Summary of Common Interpretations of Quantum Mechanics
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Divine Action and the World of Science: What Cosmology and Quantum Physics Teach Us About the Role of Providence in Nature 247 Bruce L
Journal of Biblical and Theological Studies JBTSVOLUME 2 | ISSUE 2 Christianity and the Philosophy of Science Divine Action and the World of Science: What Cosmology and Quantum Physics Teach Us about the Role of Providence in Nature 247 Bruce L. Gordon [JBTS 2.2 (2017): 247-298] Divine Action and the World of Science: What Cosmology and Quantum Physics Teach Us about the Role of Providence in Nature1 BRUCE L. GORDON Bruce L. Gordon is Associate Professor of the History and Philosophy of Science at Houston Baptist University and a Senior Fellow of Discovery Institute’s Center for Science and Culture Abstract: Modern science has revealed a world far more exotic and wonder- provoking than our wildest imaginings could have anticipated. It is the purpose of this essay to introduce the reader to the empirical discoveries and scientific concepts that limn our understanding of how reality is structured and interconnected—from the incomprehensibly large to the inconceivably small—and to draw out the metaphysical implications of this picture. What is unveiled is a universe in which Mind plays an indispensable role: from the uncanny life-giving precision inscribed in its initial conditions, mathematical regularities, and natural constants in the distant past, to its material insubstantiality and absolute dependence on transcendent causation for causal closure and phenomenological coherence in the present, the reality we inhabit is one in which divine action is before all things, in all things, and constitutes the very basis on which all things hold together (Colossians 1:17). §1. Introduction: The Intelligible Cosmos For science to be possible there has to be order present in nature and it has to be discoverable by the human mind. -
Reformulating Bell's Theorem: the Search for a Truly Local Quantum
Reformulating Bell's Theorem: The Search for a Truly Local Quantum Theory∗ Mordecai Waegelly and Kelvin J. McQueenz March 2, 2020 Abstract The apparent nonlocality of quantum theory has been a persistent concern. Einstein et. al. (1935) and Bell (1964) emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's \no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the experimentally confirmed entanglement correlations, we make clear that it is the conjunction of the three axioms that is ruled out by these correlations. We then show that by assuming local causality and no superdeterminism, we can give a direct proof of many worlds. The remainder of the paper searches for a consistent, local, formulation of many worlds. We show that prominent formulations whose ontology is given by the wave function violate local causality, and we critically evaluate claims in the literature to the contrary. We ultimately identify a local many worlds interpretation that replaces the wave function with a separable Lorentz-invariant wave-field. We conclude with discussions of the Born rule, and other interpretations of quantum mechanics. Contents 1 Introduction 2 2 Local causality 3 3 Reformulating Bell's theorem 5 4 Proving Bell's theorem with many worlds 6 5 Global worlds 8 5.1 Global branching . .8 5.2 Global divergence . -
Einstein's Interpretation of Quantum Mechanics L
Einstein's Interpretation of Quantum Mechanics L. E. Ballentine Citation: American Journal of Physics 40, 1763(1972); doi: 10.1119/1.1987060 View online: https://doi.org/10.1119/1.1987060 View Table of Contents: http://aapt.scitation.org/toc/ajp/40/12 Published by the American Association of Physics Teachers Articles you may be interested in Einstein’s opposition to the quantum theory American Journal of Physics 58, 673 (1990); 10.1119/1.16399 Probability theory in quantum mechanics American Journal of Physics 54, 883 (1986); 10.1119/1.14783 The Shaky Game: Einstein, Realism and the Quantum Theory American Journal of Physics 56, 571 (1988); 10.1119/1.15540 QUANTUM MEASUREMENTS American Journal of Physics 85, 5 (2017); 10.1119/1.4967925 Einstein’s boxes American Journal of Physics 73, 164 (2005); 10.1119/1.1811620 Development of concepts in the history of quantum theory American Journal of Physics 43, 389 (1975); 10.1119/1.9833 an Association of Physics Teachers Explore the AAPT Career Center - access hundreds of physics education and other STEM teaching jobs at two-year and four-year colleges and universities. http://jobs.aapt.org December 1972 Einstein’s Interpretation of Quantum Mechanics L. E. BALLENTINE his own interpretation of the theory are less well Physics Department known. Indeed, Heisenberg’s essay “The Develop Simon Fraser University ment of the Interpretation of the Quantum Burnaby, B.C., Canada Theory,”2 in which he replied in detail to many (Received 23 May 1972; revised 27 June 1972) critics of the Copenhagen interpretation, takes no account of Einstein’s specific arguments. -
