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arXiv:quant-ph/0205022

Comment on Hess-Philipp anti-Bell and Gill-Weihs-Zeilinger-Zukowski anti-Hess-Philipp arguments

Andrei Yu. Khrennikov

Published May 5, 2002• 6 citations
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Abstract

We present comparative analysis of Gill-Weihs-Zeilinger-Zukowski arguments directed against Hess-Philipp anti-Bell arguments. In general we support Hess-Philipp viewpoint to the sequence of measurements in the EPR-Bohm experiments as stochastic time-like process. On the other hand, we support Gill-Weihs-Zeilinger-Zukowski arguments against the use of time-like correlations as the factor blocking the derivation of Bell-type inequalities. We presented our own time-analysis of measurements in the EPR-Bohm experiments based on the frequency approach to probability. Our analysis gives strong arguments in favour of local realism. Moreover, our frequency analysis supports the original EPR-idea that quantum mechnaics is not complete.

DOI
10.48550/arxiv.quant-ph/0205022

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We present comparative analysis of Gill-Weihs-Zeilinger-Zukowski arguments directed against Hess-Philipp anti-Bell arguments. In general we support Hess-Philipp viewpoint to the sequence of measurements in the EPR-Bohm experiments as stochastic time-like process. On the other hand, we support Gill-Weihs-Zeilinger-Zukowski arguments against the use of time-like correlations as the factor blocking the derivation of Bell-type inequalities. We presented our own time-analysis of measurements in the EPR-Bohm experiments based on the frequency approach to probability. Our analysis gives strong arguments in favour of local realism. Moreover, our frequency analysis supports the original EPR-idea that quantum mechnaics is not complete.
We analyse notion of independence in the EPR-Bohm framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to demonstrate that Bell's inequality was obtained by using totally unjustified assumptions (e.g. the Bell-Clauser-Horne factorability condition). Our frequency analysis also demonstrated that Gill-Weihs-Zeilinger-Zukowski's arguments based on "the experimenter's freedom to choose settings" to support the standard Bell approach are neither justified by the structure of the EPR-Bohm experiment. Finally, our analysis supports the original Einstein's viewpoint that quantum mechanics is simply not complete.
A recent Letter by Hess and Philipp claims that Bell's theorem neglects the possibility of time-like dependence in local hidden variables, hence is not conclusive. Moreover the authors claim that they have constructed, in an earlier paper, a local realistic model of the EPR correlations. However, they themselves have neglected the experimenter's freedom to choose settings, while on the other hand, Bell's theorem can be formulated to cope with time-like dependence. This in itself proves that their toy model cannot satisfy local realism, but we also indicate where their proof of its local realistic nature fails.
We analyse notion of independence in the EPR-Bohm framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to demonstrate that Bell's inequality was obtained by using totally unjustified assumptions (e.g. the Bell-Clauser-Horne factorability condition). Our frequency analysis also demonstrated that Gill-Weihs-Zeilinger-Zukowski's arguments based on "the experimenter's freedom to choose settings" to support the standard Bell approach are neither justified by the structure of the EPR-Bohm experiment. Finally, our analysis supports the original Einstein's viewpoint that quantum mechanics is simply not complete.
Hess and Philipp recently claimed [(2001) Proc. Natl. Acad. Sci. USA 98, 14224-14227 and 14228-14233] that proofs of Bell's theorem have overlooked the possibility of time dependence in local hidden variables, hence the theorem has not been proven true. Moreover they present what is claimed to be a local realistic model of the EPR correlations. If this is true then Bell's theorem is not just unproven, but false. We refute both claims. First, we explain why time is not an issue in Bell's theorem, and second, we show that their hidden variables model violates Einstein separability. Hess and Philipp have overlooked the freedom of the experimenter to choose settings of a measurement apparatus at will: any setting could be in force during the same time period.
By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.
Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.