Exploring Alternatives to Quantum Nonlocality

Clemson University TigerPrints All Dissertations Dissertations May 2021 Exploring Alternatives to Quantum Nonlocality Indrajit Sen Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_dissertations Recommended Citation Sen, Indrajit, "Exploring Alternatives to Quantum Nonlocality" (2021). All Dissertations. 2793. https://tigerprints.clemson.edu/all_dissertations/2793 This Dissertation is brought to you for free and open access by the Dissertations at TigerPrints. It has been accepted for inclusion in All Dissertations by an authorized administrator of TigerPrints. For more information, please contact [email protected]. Exploring Alternatives to Quantum Nonlocality A Dissertation Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Physics by Indrajit Sen May 2021 Accepted by: Dr. Murray Daw, Committee Chair Dr. Antony Valentini Dr. Lucien Hardy Dr. Sumanta Tewari Abstract In this dissertation, we explore two alternatives to quantum nonlocality in a single-universe framework: superdeterminism and retrocausality. These models circumvent Bell's theorem by vio- lating the assumption that the hidden variables are uncorrelated with the measurement settings. In Chapter 1, we introduce superdeterminism and prepare the groundwork for our results in Chapter 2. We start from a review of the topic, focussing on the various qualitative criticisms raised against superdeterminism in the literature. We identify the criticism of `superdeterministic conspiracy' by Bell as the most serious, and introduce nonequilibrium extensions of superdeterministic models in an attempt to formalise the criticism. We study the different properties of these models, and isolate two conspiratorial features. First, the measurement statistics depend on the physical system used to determine the measurement settings. Second, the formal no-signalling constraints are violated although there is no causal connection between the wings. We quantify in Chapter 2 the two conspiratorial features that we found in Chapter 1. We consider a Bell scenario where, in each run and at each wing, the experimenter chooses one of N devices to determine the local measurement setting. We then show that a superdeterministic model of the scenario has to finely tuned such that measurement statistics do not depend on the physical system used to determine the measurement settings. This quantifies the first form of conspiracy identified in Chapter 1 as a fine tuning. We also show that a superdeterministic model of the scenario requires arbitrarily large correlations, quantified in terms of a formal entropy drop and in terms of mutual information, to be set up by the initial conditions. Such correlations are required to ensure that the devices that the hidden variables are correlated with are coincidentally the same as the devices in fact used for every run at each wing. This quantifies the second form of conspiracy ii identified in Chapter 2 as an arbitrary large correlation. Nonlocal and retrocausal models turn out to be non-conspiratorial according to both approaches, thereby singling out `conspiracy' as a unique, problematic feature of superdeterminism. In Chapter 3, we change tracks to focus on retrocausality. Our results regarding retrocausal models are, in contrast to superdeterminism, positive. We first show how to construct a local, -epistemic hidden-variable model of Bell correlations with wavefunctions in physical space by a retrocausal adaptation of the originally superdeterministic model given by Brans. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. Lastly, we argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. In Chapter 4, focus on the question whether retrocausal models can utilise their relativistic properties to account for relativistic effects on entangled systems. We consider a hypothetical relativistic Bell experiment, where one of the wings experiences time-dilation effects. We show that the retrocausal Brans model, introduced in Chapter 3, can be easily generalised to analyse this experiment, and that it predicts less separation of eigenpackets in the wing experiencing the time- dilation. This causes the particle distribution patterns on the photographic plates to differ between the wings { an experimentally testable prediction of the model. We discuss the difficulties faced by other hidden variable models in describing this experiment, and their natural resolution in our model due to its relativistic properties. Lastly, we argue that it is not clear at present, due to technical difficulties, if our prediction is reproduced by quantum field theory. We conclude that if it is, then the retrocausal Brans model predicts the same result with great simplicity in comparison. If not, the model can be experimentally tested. iii Dedication I dedicate this dissertation to my parents, Kajari Sen and Parimal Kanti Sen. iv Acknowledgements It seems to me that the true creator of any work, useless or wonderful, is the universe. The authors, the collaborators, the supporters are only the proximate parts visible to us of the infinite causal chain. I am, above all, indebted to Prof. Valentini for his guidance. He taught me the nuts and bolts of doing research in quantum foundations and helped me stand on my two feet as a thinker. It was also a delight to learn physics from someone who loves art. Lastly, I owe him a debt of gratitude for letting me drag him into superdeterminism. I am grateful to Prof. Daw for his kind help and support during my stay at Clemson, and for several insightful discussions. I would also like to thank Prof. Tewari and Prof. Hardy for their help at various points of the PhD. I am indebted also to my past teachers, without whom I would have never reached a PhD program in the first place. Prof. Sibasish Ghosh at IMSc guided me when I was a beginner in the world of quantum foundations. Bishweshwar sir gave me a solid foundations in classical physics. The clarity of his explanations and his helpfulness continue to inspire. I am indebted to my parents, Kajari Sen and Parimal Kanti Sen, for their support and inspiration. I am also indebted to my grandfather, Kanak Ghosh, for his constant encouragement to live the life of the mind. I am grateful to my fiancé, Sayani Ghosh, for her love and good advice. And to my friends Kumar Abhishek and Anish Ghoshal for the stimulating discussions and support. v I am thankful to Adithya Kandhadhai and Nick Underwood for the innumerable discussions over the past five years. I am also thankful to David McCall and Komal Kumari for their friendship. Lastly, I want to thank the dining hall staff and the office staff at Clemson. Without their service, I would not have been able to forget practicalities and focus on abstractions. vi Table of Contents Title Page ............................................ i Abstract ............................................. ii Dedication............................................ iv Acknowledgments ....................................... v List of Figures.......................................... ix 1 Introduction and Summary................................ 1 1.1 Short history of quantum foundations .......................... 1 1.2 Short history of the measurement-independence assumption.............. 3 1.3 Quantum nonequilibrium ................................. 6 1.4 Superdeterminism ..................................... 6 1.5 Retrocausality ....................................... 9 2 Superdeterministic hidden-variables models I: non-equilibrium and signalling . 11 2.1 Introduction......................................... 12 2.2 Nonequilibrium and signalling in superdeterministic models.............. 17 2.3 Marginal-independence in nonlocal deterministic models................ 21 2.4 Marginal-independence in superdeterministic models.................. 24 2.5 The conspiratorial character of superdeterministic signalling.............. 26 2.6 Conclusion ......................................... 28 3 Superdeterministic hidden-variables models II: conspiracy.............30 3.1 Introduction......................................... 31 3.2 Superdeterministic conspiracy as fine tuning....................... 32 3.3 Quantification of fine tuning................................ 38 3.4 Conspiracy as spontaneous entropy drop......................... 42 3.5 Discussion.......................................... 46 4 A local -epistemic retrocausal hidden-variable model of Bell correlations with wavefunctions in physical space .............................50 4.1 Introduction......................................... 51 4.2 The Brans model...................................... 53 4.3 A retrocausal interpretation of the Brans model..................... 54 4.4 Effective nonlocal signalling in non-equilibrium..................... 58 4.5 Discussion and Conclusion................................. 63 5 The effect of time-dilation on Bell experiments in the retrocausal Brans model 66 5.1 Introduction......................................... 67 vii 5.2 A relativistic Bell experiment............................... 69 5.3 The retrocausal Brans model ............................... 71 5.4 Description of the experiment in the model ....................... 72 5.5 Description in other hidden variable models......................

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