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Physics Essays

The Theory of Elementary Waves

Lewis E. Little

Published Mar 1, 1996• 24 citations
Publisher

Abstract

A fundamental error is identified in the foundations of current quantum theory. The error is shown to be the source of the various noncausal and unphysical aspects of the theory. When the error is corrected, a new theory arises, which is both local and deterministic, but which nonetheless does not conflict with Bell’s theorem. The new theory reproduces quantitatively all the predictions of current quantum mechanics, with the exception of double-delayed-choice Einstein–Podolsky–Rosen (EPR) phenomena. A shortcoming in Aspect's experiment testing such phenomena is pointed out, and a definitive experiment is proposed. The EPR paradox is resolved. The uncertainty principle is derived on a causal, deterministic basis. The theory is “automatically ” relativistic; that is, the constancy of the velocity of light c relative to all observers follows as an immediate consequence of the new quantum theory, which constancy thus acquires a simple physical explanation. General relativity also acquires a simple, physical explanation. A pictorial interpretation of Feynman diagrams is obtained. The theory provides a clear physical explanation for the Aharonov–Bohm effect and suggests an explanation for the irreversibility of quantum statistical processes. Quantum statistics, Bose and Fermi, are explained in a simple, pictorial manner. Overall, it is shown that quantum and relativistic phenomena can be understood in an objective manner, in which facts are facts, causality is valid, and reality is real. The theory provides a single framework in which all known physical phenomena can be comprehended, thus accomplishing the objective of a unified field theory. Key words: quantum theory foundations, Bell’s theorem, delayed choice, special relativity, Feynman diagrams, Aharonov–Bohm effect, general relativity, unified theory, reality

