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:2108.08249 · Journal of Modern Physics

Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect

Frank Lad

Published Jan 1, 2021• 7 citations
arXivHTMLPDF

Abstract

This paper intends to show how the fabled violation of Bell's inequality by the probabilistic specifications of quantum mechanics derives from a mathematical error, an error of neglect.I have no objection to the probabilities specified by quantum theory, nor to the inequality itself as characterized in the formulation of Clauser, Horne, Shimony, and Holt.Designed to assess consequences of Einstein's principle of local realism, the inequality pertains to a li-How to cite this paper: Lad, F. ( 2021) Quantum Violation of Bell's Inequality: A Misunderstanding Based on a Mathematical Error of Neglect.

DOI
10.4236/jmp.2021.128067

Related papers

Violation of probabilistic inequality Clauser-Horne-Shimony-Holt in Quantum Mechanics

Felipe Andrade Velozo, Diogo Francisco Rossoni, José A. C. Nogales +2 more

In 1982, Alain Aspect, and collaborators performed an experiment, in order to observe the violation of the inequality of Clauser-Horne-Shimony-Holt. After the experiment, they used the data in the inequality and concluded that the inequality, obtained through probabilistic arguments, was violated confirming the conclusions obtained by John S. Bell that was not possible a theory of hidden variables in the conditions suggested by Einstein, Podolsky and Rosen. The aim of this work is to verify the validity of the inequalities in the conditions of the probabilistic theory, in order to hold with the axioms of the probability.

arXiv:1611.04855•Oct 31, 2016•0 citations

Violation of Bell Inequalities: Mapping the Conceptual Implications

Brian Drummond

This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions.

arXiv:2106.14767•Jun 28, 2021•3 citations

Bell inequality violation in relativity theory

Aleksandr V. Belinsky, Джадан Игорь Иванович

Abstract A violation of Bell local realism inequalities in Clauser–Horne–Shimony–Holt form has been discovered in a relativistic Gedankenexperiment. This means that there are no definite joint probabilities and this finds a classical explanation in the structure of special relativity. The discovered nonlocality is weaker than Albert Einstein’s quantum ‘spooky action at a distance’, and its presence suggests certain parallels between special relativity and quantum mechanics.

Laser Physics Letters•Jun 25, 2024•2 citations

Violation of Bell’s Inequality in the Clauser-Horne-Shimony-Holt Form with Entangled Quantum States Revisited

Carlo Cafaro, Christian Corda, Philip Cairns +1 more

arXiv:2302.14046•International Journal of Theoretical Physics•May 1, 2024•4 citations

A logical loophole in the derivation of the CHSH Bell-type inequality

G. Coddens

We point out a loophole in the derivation of the Bell inequalities in the form proposed by Clauser, Horne, Shimony and Holt (CHSH). In this derivation it is assumed that statistical independence is a necessary consequence of locality, but this is not a logical necessity.

arXiv:1309.6057•Sep 24, 2013•0 citations

The Clauser-Horne-Shimony-Holt inequality in the context of a broad random variable

Felipe Andrade Velozo, José A. C. Nogales, Gustavo Figueiredo Araújo

In this work we aim to analyze the Clauser-Horne-Shimony-Holt CHSH inequality strictly in the context of probability theory. In the course of assembling inequality we have to take care not to produce assumptions a priori, that is, physically or intuitively accepted suppositions. Of course, this does not mean that after these considerations, we put the adequate physical conditions suitable and generally accepted in these contexts. This allows us to clearly visualize the possibility of finding a greater inequality than that of CHSH in which it is included. This inequality does not contradict the CHSH inequality. This result is suported by using a robust computational simulation, showing the possibility for obtaining an inequality for quantum mechanics that is not violated and allows random hidden variables without any conflict with Bell's inequality.

arXiv:1805.11200•May 28, 2018•1 citation
This paper intends to show how the fabled violation of Bell's inequality by the probabilistic specifications of quantum mechanics derives from a mathematical error, an error of neglect.I have no objection to the probabilities specified by quantum theory, nor to the inequality itself as characterized in the formulation of Clauser, Horne, Shimony, and Holt.Designed to assess consequences of Einstein's principle of local realism, the inequality pertains to a li-How to cite this paper: Lad, F. ( 2021) Quantum Violation of Bell's Inequality: A Misunderstanding Based on a Mathematical Error of Neglect.
In 1982, Alain Aspect, and collaborators performed an experiment, in order to observe the violation of the inequality of Clauser-Horne-Shimony-Holt. After the experiment, they used the data in the inequality and concluded that the inequality, obtained through probabilistic arguments, was violated confirming the conclusions obtained by John S. Bell that was not possible a theory of hidden variables in the conditions suggested by Einstein, Podolsky and Rosen. The aim of this work is to verify the validity of the inequalities in the conditions of the probabilistic theory, in order to hold with the axioms of the probability.
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions.
In this work we aim to analyze the Clauser-Horne-Shimony-Holt CHSH inequality strictly in the context of probability theory. In the course of assembling inequality we have to take care not to produce assumptions a priori, that is, physically or intuitively accepted suppositions. Of course, this does not mean that after these considerations, we put the adequate physical conditions suitable and generally accepted in these contexts. This allows us to clearly visualize the possibility of finding a greater inequality than that of CHSH in which it is included. This inequality does not contradict the CHSH inequality. This result is suported by using a robust computational simulation, showing the possibility for obtaining an inequality for quantum mechanics that is not violated and allows random hidden variables without any conflict with Bell's inequality.