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Interpreting Quantum Mechanics in Terms of Random Discontinuous Motion of Particles Interpreting Quantum Mechanics in Terms of Random Discontinuous Motion of Particles by Shan Gao THESIS submitted for the degree of Doctor of Philosophy Unit for History and Philosophy of Science Centre for Time, SOPHI Faculty of Science Department of Philosophy Supervisors: Dr. Dean Rickles Prof. Huw Price University of Sydney Sydney, Australia March 2012 c Shan Gao 2011 All rights reserved This thesis is copyright. Subject to statutory exception and to provisions of relevant collective licensing agreements, no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the author. This thesis is dedicated to Erwin Schr¨odinger,who introduced the wave function, discovered its equation named after him, and argued that quantum mechanics is in- complete by his famous cat paradox. Abstract This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schr¨odingerequation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity. 4 Acknowledgement The idea of random discontinuous motion of particles came to my mind when I was a post- graduate at the Institute of Electronics, Chinese Academy of Sciences in 1993. I am happy that finally it has a more logical and satisfying formulation in this PhD thesis. During the writing of the thesis, I have been supported financially by a University of Sydney Interna- tional Scholarship and a Postgraduate Scholarship in Quantum Foundations provided by the Unit for HPS and Centre for Time (SOPHI), as well as by two Lucy Firth Scholarships in Philosophy provided by the Department of Philosophy. I would like to express my deepest gratitude to my supervisors, Dean Rickles and Huw Price, whose understanding, motivation and personal guidance was indispensable during my PhD studies. I am deeply indebted to them for their continuous encouragement, stimulating suggestions and healthy criticism which helped me greatly during my research and writing of this thesis. Their professional approach and accuracy was particularly beneficial to my study. I wish to express my warm and sincere thanks to the head of the Unit for HPS, Ofer Gal, the postgraduate coordinator, Hans Pols, and Debbie Castle. I am grateful for their personal support and for their reassurance regarding technical conditions during my PhD work. I would like to take this opportunity to thank all the other members of the Unit for their help and encouragement throughout the years. I would like to gratefully thank David Miller, Rod Sutherland, Hans Westman and Owen Maroney for helpful discussions and useful suggestions. I owe a debt of gratitude to all the PhD students here who I shared good times and had fun with. My deepest gratitude goes to my parents, Qingfeng Gao and Lihua Zhao, who spared no effort to provide the best possible environment for me to grow up in and their constant support during my extended studies. They have always allowed me to have the freedom of choice, and for that I am truly grateful. I am also thankful to my brother, Yuan Gao, and to all my friends, as they have always been willing to share their thoughts with me and provide alternative viewpoints which have helped me think in a more holistic fashion. Finally, I am deeply indebted to my wife Huixia and my daughter Ruiqi for their un- flagging love and support throughout my study; this dissertation would have been simply impossible without them. Moreover, they have never let me forget the true values of life. 5 Publications 1. On Di´osi-Penrose criterion of gravity-induced quantum collapse, International Journal of Theoretical Physics, 49, 849-853 (2010). 2. The wave function and quantum reality, in Proceedings of the International Conference on Advances in Quantum Theory, A. Khrennikov, G. Jaeger, M. Schlosshauer, G. Weihs (eds), AIP Conference Proceedings 1327, 334-338 (2011). 3. Meaning of the wave function, International Journal of Quantum Chemistry, 111, 4124- 4138 (2011). 4. Is gravity an entropic force? Entropy special issue \Black Hole Thermodynamics", Jacob D. Bekenstein (eds), 13, 936-948 (2011). 5. A quantum physical argument for panpsychism, Forthcoming in Journal of Consciousness Studies, 2012. 6 Contents 1 Introduction 10 2 Meaning of the Wave Function 13 2.1 Standard quantum mechanics and impulse measurements........... 14 2.2 Weak measurements................................ 16 2.3 Protective measurements.............................. 17 2.3.1 Measurements with natural protection.................. 18 2.3.2 Measurements with artificial protection................. 20 2.3.3 Further discussions............................. 21 2.4 On the mass and charge density of a quantum system............. 22 2.4.1 A heuristic argument............................ 22 2.4.2 The answer of protective measurement.................. 23 2.4.3 A specific example............................. 24 2.5 The physical origin of mass and charge density................. 26 2.5.1 The mass and charge density is effective................. 27 2.5.2 The ergodic motion of a particle is discontinuous............ 28 2.5.3 An argument for random discontinuous motion............. 30 2.6 The wave function as a description of random discontinuous motion of particles 31 2.6.1 An analysis of random discontinuous motion of particles........ 31 2.6.2 Interpreting the wave function...................... 33 3 Schr¨odinger'sEquation and the Conservation Laws 36 3.1 Spacetime translation and its invariance..................... 37 3.2 Relativistic invariance............................... 39 3.3 Derivation of the free Schr¨odingerequation................... 40 3.4 Further discussions................................. 41 3.5 On the conservation of energy and momentum................. 43 4 A Suggested Solution to the Measurement Problem 47 4.1 The reality of wavefunction collapse....................... 48 4.1.1 Against the de Broglie-Bohm theory................... 48 4.1.2 Against the many-worlds interpretation................. 52 4.2 A conjecture on the origin of wavefunction collapse............... 56 4.2.1 The chooser in discrete time........................ 56 4.2.2 Energy conservation and the choices................... 58 4.2.3 In search of a deeper basis......................... 59 4.3 A discrete model of energy-conserved wavefunction collapse.......... 61 4.4 On the consistency of the model and experiments................ 67 4.4.1 Maintenance of coherence......................... 67 4.4.2 Rapid localization in measurement situations.............. 68 4.4.3 Emergence of the classical world..................... 70 4.5 Critical comments on other dynamical collapse models............. 72 4.5.1 Penrose's gravity-induced wavefunction collapse model......... 72 4.5.2 The CSL model............................... 76 7 CONTENTS 5 Random Discontinuous Motion and Special Relativity 79 5.1 The picture of motion distorted by the Lorentz transformation........ 79 5.1.1 Single particle picture........................... 79 5.1.2 Picture of quantum entanglement..................... 81 5.1.3 Picture of wavefunction collapse..................... 82 5.2 On the absoluteness of simultaneity........................ 84 5.3 Collapse dynamics and preferred Lorentz frame................. 86 8 I think I can safely say that nobody understands quantum mechanics... Do not keep saying to yourself, if you can possible avoid it, \But how can it be like that?" because you will get `down the drain', into a blind alley from which nobody has escaped. Nobody knows how it can be like that. | Richard Feynman, 1964 1 Introduction Quantum mechanics, according to its Schr¨odingerpicture, is a non-relativistic theory about the wave function and its evolution. There are two main problems in the conceptual foun- dations of quantum mechanics. The first one concerns the physical meaning of the wave function in the theory. It has been widely argued that the probability interpretation is not wholly satisfactory because of resorting to the vague concept of measurement - though it is still the standard interpretation in textbooks nowadays. On the other hand, the meaning of the wave function is also in dispute in the alternatives to quantum mechanics such as the de Broglie-Bohm theory and the many-worlds interpretation (de Broglie 1928; Bohm 1952; Everett 1957; De Witt and Graham 1973). Exactly what does the wave function describe then? The second problem concerns the evolution of the wave function. It includes two parts. One part concerns the linear Schr¨odingerevolution. Why does the linear non-relativistic evolution
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