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Quantum Nonequilibrium in De Broglie-Bohm Theory and Its Effects in Black Holes and the Early Universe

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Quantum Nonequilibrium in De Broglie-Bohm Theory and Its Effects in Black Holes and the Early Universe Clemson University TigerPrints All Dissertations Dissertations December 2020 Quantum Nonequilibrium in De Broglie-Bohm Theory and its Effects in Black Holes and the Early Universe Adithya Pudukkudi Kandhadai Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_dissertations Recommended Citation Kandhadai, Adithya Pudukkudi, "Quantum Nonequilibrium in De Broglie-Bohm Theory and its Effects in Black Holes and the Early Universe" (2020). All Dissertations. 2742. https://tigerprints.clemson.edu/all_dissertations/2742 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]. Quantum Nonequilibrium in De Broglie-Bohm Theory and its Effects in Black Holes and the Early Universe A Dissertation Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Physics by Adithya P. Kandhadai December 2020 Accepted by: Dr. Murray Daw, Committee Chair Dr. Antony Valentini Dr. Sumanta Tewari Dr. Dieter Hartmann Abstract Quantum mechanics is a highly successful fundamental theory which has passed every ex- perimental test to date. Yet standard quantum mechanics fails to provide an adequate description of measurement processes, which has long been rationalized with operationalist and positivist philo- sophical arguments but is nevertheless a serious shortfall in a fundamental theory. In this dissertation we introduce quantum mechanics with a discussion of the measurement problem. We then review the de Broglie-Bohm pilot-wave formulation, a nonlocal hidden-variables theory where the state of a quantum system is described by a configuration (independent of measurements) in addition to the wave function, and we apply it to fundamental problems concerning black holes and the early universe. In de Broglie-Bohm theory, general initial conditions allow for deviations from the statistical predictions of standard quantum mechanics. We review how the Born rule can be understood as the result of an equilibration process for systems with sufficient mixing before proceeding to study the implications of quantum nonequilibrium in various physical contexts. In this work we show that small perturbations to a system are themselves insufficient to drive relaxation to quantum equilibrium even over very long timescales. This has implications for the potential survival of nonequilibrium in relic particles, and renders it unlikely that field perturbations can be driven to equilibrium by small corrections to the Bunch-Davies vacuum during inflation, allowing for the possible detection of imprints of nonequilibrium in the cosmic microwave background. Using a simple model we also demonstrate how quantum nonequilibrium can propagate nonlocally through entanglement, providing a mechanism for information flow from black holes. This opens up a possible path to the resolution of the black hole information paradox by allowing for information to be released in hidden variable degrees of freedom during black hole evaporation. Finally, we consider whether features in the angular power spectrum of temperature anisotropies ii in the cosmic microwave background radiation could arise from quantum nonequilibrium initial conditions. Preliminary results indicate that this approach can provide a natural explanation for the power deficit anomaly at large angular scales, as well as oscillatory features in the same regime. iii Dedication I dedicate this thesis to the Department of Physics and Astronomy at Clemson University, which counts some wonderful people among its faculty and staff and has always supported me during my years as a graduate student. iv Acknowledgments This dissertation would not have been possible but for the contributions and assistance of several people. On the scientific front, I would like to first thank Dr. Antony Valentini, who served as my supervisor for five years. I could not have asked for a better mentor to guide me through the beginning of my career in physics. Antony's enthusiasm for physics and life in general are an inspiration and I hope the future has more fruitful collaborations in store for us. I would also like to thank my friends and fellow researchers in quantum foundations Dr. Samuel Colin, Dr. Philipp Roser, Dr. Nick Underwood, and Indrajit Sen for interesting discussions from which I learned a great deal. The other members of my committee Dr. Murray Daw, Dr. Sumanta Tewari, and Dr. Dieter Hartmann have been helpful and encouraging at various points. My family, in particular my parents, grandparents, and brothers, have stayed in touch from long distance and made my