Quantum Trajectory Distribution for Weak Measurement of A
Quantum Trajectory Distribution for Weak Measurement of a Superconducting Qubit: Experiment meets Theory Parveen Kumar,1, ∗ Suman Kundu,2, † Madhavi Chand,2, ‡ R. Vijayaraghavan,2, § and Apoorva Patel1, ¶ 1Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, India 2Department of Condensed Matter Physics and Materials Science, Tata Institue of Fundamental Research, Mumbai 400005, India (Dated: April 11, 2018) Quantum measurements are described as instantaneous projections in textbooks. They can be stretched out in time using weak measurements, whereby one can observe the evolution of a quantum state as it heads towards one of the eigenstates of the measured operator. This evolution can be understood as a continuous nonlinear stochastic process, generating an ensemble of quantum trajectories, consisting of noisy fluctuations on top of geodesics that attract the quantum state towards the measured operator eigenstates. The rate of evolution is specific to each system-apparatus pair, and the Born rule constraint requires the magnitudes of the noise and the attraction to be precisely related. We experimentally observe the entire quantum trajectory distribution for weak measurements of a superconducting qubit in circuit QED architecture, quantify it, and demonstrate that it agrees very well with the predictions of a single-parameter white-noise stochastic process. This characterisation of quantum trajectories is a powerful clue to unraveling the dynamics of quantum measurement, beyond the conventional axiomatic quantum -
Tsekov, R., Heifetz, E., & Cohen, E
Tsekov, R., Heifetz, E., & Cohen, E. (2017). Derivation of the local- mean stochastic quantum force. Fluctuation and Noise Letters, 16(3), [1750028]. https://doi.org/10.1142/S0219477517500286 Peer reviewed version Link to published version (if available): 10.1142/S0219477517500286 Link to publication record in Explore Bristol Research PDF-document This is the author accepted manuscript (AAM). The final published version (version of record) is available online via World Scientific at http://www.worldscientific.com/doi/abs/10.1142/S0219477517500286. Please refer to any applicable terms of use of the publisher. University of Bristol - Explore Bristol Research General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/ Derivation of the Local-Mean Stochastic Quantum Force Roumen Tsekov Department of Physical Chemistry, University of Sofia, 1164 Sofia, Bulgaria Eyal Heifetz Department of Geosciences, Tel-Aviv University, Tel-Aviv, Israel Eliahu Cohen H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, U.K (Dated: May 16, 2017) Abstract We regard the non-relativistic Schr¨odinger equation as an ensemble mean representation of the stochastic motion of a single particle in a vacuum, subject to an undefined stochastic quantum force. The local mean of the quantum force is found to be proportional to the third spatial derivative of the probability density function, while its associated pressure is proportional to the second spatial derivative. The latter arises from the single particle diluted gas pressure, and this observation allows to interpret the quantum Bohm potential as the energy required to put a particle in a bath of fluctuating vacuum at constant entropy and volume. -
Understanding the Born Rule in Weak Measurements
Understanding the Born Rule in Weak Measurements Apoorva Patel Centre for High Energy Physics, Indian Institute of Science, Bangalore 31 July 2017, Open Quantum Systems 2017, ICTS-TIFR N. Gisin, Phys. Rev. Lett. 52 (1984) 1657 A. Patel and P. Kumar, Phys Rev. A (to appear), arXiv:1509.08253 S. Kundu, T. Roy, R. Vijayaraghavan, P. Kumar and A. Patel (in progress) 31 July 2017, Open Quantum Systems 2017, A. Patel (CHEP, IISc) Weak Measurements and Born Rule / 29 Abstract Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives it an ensemble interpretation, predicting proportions of various outcomes over many experimental runs. Understanding gradual weak measurements requires replacing this scenario with a dynamical evolution equation for the collapse of the quantum state in individual experimental runs. We revisit the framework to model quantum measurement as a continuous nonlinear stochastic process. It combines attraction towards the measured operator eigenstates with white noise, and for a specific ratio of the two reproduces the Born rule. This fluctuation-dissipation relation implies that the quantum state collapse involves the system-apparatus interaction only, and the Born rule is a consequence of the noise contributed by the apparatus. The ensemble of the quantum trajectories is predicted by the stochastic process in terms of a single evolution parameter, and matches well with the weak measurement results for superconducting transmon qubits. 