FACULTÉ DES LETTRES SECTION DE PHILOSOPHIE The Arrow of Time and Time Symmetry in non-Relativistic Quantum Mechanics On why we have sound reasons to believe in a quantum arrow of time THÈSE DE DOCTORAT présentée à la Faculté des lettres de l’Université de Lausanne pour l’obtention du grade de Docteur ès lettres par Cristian Ariel López Directeur de thèse Prof. Michael Esfeld Prof. Olimpia Lombardi LAUSANNE 2019 Index Introduction 3 Part 1 Introduction 14 Chapter I Unpacking the Problem of the Arrow of Time: 18 From Metaphysics to Physics Chapter II Unpacking the Problem of the Arrow of Time: 52 From Physics back to Metaphysics Part 2 Introduction 82 Chapter III Standard Quantum Mechanics (SQM): SQM’s 85 formalism and symmetry group Chapter IV The Physics and Metaphysics of Time Reversal: Is 100 the Schrödinger equation time-reversal invariant? Chapter V The Arrow of Time and SQM at the Crossroads: 142 The Orthodoxy, Time Reversal and Time-reversal symmetry 1 | P a g e Part 3 Introduction 164 Chapter VI Towards a Full-blooded Quantum Theory: The 168 measurement problem and interpretations Chapter VII Orthodox Quantum Mechanics (OrQM): Time 186 Asymmetry and the Collapse of the Wave Function Chapter VIII GRW-type theories: Time Asymmetry and 212 Spontaneous Quantum Jumps Chapter IX Bohmian Mechanics (BM): The Arrow of Time and 234 the Special Role of Time Reversal Final Remarks 259 References 263 2 | P a g e 훂. Introduction Or what all this is going to be about… “Inside time there is another time “Dentro del tiempo hay otro tiempo, Ever still Quieto Lacking hours, weight and shadow Sin horas ni peso ni sombra Solely alive Sólo vivo Like that old man on the bench Como el viejo del banco Self-absorbed identical endless Unimismado idéntico perpetuo Always unseen Nunca lo vemos It’s transparency” Es la transparencia” (Octavio Paz, “The same time”) (Octavio Paz, “El mismo tiempo”) We, raised and educated in the Western civilization, believe that past is somehow behind us while future is somewhere ahead. Because of this, we use expressions like “c’mon face the past!” as if one were commanding the other to spatially turn around and see (face) the past; or “winter (or future) is coming” as if things were moving, approaching to us from the front. Notwithstanding how deeply-ingrained these beliefs are in our Western-minded metaphoric mapping of time, some people have come to adopt a quite different world view: you might get a blank stare in return if you command an Aymara (ancient people still living in the Andes highlands) to face the past. Well, that’s what she always does: walking back to the future (which lies behind her), always seeing, facing her past. Winter wouldn’t be coming to her (from the front) but reaching, hunting her from the back, as if their entire metaphoric mapping of time were turned radically upside down1. Or would it be rather the other way around and we, Western-minded thinkers, have being having our world view turned upside down all along? Probably neither option, as a good deal of we call ‘time’ is culturally made and, consequently, it varies along places and time. Nonetheless, beyond what we, as human beings, might come 1 Take a look at this must-read paper about our metaphoric mapping of time: Núñez, R. and Sweetser, E. (2006). “With the Future Behind Them: Convergent Evidence from Aymara Language and Gesture in the Crosslinguistic Comparison of Spatial Construals of Time”. Cognitive Science 30: 401-450 3 | P a g e to think about our experienced, culturally-made time, Nature might conceal something that we can still call ‘time’; time that probably lacks many of the (colorful) culturally-based properties that human beings have largely thought it has. Probably flowless, coming from and going nowhere. Neither back nor in front. Lacking hours, identical even transparent. And yet, maybe capturing one of its more irrevocable and persistent (even essential) properties: its directionality. And about this the thesis is going to be. *** Time is bewildering. Take any property one typically ascribes to time and this will surely enclose a deep, largely-discussed philosophical problem. In this light, time looks like a still alive fertile terrain for philosophical inquiry. Beyond its unquestionable philosophical richness, time has a hard-to-handle dual feature, neatly condensed in Augustine’s words. “What is time? If nobody asks me, I know; but if I were desirous to explain it to one that should ask me, plainly I know not” On the one hand, time is familiar, too familiar to us. Allegedly, one knows what time is because one has daily experience of it. Time is so constitutive of our language, of our knowledge, of our day-to-day lives, of our very existence as human beings that one thinks one has a fair, well- grounded grasp of its essential features. Unquestionably, time is there, flying away in front of us –one witnesses how things are unavoidably devoured by time, slipping into non-existence, over and over. It intuitively seems that one knows what time is, and yet philosophical inquiry just comes into play when details need to be spelled out just a tiny bit further. On the other hand, as one starts looking into our daily experience of time and its alleged properties, we quickly lose the North. In this sense, time is so elusive, that one is rapidly left clueless about where our inquiry should start off and how it should be properly conducted. Is time object of philosophical investigation exclusively? Or does it fall better under scientific inquiry? If the latter is the case, which science would be the most adequate to delve into the nature of time? Further, various problems around time have been so intertwined that it is already an uphill task to start to disentangle them. 4 | P a g e About the topic The so-called problem of the arrow of time, the philosophical problem I am here mainly interested in, is not alien to this general landscape. In a quite comprehensive way, the problem concerns a simple and intuitively graspable property, to wit: Does time (whatever it comes to be) objectively2 instantiate the property of “having a privileged direction”? By “privileged direction” it is commonly meant that there would be a sharp distinction between the past-to-future direction and the future-to-past one. However, the problem is too vague and abstract to be researched systematically. Which would be the more appropriate way to address the problem? How can we come to know (or to identify) the property of “having a privileged direction”? Something else should be add to the formulation to narrow the problem down. In effect, such a problem might be investigated along different branches, ranging over psychology and the neurosciences, to pure metaphysics and physics. A longstanding tradition, tracing back to the late nineteenth century, has nonetheless addressed the problem exclusively within physics and the problem becomes a problem to be solved within physics ever since. In accordance with this, it may be broadly reworded as following. If physics is in the business of studying how matter moves in space-time, well, it is likely that physics has something to say about space-time’s structure (particularly, time’s) through this study. In accordance with this, it may be broadly reworded as following: Does time (whatever it comes to be) objectively instantiate the property of “having a privileged direction” according to some of our best physical theories? We are now getting closer to a sense of the overall problem, but we are not quite there yet. One of the central claims of this thesis is that such a way to pose the problem has been understood quite differently by many authors: Though loads of ink have been spilled since the nineteenth century in discussing about the (seemingly) directed nature of time, it is not often clear what the problem is really about. Indeed, the problem of the arrow of time seems to enclose a bunch of closely-related, but conceptually different problems. Literature on the problem of the arrow 2 My usage of the word “objectively” here refers to a mind-independent property, that is, a property that is instantiated by the world out there and that is independent of any subjective feature of whom knows this property. This is close to the Nagelian sense of objectivity: being a property of nature that remains invariant under a change of perspective –that is, it’s independent of a perspective (the so-known “view from nowhere”). In this case, “having a direction of time” would be a property that is independent of agents knowing such a property and that, at least in principle, it’s independent of the perspective from which they know about the direction of time. 5 | P a g e of time in physics has not been always careful in keeping the scenario clear. In 1974, John Earman already complained about how poorly understood and how uninformative the problem of the arrow of time had been so far: […] “very little progress has been made on the fundamental issues involved in "the problem of the direction of time." By itself, this would not be especially surprising since the issues are deep and difficult ones. (…) It seems not a very great exaggeration to say that the main problem with "the problem of the direction of time" is to figure out exactly what the problem is or is supposed to be!” (1974: 15) Curiously, others have also raised their voices in complaining about this uneasy situation: what are we really discussing when dealing with the problem of the arrow of time? A good part of this thesis deals with this imperative clarification: Sometimes progress, especially in foundational matters, can initially come from clarifying the problem at dispute.