respond that these are valid remarks that deserve further investigation, in order to elaborate in more detail the way in which different factors can contribute to the emergence of a particular stable fit. I do not see the work I have presented here as in opposition to the claim that social factors also play a role. Rather, both social and epistemological factors shape the way in which scientific work is carried out. The work I have presented here can therefore be read as a reflection on the epistemological part of a more comprehensive account of how experimental knowledge comes to be seen as established. How we are to conceptualize the precise interaction between epistemological and social factors is to be left as work for the future.

373 See Goldberg (1970) on Abraham’s life and work during this period, and the entry on Max Abraham in the author catalogue of the Sources for History of Quantum Physics, composed by Thomas Kuhn, John L. Heilbron, Paul Forman and Lini Allen, consultable online at www.amphilsoc.org/guides/ahqp/index.htm.

249

Appendix A

Experimental Inferences and Interpretations

In this dissertation, I analyse the experiments discussed in terms of experimental inferences and interpretations. An experimental inference links a manipulation of an entity by means of an experimental set-up to the production of an effect which scientists take to be informative about properties of the entity manipulated. Both entity and set-up are characterized in terms of properties that scientists take to be relevant. In such an inference, I distinguish the properties of the entity manipulated and the properties of the experimental set-up used to manipulate the entity by means of brackets (), and I indicate that they are made to interact with each other by means of the plus sign +. This interaction will bring about certain effects, where I denote the link between cause and effect by means of a causal arrow −→c . When multiple properties occur together without interacting, I indicate this with the &- sign. The link between effect and information I denote by means of an inferential arrow −→i . Interpretations of these experimental inferences offer, on the basis of a model of the entity manipulated, detailed theoretical accounts of the influence of the manipulation on the entity manipulated. They offer, more specifically, a conceptualization of the effect produced by the manipulation, and in this way they allow scientists to obtain specific information about the entity manipulated out of the experimental results. In what follows, I will give a short overview of the experimental inferences and interpretations discussed in this work.

Experiment and the Electron’s Velocity-Dependence of Mass I characterized Kaufmann’s experiments in terms of the following experimental inference, discussed on page 55:

[Kaufmann’s Experimental Inference]: c i e µ + (E&B) −→ y0&ρ −→ µ0η

The first element of the inference, (/µ), denotes the entity manipulated, the electron, characterized in terms of its relevant properties, namely a charge and a mass µ. The relevant properties of the experimental set-up used to manipulate this entity are the applied electric and magnetic fields (E, B). When an electron is made to interact with these fields, it will be deflected in a certain way. When such ma-

251 Appendix A. Experimental Inferences and Interpretations nipulated electrons end up on the photographic plate of Kaufmann’s experimental set-up, they will causally produce dots on this plate, which have a specific magnetic deflection y0 and which together form a curve with a specific curvature ρ. These form Kaufmann’s data. They indicated to Kaufmann that a part of the electron’s e mass, its electromagnetic mass µ0, was changed by a velocity-dependent factor η. For this inference to provide information about the precise dependency of the electron’s electromagnetic mass on its velocity, it needs to be interpreted. Such an interpretation gives an account of how, according to the electron-model employed, the influence of the manipulation on the entity is to be conceptualized. A first interpretation of Kaufmann’s experimental inference was offered by Abraham (disussed on page 56):

[Abraham’s Electromagnetic Interpretation]: c i e −dG i e i µ + (E&B) −→ quasi-stat. −→ F = dt −→ µ⊥ −−→ m+µe η y0,ρ 0⊥

According to this interpretation, the experimental manipulation endows the electron with quasi-stationary acceleration. This allowed Abraham to conceptualize the force exercised by the electromagnetic fields on the electron, Fe, in terms of the electromagnetic momentum G, which provided him with an expression for the elec- e tron’s electromagnetic transverse mass µ⊥. Applying this equation to Kaufmann’s data y and ρ, which I denote by means of an inferential arrow with the data as 0 subscript −−−→i , then allowed Abraham to obtain information about the precise y0&ρ way in which the electron’s mass µ divides into a constant, mechanical mass m and e a velocity-dependent electromagnetic mass µ0⊥η. As such, the interpretation provided more specific and detailed information than the experimental inference could provide in itself, which only entailed that there is a velocity-dependence. A second interpretation of Kaufmann’s experimental inference was offered by Poincaré(discussed on page 66):