all-too-short trips to India enjoyable and memorable. I look forward to spending more time with them. My close friends in Clemson { Sneha Mokashi, Komal Kumari, Lea Marcotulli, Amanpreet Kaur, Meenakshi Rajagopal, Chris Moore, Tara Lenertz, and Ashwin Sudhakaran, to name but a few { have kept me in good spirits for nearly the entire duration of my years in graduate school. To them I owe a great deal of my sound mental health. Finally, I would like to thank various local businesses in Clemson for providing quality service and helping me unwind in the evenings. Nick's Tavern, Moe Joe Coffee and Music House, and Brioso's Fresh Pasta all have excellent food and drinks. v Contents Title Page ............................................ i Abstract ............................................. ii Dedication............................................ iv Acknowledgments ....................................... v List of Tables ..........................................viii List of Figures.......................................... ix 1 Introduction to quantum mechanics........................... 1 1.1 Historical development of quantum mechanics...................... 1 1.2 Copenhagen interpretation................................. 3 1.3 The measurement problem................................. 4 1.4 Formulations without a measurement problem...................... 7 2 Review of de Broglie-Bohm theory ........................... 9 2.1 Hamilton-Jacobi equation and quantum potential.................... 11 2.2 Born rule and quantum equilibrium............................ 14 2.3 Quantum nonequilibrium and dynamical relaxation................... 15 2.4 Measurements in de Broglie-Bohm theory ........................ 20 2.5 De Broglie-Bohm field theory............................... 23 3 Review of quantum relaxation dynamics........................29 3.1 Long-time relaxation in de Broglie-Bohm theory .................... 30 4 Perturbations and quantum relaxation.........................36 4.1 Oscillator model ...................................... 39 4.2 Method ........................................... 41 4.3 Behaviour of trajectories over very long timescales ................... 42 4.4 Conclusion ......................................... 57 5 Information flow from black holes with de Broglie-Bohm nonlocality . 59 5.1 Review of the black hole information paradox...................... 59 5.2 Pilot-wave field theory on curved spacetime....................... 65 5.3 Nonlocal propagation of quantum nonequilibrium.................... 67 5.4 Simulations......................................... 73 5.5 Conclusion ......................................... 80 6 Quantum nonequilibrium in primordial perturbations................81 vi 6.1 Introduction to ΛCDM cosmology ............................ 81 6.2 Inflationary cosmology................................... 85 6.3 CMB anisotropies and theoretical modeling....................... 89 6.4 Review of previous work modeling the width deficit function.............. 93 6.5 Oscillations in the width deficit function......................... 99 6.6 Primordial spectrum with a power deficit ........................ 102 6.7 Method ........................................... 105 6.8 Results............................................ 107 vii List of Tables 6.1 The values of the ΛCDM parameters as well as the newly introduced parameters in ξ(k) for Fig. 6. ....................................... 108 viii List of Figures 3.1 Plots of H¯ (t) for the initial wave function with 25 energy states. The three different grids used by the authors yield the three H¯ curves, each given a different color. The dashed line is a best fit to an exponential function of the form a exp[−b(t=2π)] + c, with the best fit values of a, b and c dispayed above. The residue coefficient c is found to be comparable to the error in H¯ . (Reproduced from ref. [35].)........... 32 3.2 Plots of H¯ (t) for the initial wave function with 4 energy states. The relaxation shows clear signs of saturation after ∼ 20 periods. The exponential function fit to this data has a best fit residue coefficient c = 0:07, significantly more than the uncertainty in H¯ . (Reproduced from ref. [35].).............................. 33 3.3 Trajectories for the initial wave function with 25 energy states, where relaxation was nearly complete at t = 10π. In part (a) we see that the ten selected trajectories explore various regions of the support of j j2, with no indication of `forbidden zones'. In part (b) we see that all ten small initial squares yield scattered final points at the end of five periods. (Reproduced from ref. [35].)..................... 34 3.4 Trajectories for the initial wave function with 4 energy states, where relaxation
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