In Search of an Ontology for Quantum Field Theory Dissertation zur Erlangung der Doktorw¨urde, dem Promotionsausschuß Dr. phil. der Universit¨atBremen vorgelegt von Meinard Kuhlmann Bremen, den 6. Juni 2000 Contents Preface 4 List of Abbreviations 6 I Introduction 7 II Context, Methods and Presuppositions 15 1 Philosophical Background 16 1.1 The Development of Atomism in the History of Philosophy . 18 1.2 Philosophical Versus Scientific Atomism . 23 1.3 Atomism and Reductionism . 24 2 Ontology and Physics 27 2.1 \On What There Is": Notions of Ontology . 27 2.2 The Analytical Tradition of Ontology . 30 2.3 Excursion: No-Go Theorems in Quantum Physics . 32 3 Fundamentals of Quantum Physics 35 3.1 The Legacy of Quantum Mechanics . 35 3.2 The Standard Formalism of QFT and its Problems . 40 3.3 The Relation of QFT and AQFT . 43 3.4 Basic Ideas of AQFT . 45 1 CONTENTS 2 4 (A)QFT as Objects of Philosophy 48 4.1 Quantum Mechanics versus QFT . 48 4.2 QFT versus Algebraic QFT . 52 4.3 The Philosophical Interest in (A)QFT . 56 III Classical Ontologies 59 5 Classical vs. Revisionary Ontologies 60 5.1 Introduction . 61 5.2 Aristotle's Theory of Substances . 64 5.3 Substances under Attack . 69 6 The Particle Interpretation of QFT 73 6.1 The Particle Concept . 74 6.2 Theory and Experiment in Elementary Particle Physics - Is a Particle Track a Track of a Particle? . 77 6.3 Localization Problems . 80 6.3.1 The Clash of Causality and Localizability . 82 6.3.2 Locating the Origin of Non-Localizability . 87 6.4 Further Problems for a Particle Interpretation of QFT . 93 6.5 Results . 95 7 Field Interpretations of QFT 96 7.1 The Field Concept . 97 7.2 Fields as Basic Entities of QFT . 98 7.2.1 The Role of Field Operators in QFT . 98 7.2.2 Indirect Evidence for Fields . 101 IV Revisionary Ontologies 102 8 Process Ontology 103 8.1 The Strands of Process Ontology . 103 8.2 Why Process Ontology in QM and QFT? . 104 CONTENTS 3 8.3 A `Case Study': Consequences of the Ontological Hypothe- ses for the Interpretation of Feynman Diagrams . 107 8.4 Evaluation of the `Case Study' . 114 8.5 Remaining Problems . 115 9 Trope Ontology 117 9.1 Introduction - The Ontological Status of Properties . 118 9.2 Trope Ontology as a Solution to the Problem of Universals . 122 9.3 The Bundle Theory of Tropes . 124 9.4 Evaluation . 126 V Proposal for a New Ontology of QFT 128 10 Dispositional Trope Ontology 129 10.1 Introduction . 129 10.2 Dispositional Tropes of `Many-Particle Systems' . 131 10.2.1 `Elementary Particles' . 131 10.2.2 Individuality of Quantum Objects . 132 10.2.3 Dispositions and Tropes . 136 10.2.4 An Example . 139 10.3 From Many-Particle Systems to Fields . 140 10.4 Reconciliation of Theory and Experience . 141 10.5 Summing Up . 143 VI Conclusion 144 11 The Interplay of Physics and Philosophy 145 12 Evaluation and Comparison 148 12.1 General Remarks . 148 12.2 Comparison of Ontological Approaches to QFT . 150 12.2.1 Particles Versus Fields . 150 12.2.2 Processes Versus Tropes . 154 CONTENTS 4 12.2.3 The Merits of Dispositional Trope Ontology . 155 VII Glossaries 159 Physics Glossary 160 Philosophy Glossary 163 VIII Appendices 165 A The Quantum Theory of Measurement 166 B Assumptions of AQFT 169 C Proof of Malament's No-Go Theorem 174 References 178 Acknowledgement 191 Preface Some parts of this book have been or will be published in extended or shortened versions and/or in a different arrangement. Parts of chapter 1 will appear as the introduction in Kuhlmann et al. (2000). Parts of sec- tion 3.1 and chapter 8 have appeared as \Processes as objects of quantum field theory" Kuhlmann (2000). Parts of chapters 5 and 9 have appeared as \Quanta and tropes: Trope ontology as descriptive metaphysics of quantum field theory" Kuhlmann (1999a) and as \Quanten und Tropen - Philoso- phie der Physik und Sprachphilosophie" Kuhlmann and St¨ockler (2000). Parts of chapter 6 have appeared as \Was sagt das Vakuum ¨uber Teilchen aus? Neuere Ergebnisse aus der theoretischen Physik schaffen zus¨atzliche Probleme f¨urden Teilchenbegriff" Kuhlmann (1999b). 5 List of Abbreviations AQFT Algebraic Quantum Field Theory CCR Canonical Commutation Relations GRT General Relativity Theory prob Probability SRT Special Relativity Theory QFT Quantum Field Theory QM Quantum Mechanics 6 Part I Introduction 7 Introduction Which questions will be explored? The philosophical topic of this thesis is ontology restricted to the investigation of the most general struc- tures of what there is in the world. We will ask which kinds of things and modes of being there are in the most general sense. However, the questions which are of concern in the present work are only relative ones. What is being discussed are the ways to conceive of the world which are compat- ible with the mathematical formalism of QFT. No