[Poincar´e’sRelativistic Interpretation]: c i −dG i i µ + (E&B) −→ relativistic motion −→ F = dt −→ µ⊥ −−→ m+µ η y0,ρ 0⊥

The application of electric and magnetic fields to the electron, on his view, would endow the electron with relativistic motion. Because of this, the force experienced by the electron could no longer be conceptualized purely in terms of the electric and magnetic fields. A non-electromagnetic force, exercised by the Poincaréstresses, also had to contribute to the total force F exercised on the electron. It was this total force that, on Poincaré’saccount, was responsible for the electron’s electromagnetic momentum G, which in turn provided him with an expression for the velocity- dependence of the electron’s relativistic transverse mass µ⊥. Applying this to the experimental data obtained could then provide Poincaréwith information about which part of the electron’s mass was velocity-dependent. A third interpretation of Kaufmann’s experimental inference was offered by von Laue (discussed on page 123):

252 Experiment, Time and Theory

[von Laue’s Relativistic Interpretation]: 0 0 0 c i dp i i (p&E &V &P ) + (E&B) −→ hyperbolic motion −→ F = dt −→ µ⊥ −−→ (α+p)/c2 y0,ρ

On this interpretation, the electron is characterized in terms of its pressure p, its mechanical energy E0, its volume V 0 and its stress tensor P0 (where the 0-superscript denotes these properties in the electron’s rest frame). Applying electric and magnetic ﬁelds to such an electron will endow it with hyperbolic motion, which is a conceptualization of motion that incorporates the quasi-stationary acceleration that, on Abraham’s interpretation, was brought about by the manipulation. This means that the electron in motion can be treated as if it is a rigid body. The total force exercised on the electron can then be conceptualized in terms of its relativistic momentum p, from which an expression for the electron’s transverse mass µ⊥ can be derived. Applying this to the data y0 and ρ obtained in the diﬀerent experiments then provided von Laue with information about the possible sources of energy that could give rise to the velocity-dependence of the electron’s momentum.

Experiment and the State of Magnetization of Superconductors With regards to Kamerlingh Onnes and Tuyn’s experiments, we obtained the following experimental inference (discussed on page 142):

[Kamerlingh Onnes and Tuyn’s Experimental Inference]: c i (T < TC &H < HC ) + (∆H) −→ I(∞) −→ B

The first element of the inference denotes the entity manipulated, the electrons present in a metal that is cooled below the threshold temperature TC and to which a field with a strength below the critical field strength HC is applied. This entity is then manipulated by means of variations in the applied magnetic field (∆H). These variations induce persistent currents I(∞) on the superconducting material. These currents allowed for the measurement of different properties of the superconducting material which in turn could be taken to provide information about the magnetic flux B present in the material. A first interpretation of this experimental inference was offered by Lorentz’s electron-model (see the discussion on page 143):

[The Perfect Conductivity Interpretation]: c i i (R = 0) + (∆H) −→ C(α ± ∆H) −→ Nev −−−→ B = H0 I(∞)

On this interpretation, lowering the temperature and applying a magnetic field brings the electrons in such a state that the material becomes a perfect conductor: it displays zero resistance (R = 0). Varying the applied magnetic field to it then brings the electrons in such a state of motion that the magnetic field they induce will compensate this variation: C(α ± ∆H). This allowed Lorentz to represent these electrons within his electron-theory of conduction as a stream Nev. Applying this expression to the data obtained by Kamerlingh Onnes and Tuyn from the persistent currents then provided Lorentz with the information that the magnetic flux inside the superconductor had to be equal to the field applied before the transition: B = H0.

