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Physics Essays

A discussion about the hidden variables in quantum mechanics

Spiros Koutandos

Published Dec 3, 2020• 5 citations
Publisher

Abstract

In the present paper, we attempt to bring to light some of the hidden variables of quantum mechanics by continuing the work of others who introduced constant curvature to spacetime. The article is also a continuation of a previous one [S. Koutandos, Phys. Essays 33, 208 (2020)] published in this journal proving London equations. We find that there is dilation of volume and that mass may have a surface density. Unlike the case of superconductors, however these surfaces collapse to a point. This is where the difficulty in measurement comes from.

DOI
10.4006/0836-1398-33.4.513

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In the present paper, we attempt to bring to light some of the hidden variables of quantum mechanics by continuing the work of others who introduced constant curvature to spacetime. The article is also a continuation of a previous one [S. Koutandos, Phys. Essays 33, 208 (2020)] published in this journal proving London equations. We find that there is dilation of volume and that mass may have a surface density. Unlike the case of superconductors, however these surfaces collapse to a point. This is where the difficulty in measurement comes from.
In continuation of some previous work published by this author in an open access journal [S. Koutandos, IOSR J. Appl. Phys. 10, 26 (2018); 10, 35 (2018); 9, 47 (2017); 11, 72 (2019)], he now derives the London equations from an expansion of the rotation of vorticity. Vorticity is a vector quantity described in fluid mechanics which characterizes the angular motion of a point particle as it moves. A small ball, for example, found in a field of vorticity would turn around itself. This is in accordance with the existence of the spin of a particle. We claim that due to the dipolar nature of the electric charge, its rotation vortex effects appear. It is found that the total time derivative of the radius possibly due to Brownian motion is different from the velocity but is used as a starting point in describing a fluid-like flow for the electron where all the quantities behave accordingly. Finally, we ascribe the relativistic radius of the electron to a curvature of spacetime from the mass energy equivalence for the electric energy. This paper may also be looked at as one more discussion about the hidden variables quest in quantum mechanics, offering some progress in understanding them.
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure subject. Whereas to most physicists the possibility of a classical reinterpretation of quantum mechanics remains remote and perhaps irrelevant to current problems, a minority have kept the issue alive throughout this period. (See Freistadt [5] for a review of the problem and a comprehensive bibliography up to 1957.) As far as results are concerned there are on the one hand purported proofs of the non-existence of hidden variables, most notably von Neumann’s proof, and on the other, various attempts to introduce hidden variables such as de Broglie [4] and Bohm [1] and [2]. One of the difficulties in evaluating these contradictory results is that no exact mathematical criterion is given to enable one to judge the degree of success of these proposals. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.
As was Einstein s original idea we suppose that the speed of light is altered in the presence of mass by a change in its dielectric susceptibility. Our explanation of the phenomena of quantum mechanics is a continuation of Einstein search for hidden variables. Mass induces a curvature in spacetime. This has two effects. New volume is created and this would mean that there is not exactly a point particle but matters in a way occupies some volume. Another result is that spacetime becomes cyclic and quantities like the action are quantized because they depend on angles through which the observer witnesses the events.