assumptions are being made about the truth of QFT or its relation to reality. Questions about truth, reality, \the world" and their connection have no direct impact on the study. Moreover, being as such will not be an issue at all. QFT is thus the unquestioned starting point of the following investigation. The only sense in which this procedure will be reflected upon is with regard to the conceptual consistency and maturity of QFT and the status of QFT within physics. The immediate question why QFT of all scientific theories has been chosen for this enterprise has a straightforward answer. If any theory about nature can lay claim on being the most fundamental one it is QFT. This is not to say that everything can or should be reduced to QFT. However, when special sciences come under ontological consideration at all, QFT is of outstanding importance. Accordingly, it is of particular interest which picture of the world this theory paints. The term `ontology' is often used in a twofold way, at least in the tradition of analytical philosophy which is the philosophical background of the present work. Besides the search for or the theory of the most general structures of being, `ontology' denotes the domain itself to which 8 9 a language or theory refers. Following this tradition I will freely make use of both senses of `ontology' as well. It is not presupposed that there is one definite set of basic entitites to which QFT refers and which one could simply, or after some closer investigation, read off QFT. The only two things I will presuppose with respect to ontological questions is, firstly, that these questions make sense at all and, secondly, that special sciences like physics constitute objects whose conceptual analysis yields a valuable contribution to the general ontological questions. What kind of answers should be expected? This thesis will hope- fully purvey inspiring information about QFT and some ways one can and cannot imagine the world to be in line with QFT. However, it will not supply the right or appropriate ontology of QFT. Not only is the number of proposals as well as the number of issues to be taken into account al- most impossible to exhaust. Moreover, there might never be a final unified answer. Although a final answer to the posed questions should not be expected it will become clear in the course of this investigation that not all problems are equally important and not all options are equally viable. Eventually, I will introduce and explain a new option for the ontology of QFT and justify my preference for this option. Historical and systematical background. The ontological analysis of QFT is a relatively new area of philosophical concern. Nevertheless it clearly has a well-known immediate historical and systematical background. In a sense it is a follow-up to the famous discussion about the wave-particle duality which originated with the formation of quantum mechanics (QM). Quantum objects seem to defy a representation in classical terms. With the quantum measurement problem the very idea of an objective ascrip- tion of properties to things came under suspicion. Finally, Heisenberg's uncertainty relations together with the non-classical behaviour of systems containing so-called identical particles endanger the individuality of quan- 10 tum objects. All these questions still linger on in the present investigation. There is, however, a much longer tradition of kindred questions in the history of atomism beginning with ancient greek philosophy. Here we have similar considerations about the building blocks of the world and their properties. Nevertheless, there is a pivotal difference between the old atom- ist's reasoning and the way we proceed nowadays. Except for its very last period the history of atomism consists exclusively of conceptual considera- tions. In contrast to that the ontological study of QFT starts with a theory which has been exceedingly well corroborated in a plethora of experiments. Main results in this thesis. Besides an account of the current state of research and of some systematical as well as historical foundations this work contains four original contributions by the present author to the ongoing research. The first point is preparatory and consists in the embedding of the main topic of this thesis into philosophy of physics on the one side and general philosophy on the other side. Each of the next three contributions to the research concerns a different option for the ontology of QFT. The reference to different options is not the only feature which distinguishes these three contributions. Moreover, their nature differs in at least one respect which makes it possible to say that the first contribution is in a negative context, the second in neutral one and the third in a positive context.