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arXiv:0709.1096

Remarks on Our Understanding of Quantum Mechanics

Elias P. Gyftopoulos

Published Sep 7, 2007• 1 citation
arXivHTMLPDF

Abstract

Interpretations of key concepts, such as uncertainty relations, kinetic energy, value of an observable, probability distributions, the projection or collapse of a wave function postulate, and discrete versus continuous values, that appear in several excellent textbooks on quantum mechanics are reviewed and found not to be consistent with our current understanding of quantum theory. Possible alternatives are suggested.

DOI
10.48550/arxiv.0709.1096

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Interpretations of key concepts, such as uncertainty relations, kinetic energy, value of an observable, probability distributions, the projection or collapse of a wave function postulate, and discrete versus continuous values, that appear in several excellent textbooks on quantum mechanics are reviewed and found not to be consistent with our current understanding of quantum theory. Possible alternatives are suggested.
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We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of a state, its dynamical evolution rule and another rather trivial postulate proposed here (Read-Off Postulate). The wave function collapse and the probability rule are replaced with intrinsic properties of the theory, i.e. decoherence and relative frequency, respectively. Interpretation of the wave function as a faithful representation of the reality naturally emerges, although quantum reality has a peculiar feature which distinguishes it from classical reality.
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented which is motivated by retaining the point of view of classical mechanics as much as possible, and which is consistent with relativity theory. Everything can be written down in terms of well-known mathematical formulations that can be found in every textbook about quantum mechanics. Therefore, in this version, almost no formulas are used.
A survey is made of the hitherto proposed answers to the following crucial questions arising in the physical interpretation of the mathematical formalism of wave mechanics: (I) What is the meaning of the dynamical variables and of their eigenvalues? (II) What is the meaning of the wave function? (III) What is the nature and origin of Heisenberg's uncertainty relations? (IV) What is the nature of the systems dealt with by wave mechanics? Taking into account the interpretations that have been proposed in the last few years, a surprisingly large number of answers is found. The present situation in quantum mechanics is compared with similar crises in the past history of physics. The mere multiplicity of consistent interpretations of quantum mechanics is regarded as a warning against the dogmatic adherence to any one of them, to the exclusion of new possibilities.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.