Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0705.3378

Bell's Theorem refuted with a Kolmogorovian counterexample

Johannes F. Geurdes

Published May 23, 2007• 2 citations
arXivHTMLPDF

Abstract

The statistics behind Bell's inequality is demonstrated to allow a Kolmogorovian (i.e. classical) model of probabilities that recovers the quantum covariance.
DOI
10.48550/arxiv.0705.3378

Related papers

Bell's Inequality Refuted on Bell's Own Terms

Gordon Watson

Bell's famous inequality contradicts ours. But ours holds algebraically, experimentally, classically and quantum-mechanically: Bell's does not. So Bell's inequality is refuted on Bell's terms as we identify his naively-realistic error and correct it.

•Jul 1, 2018•0 citations

Bell’s Theorem Refuted via Elementary Probability Theory

Gordon Watson

•Oct 1, 2020•0 citations

Comparison between local Kolmogorovian models and Bell's inequality

Augusto Garuccio, D. Gutkowski

Foundations of Physics Letters•Feb 1, 1990•1 citation

Bell-Type Inequalities in Fuzzy Probability Calculus

Jarosław Pykacz

Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogorovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities based on the most frequently used Zadeh intersection or probabilistic intersection, but it allows to distinguish all these models from fuzzy probability models based on Giles (Łukasiewicz) intersection. It is proved that if we use fuzzy set intersections pointwisely generated by Frank's fundamental triangular norms Ts(x,y), then the borderline between fuzzy probability models that can be distinguished from Kolmogorovian ones and these fuzzy probability models that cannot be distinguished is for .

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems•Apr 1, 2001•18 citations

Experimental Data Does Not Violate Bell's Inequality for "Right Kolmogorov Space''

Fischer, Paul, David Avis, Astrid Hilbert +1 more

•Jan 1, 2008•0 citations

BELL-TYPE INEQUALITIES IN FUZZY PROBABILITY CALCULUS

Jarosław Pykacz, Bart D’Hooghe

Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogorovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities based on the most frequently used Zadeh intersection or probabilistic intersection, but it allows to distinguish all these models from fuzzy probability models based on Giles (Łukasiewicz) intersection. It is proved that if we use fuzzy set intersections pointwisely generated by Frank's fundamental triangular norms Ts(x,y), then the borderline between fuzzy probability models that can be distinguished from Kolmogorovian ones and these fuzzy probability models that cannot be distinguished is for [Formula: see text].

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems•Apr 1, 2001•15 citations
Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogorovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities based on the most frequently used Zadeh intersection or probabilistic intersection, but it allows to distinguish all these models from fuzzy probability models based on Giles (Łukasiewicz) intersection. It is proved that if we use fuzzy set intersections pointwisely generated by Frank's fundamental triangular norms Ts(x,y), then the borderline between fuzzy probability models that can be distinguished from Kolmogorovian ones and these fuzzy probability models that cannot be distinguished is for .
Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogorovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities based on the most frequently used Zadeh intersection or probabilistic intersection, but it allows to distinguish all these models from fuzzy probability models based on Giles (Łukasiewicz) intersection. It is proved that if we use fuzzy set intersections pointwisely generated by Frank's fundamental triangular norms Ts(x,y), then the borderline between fuzzy probability models that can be distinguished from Kolmogorovian ones and these fuzzy probability models that cannot be distinguished is for [Formula: see text].