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Event-independence, collective-independence,EPR-Bohm experiment and incompleteness of quantum mechanics

Andrei Yu. Khrennikov

Published Jan 1, 2002• 3 citations
OpenAlex

Abstract

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.

Related papers

Event Independence, Collective Independence, EPR‐Bohm Experiment, and Incompleteness of Quantum Mechanics

Andrei Yu. Khrennikov

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.

arXiv:quant-ph/0205081•Physics Essays•Jun 1, 2003•2 citations

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

Andrei Yu. Khrennikov

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.

arXiv:quant-ph/0205022•May 5, 2002•6 citations

Einstein and Bell, von Mises and Kolmogorov: reality and locality, frequency and probability

Andrei Yu. Khrennikov

We perform frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes. In fact, frequencies for hidden variables for quantum particles and measurement devices may fluctuate from run to run of an experiment. These fluctuations of frequencies for micro-parameters need not contradict to the stabilization of frequencies for physical observables. If, nevertheless, micro-parameters are also statistically stable, then violations of Bell's inequality and its generalizations may be a consequence of dependence of collectives corresponding to two different measurement devices. Such a dependence implies the violation of the factorization rule for the simultaneous probability distribution. Formally this rule coincides with the well known BCHS locality condition (or outcome independence condition). However, the frequency approach implies totally different interpretation of dependence. It is not dependence of events, but it is dependence of collectives. Such a dependence may be induced by the same preparation procedure.

arXiv:quant-ph/0006016•Jun 4, 2000•5 citations

Bell Inequalities

Reinhold A. Bertlmann, Nicolai Friis

Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger

•Sep 7, 2023•1 citation

Bell's inequality: Physics meets Probability

Andrei Yu. Khrennikov

We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation of Bell's type inequalities is a well known sufficient condition of incompatibility of random variables -- impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell's inequality -- a few pairs of random variables (two dimensional vector variables) involved in the EPR-Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus one can choose between: a) completeness of quantum mechanics; b) nonlocality; c) `` death of reality''; d) non-Kolmogorovness. In any event, violation of Bell's inequality has a variety of possible interpretations. Hence, it could not be used to derive the unique conclusion on the relation between quantum and classical models.

arXiv:0709.3909•Sep 25, 2007•32 citations

EPR, Bell, GHZ, and Hardy theorems, and quantum mechanics

M. Socolovsky

We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell, Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting the idea that quantum mechanics is a complete, causal, non local, and non separable theory.

arXiv:quant-ph/0508077•Aug 9, 2005•0 citations
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.
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.
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 perform frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes. In fact, frequencies for hidden variables for quantum particles and measurement devices may fluctuate from run to run of an experiment. These fluctuations of frequencies for micro-parameters need not contradict to the stabilization of frequencies for physical observables. If, nevertheless, micro-parameters are also statistically stable, then violations of Bell's inequality and its generalizations may be a consequence of dependence of collectives corresponding to two different measurement devices. Such a dependence implies the violation of the factorization rule for the simultaneous probability distribution. Formally this rule coincides with the well known BCHS locality condition (or outcome independence condition). However, the frequency approach implies totally different interpretation of dependence. It is not dependence of events, but it is dependence of collectives. Such a dependence may be induced by the same preparation procedure.
Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation of Bell's type inequalities is a well known sufficient condition of incompatibility of random variables -- impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell's inequality -- a few pairs of random variables (two dimensional vector variables) involved in the EPR-Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus one can choose between: a) completeness of quantum mechanics; b) nonlocality; c) `` death of reality''; d) non-Kolmogorovness. In any event, violation of Bell's inequality has a variety of possible interpretations. Hence, it could not be used to derive the unique conclusion on the relation between quantum and classical models.