31 July 2017, Open Quantum Systems 2017, A. Patel (CHEP, IISc) Weak Measurements and Born Rule / 29 Axioms of Quantum Dynamics (1) Unitary evolution (Schr¨odinger): d d i dt |ψi = H|ψi , i dt ρ =[H,ρ] . -
Quantum/Classical Correspondence in the Light of Bell's Inequalities Contents
Quantum/Classical Correspondence in the Light of Bell’s Inequalities Leonid A. Khalfin1 and Boris S. Tsirelson2 Received November 26, 1990; revised October 31, 1991 Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable em- pirical reality following d’Espagnat, described by a mathematical superstructure over quantum dynamics for the universal wave function. Being empirical, this reality is constructed in terms of both fundamental notions and characteristics of observers. It is presupposed that considered observers perceive the world as a system of collective degrees of freedom that are inherently dissipative because of interaction with thermal degrees of freedom. Relevant problems of foundation of statistical physics are considered. A feasible example is given of a macroscopic system not admitting such classical reality. The article contains a concise survey of some relevant domains: quantum and classical Bell-type inequalities; universal wave function; approaches to quan- tum description of macroscopic world, with emphasis on dissipation; spontaneous reduction models; experimental tests of the universal validity of the quantum the- ory. Contents Introduction 880 1 KinematicsandDynamicsofCorrelations 883 2 Universal Wave Function 894 3 Reconstruction of the Classical World: Approaches to the Problem 900 4 Dissipative Dynamics of Correlations 911 5 In Search of Alternative Theories 923 6 Relationship to the Problem of the Foundations of Statistical Physics926 1Permanent address: Steklov Mathematical Institute, Russian Academy of Sciences, Leningrad Division, Fontanka 27, 191011 Leningrad, Russia. 2Permanent address: School of Mathematics, Tel Aviv University, Tel Aviv 69978, Israrel. -
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. -
Many Worlds? an Introduction
Many Worlds? An Introduction Simon Saunders This problem of getting the interpretationprovedtoberathermoredifficult than just working out the equation. P.A.M. Dirac Ask not if quantum mechanics is true, ask rather what the theory implies. What does realism about the quantum state imply? What follows then, when quantum theory is applied without restriction, if need be to the whole universe? This is the question that this book addresses. The answers vary widely. According to one view, ‘what follows’ is a detailed and realistic picture of reality that provides a unified description of micro- and macroworlds. But according to another, the result is nonsense—there is no physically meaningful theory at all, or not in the sense of a realist theory, a theory supposed to give an intelligible picture of a reality existing independently of our thoughts and beliefs. According to the latter view, the formalism of quantum mechanics, if applied unrestrictedly, is at best a fragment of such a theory, in need of substantive additional assumptions and equations. So sharp a division about what appears to be a reasonably well-defined question is all the more striking given how much agreement there is otherwise, for all parties to the debate in this book are agreed on realism, and on the need, or the aspiration, for a theory that unites micro- and macroworlds, at least in principle. They all see it as legitimate—obligatory even—to ask whether the fundamental equations of quantum mechanics, principally the Schrodinger¨ equation, already constitute such a system. They all agree that such equations, if they are to be truly fundamental, must ultimately apply to the entire universe. -
On the Measurement Problem
