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arXiv:0905.0140

Quantum theory without logical paradoxes?

M. V. Lokajíček

Published May 1, 2009• 0 citations
arXivHTMLPDF

Abstract

In contribution published in AIP Conference Proceedings, No. 1018 (p. 40-5) some discrepancies in Copenhagen quantum mechanics have been summarized and the arguments have been gathered why in the description of microscopic reality the hidden-variable theory should be preferred. It has been shown, too, that the earlier gap in physical descriptions of the microscopic and macroscopic worlds may be practically removed. All corresponding statements have been based on proofs that have been published earlier and reproduced in the given contribution only partially. In the present paper the whole approach will be explained more systematically. Some important points newly analyzed will be added.

DOI
10.48550/arxiv.0905.0140

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The nondeterministic character of quantum measurement can, and should, be taken to imply a deeper 'hidden variable' description of a system, which reproduces quantum theory when the unknown values of the variables are marginalised over. Differences in measurements on identically prepared systems then represent differences in the hidden variables of the systems. Not to seek the hidden variables, as the Copenhagen interpretation of quantum mechanics arbitrarily instructs, is to give up all hope of improvement in advance, and is contrary to the purposes of science. Correspondingly, it can never be proven that hidden variables don't exist; the most that can be done is to place hypothetical restrictions on them and prove that the resulting theory cannot be marginalised into quantum theory - implying that the hidden variables violate the restriction. The best known example is Bell's theorem, which rules out all local hidden-variable theories and explains why the variables are so coy: it is not easy to isolate and influence something nonlocal. A promising way forward is to proceed from the Dirac theory of the electron in its natural, geometric language of Clifford algebra. This approach, due to Hestenes, suggests that the free electron is in fact a massless point particle executing zitterbewegung at the speed of light, with radius the electron Compton wavelength. This proposal improves the correspondence of the physics with the formalism and resolves many paradoxes; it also hints that the hidden variables are concerned with those parameters needed to define the electron orbit completely. These ideas all represent a demystification of quantum theory. In the 19th century, microscopes advanced to the point at which a new phenomenon, today called Brownian motion after its chronicler, could be seen. The small particles, newly made visible ('dust' particles), were observed to jiggle around in a manner the scientists could not predict, for no apparent reason. Motion of any individual dust particle could not be predicted; however, statistical details of the motion, such as the average (drift) velocity or the mean square velocity, were reproducible. The scientists of the day, probably without realising it, made an assumption: that there was a reason for the jiggling, and that if they could find this, they could predict the precise motion of individual dust particles. They never said Maybe the dust particles just behave like that and there isn't a why; maybe we can go no further and this is the end of the line. 79

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In contribution published in AIP Conference Proceedings, No. 1018 (p. 40-5) some discrepancies in Copenhagen quantum mechanics have been summarized and the arguments have been gathered why in the description of microscopic reality the hidden-variable theory should be preferred. It has been shown, too, that the earlier gap in physical descriptions of the microscopic and macroscopic worlds may be practically removed. All corresponding statements have been based on proofs that have been published earlier and reproduced in the given contribution only partially. In the present paper the whole approach will be explained more systematically. Some important points newly analyzed will be added.
In the contribution published in AIP Conference Proceedings, No. 1018 (p. 40-5) some discrepancies in Copenhagen quantum mechanics have been summarized and arguments have been gathered why in the description of microscopic reality hidden-variable theory should be preferred. It has been shown, too, that the earlier gap in physical descriptions of microscopic and macroscopic worlds has been practically removed. All corresponding statements have been based on proofs that had been published earlier and reproduced in the given contribution only partially. In the present paper the whole approach will be explained more systematically. Some important points newly analyzed will be added.
It has been shown by us recently that Einstein was right in his controversy with Bohr or that the so called hidden-variable theory should be preferred to the Copenhagen quantum mechanics. In the following paper the corresponding arguments will be shortly repeated. The main attention will be then devoted to explaining main differences between these two quantum alternatives, differing in the access to the problem of chance, causality and locality of microscopic objects. The actual meaning of the mentioned hidden variables will be discussed, too, the essence of which remained practically unclear during all past discussions. It will be shown that the theory of hidden variables (or Schrodinger equation alone) is able to represent the properties of the whole known physical reality.
It has been shown by us recently that Einstein was right in his controversy with Bohr or that the so called hidden-variable theory should be preferred to the Copenhagen quantum mechanics. In the following paper the corresponding arguments will be shortly repeated. The main attention will be then devoted to explaining main differences between these two quantum alternatives, differing in the access to the problem of chance, causality and locality of microscopic objects. The actual meaning of the mentioned hidden variables will be discussed, too, the essence of which remained practically unclear during all past discussions. It will be shown that the theory of hidden variables (or Schroedinger equation alone) is able to represent the properties of the whole known physical reality.
Why does such a successful theory like Quantum Mechanics have so many mysteries? The history of this theory is replete with dubious interpretations and controversies, and yet a knowledge of its predictions, however, contributed to the amazing technological revolution of the last hundred years. In its very beginning Einstein pointed out that there was something missing, due to contradictions with the relativity theory. So, even though Quantum Mechanics explains all the nanoscale physical phenomena, there were many attempts to find a way to “complete” it, e.g. hidden-variable theories. In this paper, we discuss some of those enigmas, with special attention to the concepts of physical reality imposed by quantum mechanics, the role of the observer, prediction limits, a definition of collapse, and how to deal with correlated states (the basic strategy for quantum computers and quantum teleportation). That discussion is carried out within the framework of accepting that there is in fact nothing important missing, rather we are just restricted by the limitations imposed by quantum mechanics. The mysteries are thus explained by a proper interpretation of those limitations, which is achieved by introducing two interpretation rules within the Copenhagen paradigm.
The nondeterministic character of quantum measurement can, and should, be taken to imply a deeper 'hidden variable' description of a system, which reproduces quantum theory when the unknown values of the variables are marginalised over. Differences in measurements on identically prepared systems then represent differences in the hidden variables of the systems. Not to seek the hidden variables, as the Copenhagen interpretation of quantum mechanics arbitrarily instructs, is to give up all hope of improvement in advance, and is contrary to the purposes of science. Correspondingly, it can never be proven that hidden variables don't exist; the most that can be done is to place hypothetical restrictions on them and prove that the resulting theory cannot be marginalised into quantum theory - implying that the hidden variables violate the restriction. The best known example is Bell's theorem, which rules out all local hidden-variable theories and explains why the variables are so coy: it is not easy to isolate and influence something nonlocal. A promising way forward is to proceed from the Dirac theory of the electron in its natural, geometric language of Clifford algebra. This approach, due to Hestenes, suggests that the free electron is in fact a massless point particle executing zitterbewegung at the speed of light, with radius the electron Compton wavelength. This proposal improves the correspondence of the physics with the formalism and resolves many paradoxes; it also hints that the hidden variables are concerned with those parameters needed to define the electron orbit completely. These ideas all represent a demystification of quantum theory. In the 19th century, microscopes advanced to the point at which a new phenomenon, today called Brownian motion after its chronicler, could be seen. The small particles, newly made visible ('dust' particles), were observed to jiggle around in a manner the scientists could not predict, for no apparent reason. Motion of any individual dust particle could not be predicted; however, statistical details of the motion, such as the average (drift) velocity or the mean square velocity, were reproducible. The scientists of the day, probably without realising it, made an assumption: that there was a reason for the jiggling, and that if they could find this, they could predict the precise motion of individual dust particles. They never said Maybe the dust particles just behave like that and there isn't a why; maybe we can go no further and this is the end of the line. 79