DOI
10.4006/1.3029212

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A fundamental error is identified in the foundations of current quantum theory. The error is shown to be the source of the various noncausal and unphysical aspects of the theory. When the error is corrected, a new theory arises, which is both local and deterministic, but which nonetheless does not conflict with Bell’s theorem. The new theory reproduces quantitatively all the predictions of current quantum mechanics, with the exception of double-delayed-choice Einstein–Podolsky–Rosen (EPR) phenomena. A shortcoming in Aspect's experiment testing such phenomena is pointed out, and a definitive experiment is proposed. The EPR paradox is resolved. The uncertainty principle is derived on a causal, deterministic basis. The theory is “automatically ” relativistic; that is, the constancy of the velocity of light c relative to all observers follows as an immediate consequence of the new quantum theory, which constancy thus acquires a simple physical explanation. General relativity also acquires a simple, physical explanation. A pictorial interpretation of Feynman diagrams is obtained. The theory provides a clear physical explanation for the Aharonov–Bohm effect and suggests an explanation for the irreversibility of quantum statistical processes. Quantum statistics, Bose and Fermi, are explained in a simple, pictorial manner. Overall, it is shown that quantum and relativistic phenomena can be understood in an objective manner, in which facts are facts, causality is valid, and reality is real. The theory provides a single framework in which all known physical phenomena can be comprehended, thus accomplishing the objective of a unified field theory. Key words: quantum theory foundations, Bell’s theorem, delayed choice, special relativity, Feynman diagrams, Aharonov–Bohm effect, general relativity, unified theory, reality
A general theory based on six postulates is introduced. The basic notions are theoretical variables that are associated with an observer or with a group of communicating observers. These variables may be accessible or inaccessible. From these postulates, the ordinary formalism of quantum theory is derived. The mathematical derivations are not given in this article, but I refer to the recent articles. Three possible applications of the general theory can be given as follows: (1) the variables may be decision variables connected to the decisions of a person or a group of persons, (2) the variables may be statistical parameters or future data, and (3) most importantly, the variables are physical variables in some context. The last application gives a completely new foundation of quantum mechanics, a foundation which in my opinion is much easier to understand than ordinary formalism. So-called paradoxes like that of Schrödinger’s cat can be clarified under the theory. Explanations of the outcomes of David Bohm’s version of the EPR (Einstein–Podolsky–Rosen) experiment and the Bell experiment are provided. Finally, references to links toward relativity theory and quantum field theory are given. The concluding remarks point to further possible developments.
1. Quantum Mechanics, Reality and Separability: Physical Developments of the Einstein-Podolsky-Rosen Argument.- Realism in Quantum Mechanics and a New Version of the EPR Experiment.- Discussion: M. Cini, F. De Martini, K. Kraus, T.W. Marshall, K.R. Popper, H. Rauch, M.C. Robinson, F. Selleri, J. Six, G. Tarozzi, J.-P. Vigier..- The Physical Origin of the Einstein-Podolsky-Rosen Paradox.- Does the Bell Inequality Hold for All Local Theories?.- Is it Possible to Save Causality and Locality in Quantum Mechanics?.- Einstein-Podolsky-Rosen Experiments and Macroscopic Locality.- On the Compatibility of Local Realism with Atomic Cascade Experiments.- Is the Einstein-Podolsky-Rosen Paradox Demanded by Quantum Mechanics?.- Infinite Wave Resolution of the EPR Paradox.- On Non Local Influences.- Einstein Locality for Individual Systems and for Statistical Ensembles.- Can Nondetected Photons Simulate Nonlocal Effects in Two-Photon Polarization Correlation Experiments?.- 2. The Stochastic Interpretation of Quantum Processes.- Quantum Theory of Measurement without Wave Packet Collapse.- A Causal Fluidodynamical Model for the Relativistic Quantum Mechanics.- On the Nonlinear Schrodinger Equation.- Recent Developments in de Broglie Nonlinear Wave Mechanics.- The Role of the Quantum Potential in Determining Particle Trajectories and the Resolution of the Measurement Problem.- When is Statistical Theory Causal?.- Radiation Damping and Nonlinearity in the Pilot Wave Interpretation of Quantum Mechanics.- Stochastic Electrodynamics and the Bell Inequalities.- Nonlocal Quantum-Potential Interpretation of Relativistic Actions at a Distance in Many-Body Problems.- 3. The Realistic Interpretation of the Wave Function: Experimental Tests on the Wave-Particle Dualism.- Third Kind Measurements and Wave-Particle Dualism.- Quantum Effects in the Interference of Light.- Tests of Quantum Mechanics by Neutron Interferometry.- A Unified Experiment for Testing both the Interpretation and the Reduction Postulate of the Quantum Mechanical Wave Function.- Epilogue.- Evolutionary Epistemology.
This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein-Podolsky-Rosen argument, Bell's theorem, and Hardy's paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie-Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.
This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein–Podolsky–Rosen argument, Bell’s theorem, and Hardy’s paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie–Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.
This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: They are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except for very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible to avoid this problem are discussed in this text. After a brief historical introduction, recalling how the very special status of the state vector has emerged in quantum mechanics, various conceptual difficulties are introduced and discussed. The Einstein–Podolsky–Rosen (EPR) theorem is presented with the help of a botanical parable, in a way that emphasizes how deeply the EPR reasoning is rooted into what is often called “scientific method.” In another section the Greenberger–Horne–Zeilinger argument, the Hardy impossibilities, as well as the Bell–Kochen–Specker theorem are introduced in simple terms. The final two sections attempt to give a summary of the present situation: One section discusses nonlocality and entanglement as we see it presently, with brief mention of recent experiments; the last section contains a (nonexhaustive) list of various attitudes that are found among physicists, and that are helpful to alleviate the conceptual difficulties of quantum mechanics.
Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of quantum physics using simple thought experiments. We derive all relevant quantum predictions using minimal mathematics, without introducing the advanced calculations that are typically used to describe quantum physics. We focus on the two key surprises of quantum physics, namely wave-particle duality, a term that was introduced to capture the fact that single quantum particles in some respects behave like waves and in other respects like particles, and entanglement, which applies to two or more quantum particles and brings out the inherent contradiction between quantum physics and seemingly obvious assumptions regarding the nature of reality. Following arguments originally made by John Bell and Lucien Hardy, we show that the so-called local hidden variables are inadequate at explaining the behavior of entangled quantum particles. This means that one either has to give up on hidden variables, i.e., the idea that the outcomes of measurements on quantum particles are determined before an experiment is actually carried out, or one has to relinquish the principle of locality, which requires that no causal influences should be faster than the speed of light and is a cornerstone of Einstein's theory of relativity. Finally, we describe how these remarkable predictions of quantum physics have been confirmed in experiments. We have successfully used the present approach in a course that is open to all undergraduate students at the University of Calgary, without any prerequisites in mathematics or physics.