International Journal of Theoretical and Mathematical Physics 2014, 4(5): 202-219 DOI: 10.5923/j.ijtmp.20140405.04 On the Measurement Problem Raed M. Shaiia Department of Physics, Damascus University, Damascus, Syria Abstract In this paper, we will see that we can reformulate the purely classical probability theory, using similar language to the one used in quantum mechanics. This leads us to reformulate quantum mechanics itself using this different way of understanding probability theory, which in turn will yield a new interpretation of quantum mechanics. In this reformulation, we still prove the existence of none classical phenomena of quantum mechanics, such as quantum superposition, quantum entanglement, the uncertainty principle and the collapse of the wave packet. But, here, we provide a different interpretation of these phenomena of how it is used to be understood in quantum physics. The advantages of this formulation and interpretation are that it induces the same experimental results, solves the measurement problem, and reduces the number of axioms in quantum mechanics. Besides, it suggests that we can use new types of Q-bits which are more easily to manipulate. Keywords Measurement problem, Interpretation of quantum mechanics, Quantum computing, Quantum mechanics, Probability theory Measurement reduced the wave packet to a single wave and 1. Introduction a single momentum [3, 4]. The ensemble interpretation: This interpretation states Throughout this paper, Dirac's notation will be used. that the wave function does not apply to an individual In quantum mechanics, for example [1] in the experiment system – or for example, a single particle – but is an of measuring the component of the spin of an electron on abstract mathematical, statistical quantity that only applies the Z-axis, and using as a basis the eigenvectors of σˆ3 , the to an ensemble of similarly prepared systems or particles [5] state vector of the electron before the measurement is: [6]. -
Philosophical, Theoretical and Experimental Propositions on Wavefunction Collapse
Imperial College of Science, Technology and Medicine Department of Physics Philosophical, Theoretical and Experimental Propositions On Wavefunction Collapse Daniel Goldwater Submitted in part fulfillment of the requirements for the degree of Doctor of Philosophy in Physics of the University of London and the Diploma of Imperial College, September 2018 Declaration I, Daniel Goldwater, confirm that the work presented in this thesis is my own. Where infor- mation has been drawn from other sources, it has been appropriately labelled and referenced in the text. The work described in chapter 4 will appear in a forthcoming paper [1]; the results of chapter 5 were reported in [2]; whilst those of chapter 6 appear in [3], and were achieved in collaboration with Dr. Sandro Donadi. Chapter 7 recounts a collaboration with Dr. James Millen, and is reported in [4]. Though I wrote the code for the simulations presented in chapter 7, it was James who produced the plots from these simulations. Copyright declaration: The copyright of this thesis rests with the author. Unless otherwise indicated, its contents are licensed under a Creative Commons Attribution-Non Commercial 4.0 International Licence (CC BY-NC). Under this licence, you may copy and redistribute the material in any medium or format. You may also create and distribute modified versions of the work. This is on the condition that: you credit the author and do not use it, or any derivative works, for a commercial purpose. When reusing or sharing this work, ensure you make the licence terms clear to others by naming the licence and linking to the licence text. -
TIME and the FOUNDATIONS of QUANTUM MECHANICS By
TIME AND THE FOUNDATIONS OF QUANTUM MECHANICS by Thomas Pashby M. Sci., University of Bristol, 2005 Submitted to the Graduate Faculty of the Dietrich School of Arts and Sciences in partial fulfilment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2014 UNIVERSITY OF PITTSBURGH DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Thomas Pashby It was defended on March 28th, 2014 and approved by John Earman, Ph.D., History and Philosophy of Science John D. Norton, Ph.D., History and Philosophy of Science Robert Batterman, Ph.D., Philosophy Gordon Belot, Ph.D., Philosophy (University of Michigan) Giovanni Valente, Ph.D., Philosophy Dissertation Directors: John Earman and John D. Norton ii Copyright c by Thomas Pashby 2014 iii TIME AND THE FOUNDATIONS OF QUANTUM MECHANICS Thomas Pashby, PhD University of Pittsburgh, 2014 Quantum mechanics has provided philosophers of science with many counterin- tuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good rea- sons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen.