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Decoherence and Its Role in Interpretations of Quantum Physics

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Decoherence and Its Role in Interpretations of Quantum Physics Decoherence and its Role in Interpretations of Quantum Physics Simon Matthew Thomas Newey Submitted in Accordance with the Requirements for the Degree of Doctor of Philosophy University of Leeds School of Philosophy, Religion and History of Science February 2019 2 The candidate confirms that the work submitted is his/her/their own and that appropriate credit has been given where reference has been made to the work of others. This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. The right of Simon Mathew Thomas Newey to be identified as Author of this work has been asserted by Simon Mathew Thomas Newey in accordance with the Copyright, Designs and Patents Act 1988 3 Acknowledgements I would like to thank my supervisors Juha Saatsi and Stephen French for their patience, support and guidance over the last four years. I am grateful to the Arts and Humanities Research Council for funding this project. I am also grateful for helpful and interesting conversations I have had over the last four years with Callum Duguid, Guido Bacciagaluppi, Karim Thébault, Richard Dawid, and Simon Saunders. 4 Abstract The purpose of this thesis is to examine different conceptions of decoherence and their significance within interpretations of quantum mechanics. I set out three different conceptions of decoherence found in the literature and examine the relations between them. I argue that only the weakest of these conceptions is empirically well supported, and that the other two rely on claims about the structure of the histories (robust patterns within the wavefunction) which we occupy which require justification. I also examine the ways in which conceptions of decoherence are used to solve aspects of the quantum measurement problem and support modern interpretations of quantum mechanics. I focus particularly on Wallace's Everettian interpretation of quantum mechanics. I argue that while decoherence is generally successful in supporting this interpretation in a variety of ways, the very strong conception of decoherence on which he relies is itself difficult to justify. I consider a variety of possible approaches to justifying the use of this strong conception of decoherence and argue that many of them are either unconvincing, or rely on controversial cosmological claims. Finally, I suggest that the best way to justify the use of this strong conception of decoherence is by appealing directly to its indispensability to an otherwise very attractive interpretation of quantum mechanics. 5 Contents Contents .................................................................................................................... 5 1 Introduction ...................................................................................................... 6 2 Decoherence and the Quantum Measurement Problem ............................... 32 3 History Spaces and the Decoherence Functional ........................................... 75 4 Circularity and the Born Rule ........................................................................ 106 5 Thébault and Dawid’s Inconsistency Objection(s) ........................................ 129 6 Interpretation Neutral Justifications for Medium Decoherence .................. 151 7 Everettian Justifications for Medium Decoherence ..................................... 181 8 Everett Without Medium Decoherence ....................................................... 204 9 Conclusion ..................................................................................................... 220 References ............................................................................................................ 237 6 1 Introduction The aim of this thesis is to carefully consider what is meant by decoherence as the term is used within the existing literature concerning the foundations and philosophy of quantum mechanics, and to examine the role played by different conceptions of decoherence within specific interpretations of quantum mechanics. Chapters 2 and 3 will carefully develop and examine three different conceptions of decoherence found in the existing literature, and why it is thought to be useful in attempts to solve the quantum measurement problem. Chapters 4 and 5 will look at a number of concerns relating to the use of decoherence for this purpose and argue that these concerns, at least as commonly presented, need not worry us particularly. In chapter 6 I will set out what I believe to be a serious problem with the conception of decoherence which is commonly used within particular interpretations of quantum mechanics, which is called medium decoherence. I will argue that this conception (which is the strongest conception I will consider in this thesis) is stronger than our empirical evidence can support, and it is far from clear that any other form of justification for this conception can be provided. Where possible in this thesis, I endeavour to provide an account of the significance of different conceptions of decoherence and the problems which they solve and produce, while remaining neutral between all interpretations which do not introduce a collapse postulate. Where this is not possible, I focus on Wallace's formulation of the Everett interpretation of quantum mechanics as set out at length in Wallace 2012. I focus on this interpretation because it is a conceptually well-developed and widely respected interpretation which very clearly and explicitly relies on, and defends, a clear conception of decoherence, unlike many others. In chapters 7 and 8, I abandon all attempts at interpretation neutrality, and 7 focus purely on the support for this strong conception of decoherence which can be offered by Wallace's Everettian interpretation. In chapter 7, I consider a proposal by Wallace that the assumptions which underlie medium decoherence could be treated as Humean laws of nature. I will argue that this approach is undermined by the difficulty of reconciling a Humean account of laws with the metaphysics of Wallace’s project. In chapter 8, I look at some of the major problems produced for Wallace’s project if the medium decoherence assumption is dropped, and suggest that this could offer an argument from explanatory indispensability capable of supporting this assumption. The concluding chapter will return to other interpretations, and argue that more research is needed to understand how these interpretations can best respond to the issue for decoherence presented in chapter 6. Before turning to decoherence and the technical issues related to it, however, this chapter will provide a very brief introduction to textbook quantum mechanics, as well as the quantum measurement problem, and three popular modern interpretations which aim to solve it. This is intended to make clear the broader nature of the philosophical problems which decoherence is thought to help with, and to motivate interest in these problems. If the reader is interested in a more extended presentation of textbook quantum mechanics and its technical aspects, then I recommend Rae 2008 as a clear and direct textbook. For a clear and extended presentation of the philosophical issues associated with quantum mechanics and a range of interpretive responses I recommend Lewis 2016. 1.1 A Short Introduction to Linear Quantum Mechanics The fundamental mathematics of text book quantum mechanics can be expressed quite simply. The central equation responsible for the normal dynamical evolution of a particle is Schrödinger's equation: 8 휕 푖ℏ 휓(풓, 푡) = 퐻̂휓(풓, 푡) 휕푡 Where 퐻̂ is the Hamiltonian energy operator, ℏ is a constant, 푖 is the square root of −1, and 휓(풓, 푡) is the wavefunction of the particle in terms of particle position and time. The wavefunction is a function which represents all possible information about the results of measurements which could be made on the particle. In the basis of a particular observable, such as position, the wavefunction can be represented as a sum of the wavefunctions which would represent the state corresponding to different possible measurement outcomes multiplied by a complex coefficient1. In a position basis: 휓(풓, 푡) = ∑ 훼푛휙푛 푛 th Where 훼푛 is the complex coefficient, and 휙푛 is the n position eigenfunction. Given that 휙푛 is a position eigenfunction, the position operator 푅̂, applied to this function, will yield: 푅̂휙푛 = 풓푛휙푛 th Where 풓푛 is the n position vector of the particle. Thus, the wavefunction can be thought of as a sum of states each of which corresponds to a particular measured value. There are many observables in terms of which this decomposition into eigenfunctions can be made, and they will not all share the same eigenfunctions. A distinctive feature of quantum mechanics is that the wavefunction representing a state of the particle will very often be a sum of multiple position eigenfunctions, each of which corresponds to a different position eigenvalue. This does not mean that there are multiple particles at different positions. Rather, the wavefunction which describes the state of a single particle includes components which correspond to multiple 1 For it to be possible to decompose a wavefunction like this, the measurement involved must have eigenstates which form a complete orthonormal basis. 9 classically incompatible positions. This distinctively quantum state of affairs is known as a superposition. The real physical state of affairs which a superposition wavefunction represents is a matter of much disagreement, as
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