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:quant-ph/9811072

Bell's Theorem and "Classical" Probability Theory

H. Razmi, Mohammad Golshani

Published Nov 25, 1998• 0 citations
arXivHTMLPDF

Abstract

Using CH model of Bell’s theorem and only by applying the conditional probability definition in ”classical ” probability theory,without imposing the locality condition,we are able to show that the stochastic realistic (CH) model cannot reproduce all of the predictions of quantum mechanics. PACS number: 03.65.Bz It is generally claimed that Bell inequalities are inconsistent with experimental data and with the predictions of quantum mechanics.A condition often used in the derivation of Bell inequalities is the so-called locality condition.The temptation is to attribute Bell inequalities violation to the violation of locality. In this paper we are going

Related papers

ON THE ROLE OF LOCALITY CONDITION IN BELL'S THEOREM

H. Razmi

For a special stochastic realistic model in certain spin-correlation experiments and without imposing the locality condition, an inequality is found. Then, it is shown that quantum theory is able (is possible) to violate this inequality. This shows that, irrespective of the locality condition, the quantum entanglement of the spin singlet-state is the reason for the violation of Bell's inequality in Bell's theorem.

arXiv:quant-ph/0301008•International Journal of Quantum Information•Mar 1, 2003•1 citation

Locality Is An Unnecessary Assumption of Bell's Theorem

H. Razmi, Mehdi Golshani

Without imposing the locality condition,it is shown that quantum mechanics cannot reproduce all the predictions of a special stochastic realistic model used in certain spin-correlation experiments.This shows that the so-called locality condition is an unnecessary assumption of Bell's theorem.

arXiv:quant-ph/9812029•Dec 14, 1998•0 citations

Collapse of Bell’s Theorem

Guangye Chen

Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.

Journal of Modern Physics•Jan 1, 2019•4 citations

Classicality and Bell’s theorem

Márton Gömöri, Carl Hoefer

Abstract A widespread view among physicists is that Bell’s theorem rests on an implicit assumption of “classicality,” in addition to locality. According to this understanding, the violation of Bell’s inequalities poses no challenge to locality, but simply reinforces the fact that quantum mechanics is not classical. The paper provides a critical analysis of this view. First we characterize the notion of classicality in probabilistic terms. We argue that classicality thus construed has nothing to do with the validity of classical physics, nor of classical probability theory, contrary to what many believe. At the same time, we show that the probabilistic notion of classicality is not an additional premise of Bell’s theorem, but a mathematical corollary of locality in conjunction with the standard auxiliary assumptions of Bell. Accordingly, any theory that claims to get around the derivation of Bell’s inequalities by giving up classicality, in fact has to give up one of those standard assumptions. As an illustration of this, we look at two recent interpretations of quantum mechanics, Reinhard Werner’s operational quantum mechanics and Robert Griffiths’ consistent histories approach, that are claimed to be local and non-classical, and identify which of the standard assumptions of Bell’s theorem each of them is forced to give up. We claim that while in operational quantum mechanics the Common Cause Principle is violated, the consistent histories approach is conspiratorial. Finally, we relate these two options to the idea of realism, a notion that is also often identified as an implicit assumption of Bell’s theorem.

European Journal for Philosophy of Science•Sep 1, 2023•0 citations

Violations of Locality Beyond Bell's Theorem

Zeng‐Bing Chen, Sixia Yu, Zhang, Yong-De

Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.

arXiv:quant-ph/0307143•Jul 20, 2003•1 citation

A Study on Bell's Theorem

Tan Tian-rong

This paper proves that Bell's inequality is originated from classical probability theory,and thereby is related neither to locality nor to hidden variables.But it is also possible to derive spin correlation formula in quantum mechanics according to the classical probabilistic theory.This fact indicates that on cer- tain conditions,classical probabilistic theory would be inconsistent with quantum mechanics,but under other conditions,classical probabilistic theory and quantum mechanics would,reach the same goal by different means.Still further,this paper confirms that all of the probability operation rules in classical probability theo- ry,containing joint probability operation rules,are suitable for micro processes,but the event operation rules in classical probability theory are unsuitable.The reason obtaining Bell's inequality lies in the steps applying Boolean algebra rules on the non-Boolean micro event space.

Journal of Changzhou Institute of Technology•Jan 1, 2008•0 citations
Using CH model of Bell’s theorem and only by applying the conditional probability definition in ”classical ” probability theory,without imposing the locality condition,we are able to show that the stochastic realistic (CH) model cannot reproduce all of the predictions of quantum mechanics. PACS number: 03.65.Bz It is generally claimed that Bell inequalities are inconsistent with experimental data and with the predictions of quantum mechanics.A condition often used in the derivation of Bell inequalities is the so-called locality condition.The temptation is to attribute Bell inequalities violation to the violation of locality. In this paper we are going
Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.
Abstract A widespread view among physicists is that Bell’s theorem rests on an implicit assumption of “classicality,” in addition to locality. According to this understanding, the violation of Bell’s inequalities poses no challenge to locality, but simply reinforces the fact that quantum mechanics is not classical. The paper provides a critical analysis of this view. First we characterize the notion of classicality in probabilistic terms. We argue that classicality thus construed has nothing to do with the validity of classical physics, nor of classical probability theory, contrary to what many believe. At the same time, we show that the probabilistic notion of classicality is not an additional premise of Bell’s theorem, but a mathematical corollary of locality in conjunction with the standard auxiliary assumptions of Bell. Accordingly, any theory that claims to get around the derivation of Bell’s inequalities by giving up classicality, in fact has to give up one of those standard assumptions. As an illustration of this, we look at two recent interpretations of quantum mechanics, Reinhard Werner’s operational quantum mechanics and Robert Griffiths’ consistent histories approach, that are claimed to be local and non-classical, and identify which of the standard assumptions of Bell’s theorem each of them is forced to give up. We claim that while in operational quantum mechanics the Common Cause Principle is violated, the consistent histories approach is conspiratorial. Finally, we relate these two options to the idea of realism, a notion that is also often identified as an implicit assumption of Bell’s theorem.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
This paper proves that Bell's inequality is originated from classical probability theory,and thereby is related neither to locality nor to hidden variables.But it is also possible to derive spin correlation formula in quantum mechanics according to the classical probabilistic theory.This fact indicates that on cer- tain conditions,classical probabilistic theory would be inconsistent with quantum mechanics,but under other conditions,classical probabilistic theory and quantum mechanics would,reach the same goal by different means.Still further,this paper confirms that all of the probability operation rules in classical probability theo- ry,containing joint probability operation rules,are suitable for micro processes,but the event operation rules in classical probability theory are unsuitable.The reason obtaining Bell's inequality lies in the steps applying Boolean algebra rules on the non-Boolean micro event space.