Kolmogorovian Model for Epr-Experiment

Avis, David; Fischer, Paul; Hilbert, Astrid; Khrennikov, Andrei

doi:10.1142/9789814295437_0010

Cited by 2 publications

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“…The work in this paper is based directly on the arguments Avis et al and Khrennikov used [1,4] to construct a single Kolmogorov probability space for the CHSH experiments. However, we come to different conclusions.…”

Section: Hidden Variables On a Single Probability Spacementioning

confidence: 99%

“…However, we come to different conclusions. We use the random variables set out in Section 3, Proper random experiment, of [1] and derive results which show that the inequality (2) in [1] (ie equation ( 2) above ) is in error by being too weak.…”

Section: Hidden Variables On a Single Probability Spacementioning

confidence: 99%

“…In a series of papers Khrennikov and co-workers [1][2][3][4] have made strong claims that the experimental violation of the CHSH inequalities is a consequence of an erroneous use of experimental data. It is suggested that the experimental violations of the CHSH inequality arise through incorrectly combining data from a number of experiments and suggest that mixing the data from different experimental contexts is an improper use of statistical data.…”

Section: Introductionmentioning

confidence: 99%

“…Avis et al [1] give a detailed analysis of a EPR-Bohm-Bell experiments and suggests a single probability space for the analysis of such experiments; they describe this as a proper probability space. It is also described as a common Kolmogorov probability space in Khrennikov [4].…”

Section: Introductionmentioning

confidence: 99%

“…It is also described as a common Kolmogorov probability space in Khrennikov [4]. In [1,4] they assume a CHSH inequality of the form |< A (1) , B (1) > − < A (1) , B (2) > + < A (2) , B (2) > + < A (2) , B (1) >| ≤ 2 (1) for random variables A i and B i defined on a single Kolmogorov probability space which they construct to describe four separate experiments; A i and B i and are defined below. They then claim that the "Bellian" variables a i and b i used to describe a single experiment obey the modified CHSH inequality (eg equation ( 2) in [1])…”

Section: Introductionmentioning

confidence: 99%

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CHSH Inequality on a single probability space

Care

2016

Preprint

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Khrennikov and co-workers have suggested in a series of papers that it is inappropriate to combine data from different experiments when undertaking experimental tests of Bell's inequalities. They suggest that a correct analysis, using a single probability space, leads to inequalities which are not violated by experiment. If correct, this would be contrary to the normal interpretation of such experimental data.However, in this note, a generalised Clauser-Horne-Shimony-Holt (CHSH) inequality is derived for a system of four experiments constructed on a single probability space which combines the data from the four experiments. In contradiction to Khrennikov et al, it is shown that this leads to the standard CHSH inequality which is normally used to interpret experimental data. Thus the commonly accepted conclusion that experimental violations of Bell's inequality imply that local realistic models are inconsistent with the predictions of quantum mechanics has not been challenged.

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Section: Hidden Variables On a Single Probability Spacementioning

confidence: 99%

Section: Hidden Variables On a Single Probability Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CHSH Inequality on a single probability space

Care

2016

Preprint

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On universality of classical probability with contextually labeled random variables

Dzhafarov

Kon

2018

Journal of Mathematical Psychology

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One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these claims are unjustified, illustrating this on the issues of (non)existence of joint distributions, probabilities of ordered events, and additivity of probabilities. The specific focus of this note is on showing that the mistakes underlying these claims can be precluded by labeling all random variables involved contextually. Moreover, contextual labeling also enables a valuable additional way of analyzing probabilistic aspects of empirical situations: determining whether the random variables involved form a contextual system, in the sense generalized from quantum mechanics. Thus, to the extent the Wang-Busemeyer QQ equality for the question order effect holds, the system describing them is noncontextual. The double-slit experiment and its behavioral analogues also turn out to form a noncontextual system, having the same probabilistic format (cyclic system of rank 4) as the one describing spins of two entangled electrons.

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Kolmogorovian Model for Epr-Experiment

Cited by 2 publications

References 0 publications

CHSH Inequality on a single probability space

CHSH Inequality on a single probability space

On universality of classical probability with contextually labeled random variables

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