253 Appendix A. Experimental Inferences and Interpretations

A second interpretation of this experimental inference was oﬀered by Fritz and Heinz London’s diamagnetic programme (see page 181):

[The Zero Permeability Interpretation]: c i i (Ψ) + (∆H) −→ Ψ −→ J −−−−→ (B = 0)&(0 < B ≤ H0) I(∞),B

On this interpretation, lowering the temperature and applying a magnetic field brings the electrons in a state Ψ, which could not be specified yet since it was unknown which interaction was responsible for the coupling of the electrons. Vary- ing the applied field would only disturb this state weakly, in such a way that the superconducting state would remain stable with persistent currents, which can be represented in terms of the Londons’ equation for the superconducting current J. Applying this expression to the data obtained from the external magnetic flux B studied in Meissner and Ochsenfeld’s parallel cylinders experiment then suggested to the London brothers that the magnetic flux inside a pure superconductor had to be equal to zero: B = 0. It also suggested to them a way to account for the frozen in flux obtained in Kamerlingh Onnes and Tuyn’s experiments. Hence, applying their interpretation, if it could be worked out, to the observations on the persistent currents in these experiments would also show them that when there are superconducting rings, there would be frozen in flux, which could however be weaker than the applied field before transition: (0 < B ≤ H0). A final interpretation was offered by Fritz London (see page 193):

[The Intermediate State Interpretation]: c 0 0 i i (E¯&B¯) + (∆H) −→ E¯ &B¯ −→ J −−−−−−→ (B = 0)&(0 < B ≤ H0) I(∞),B,R

On this interpretation, lowering the temperature and applying a magnetic field brings the electrons in such a state that the material displays the intermediate state, which is characterized in terms of the mean field strengths (E¯, B¯) that govern the superconducting regions in the material. Varying the applied field then changes the mean field strengths (E¯ 0, B¯ 0). This brings about a variation in the persistent currents, which can again be described in terms of the Londons’ equation for the superconducting current J. Applying this expression to the data obtained from the persistent currents, resistance and external magnetic flux in the different experiments then indicated that a superconducting material could contain both pure superconducting regions (B = 0) and superconducting rings with frozen in flux (0 < B ≤ HC ).

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Experiment, Time and Theory

On the scientiﬁc exploration of the unobservable

Jan Potters

Abstract: This dissertation concerns an investigation of the epistemological state of experimental results: how are we to characterize the information provided by experiments? More specifically, it will be investigated whether we can say that an experiment in itself leads to factual knowledge. The motivation for this research question, which will be elaborated in chapter 1, derives from the scientific realism-debate, which concerns the question whether we can say that a successful scientific theory provides knowledge about what goes on beyond the observable. Because of problems with standard scientific realism, Nancy Cartwright and Ian Hacking proposed that knowledge of the unobservable is not to be found in scientific theory, but rather in successful scientific experiments. It will turn out, however, that this suggestion also suffers issues, which will lead to the research question of this dissertation. This research question will then be investigated by means of a historical and philosophical study of two series of experiments: experiments on the velocity-dependence of the electron’s mass (chapter 2), and experiments on the state of magnetization of superconductors (chapter 3). The starting point in both chapters will be an experiment that was taken for a while to provide specific knowledge, but which was later believed not to provide such certain knowledge. Studying such experiments can offer insight into the research question in the sense that it allows for the investigation of those factors that play a role in the conviction that these experiments provided specific knowledge, and of how this conviction transformed over time. On the basis of these two chapters it will then be argued, in chapter 4, that experiments can only be taken to provide information given a theoretical interpretation of the functioning of the experiment, and that this information should not be seen as factual knowlefdge, but rather as knowledge concerning the plausibility of the theory with respect to other theoretical interpretations of the experiment. On the basis of work by Friedrich Steinle, Michela Massimi and Uljana Feest, a philosophical framework will be elaborated, an epistemology of exploration, that conceptualizes how this plausibility has to be understood in a historical-philospohical way. It will be argued, more specifically, that this information regarding the plausibility of a theoretical interpretation of an experiment can change over time, as a consequence of the development of new experiments and theories, and that this can entail that earlier experimental results will be reinterpreted. On the basis of this it will then be argued that the realism-debate, both the theory-driven and the experiment-driven formulation of it, have a problematic conception of what counts as scientific success. Both assume that it is directly observable that a theory or experiment is successful. However, on the basis of the epistemology of exploration elaborated here, it will be argued that what counts as a scientific success is historically variable, and is shapen by what is seen as earlier successful theories and experiments.

275 Experiment, Tijd en Theorie

Over de wetenschappelijke exploratie van het onobserveerbare

Jan Potters

Abstract: Deze verhandeling betreft een onderzoek naar het epistemologische statuut van experimentele resultaten: hoe kunnen we de informatie die experimenten ons opleveren karakteriseren? Meer specifiek wordt er onderzocht of we kunnen stellen dat een experiment op zich tot feitelijke kennis kan leiden. De motivatie voor deze onderzoeksvraag, die behandeld wordt in hoofdstuk 1, komt voort uit het wetenschappelijk realisme-debat, dat de vraag betreft of we kunnen stellen dat een succesvolle wetenschappelijke theorie ons kennis oplevert over wat er zich afspeelt voorbij het observeerbare. Vanwege problemen met standaard wetenschappelijk realisme stelden Nancy Cartwright en Ian Hacking voor dat kennis over het onobserveerbare niet moet worden gezocht in wetenschappelijke the- orieën,maar eerder in succesvolle wetenschappelijke experimenten. Deze suggestie blijkt echter op haar beurt onderhevig aan problemen, wat leidt tot de onderzoeksvraag van deze verhandeling. Deze onderzoeksvraag wordt dan onderzocht aan de hand van een historisch-filosofische studie van twee reeksen van experimenten: experimenten betreffende de snelheidsafhanke- lijkheid van de massa van elektronen (hoofdstuk 2), en experimenten betreffende de magnetische toestand van supergeleiders (hoofdstuk 3). Het vertrekpunt in beide hoofdstukken is een experiment waarvan gedurende een bepaalde periode gedacht werd dat het specifieke kennis opleverde, maar waarvan naderhand bleek dat deze kennis toch niet zo zeker was. Het bestuderen van zulke experimenten kan inzicht bieden in de onderzoeksvraag in die zin dat het toelaat om te onderzoeken welke factoren een rol speelden in de overtuiging dat deze experimenten specifieke kennis opleverden, en hoe deze overtuiging doorheen de tijd veranderde. Op basis van deze twee hoofdstukken wordt er dan beargumenteerd, in hoofdstuk 4, dat experimenten enkel informatie kunnen opleveren gegeven een theoretische interpretatie van het functioneren van het experiment, en dat deze informatie niet gezien mag worden als feitelijke kennis, maar eerder als kennis aangaande de plausibiliteit van de theorie ten opzichte van andere theoretische interpretaties van het experiment. Op basis van werk van Friedrich Steinle, Michela Massimi en Uljana Feest wordt er dan een filosofisch kader uitgewerkt, een epistemologie van de exploratie, betreffende hoe deze plausibiliteit historisch-filosofisch begrepen moet worden. Meer specifiek wordt er beargumenteerd dat deze informatie over de plausibiliteit van een theoretische interpretatie van een experiment kan veranderen doorheen de tijd, als gevolg van de ontwikkeling van nieuwe experimenten en nieuwe theorieën,en dat dit ertoe kan leiden dat eerdere experimentele resultaten anders ge¨ınterpreteerd worden. Op basis hiervan wordt er dan beargumenteerd dat het realisme- debat, zowel in de theorie-gerichte als in de experiment-gerichte vorm, een problematische conceptie heeft van wat wetenschappelijk succes betekent. Allebei gaan ze ervan uit dat het direct duidelijk observeerbaar is dat een theorie of experiment succesvol is. Op basis van de hier ontwikkelde epistemologie van de exploratie wordt er echter getoond dat wat telt als een wetenschappelijk succes historisch variabel is, en bepaald door wat beschouwd wordt als eerdere succesvolle theorieënen experimenten.

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