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:hep-th/9309077 · Contributed to

Another Look at Bell's Inequalities and Quantum Mechanics

Apoorva Patel

Published Sep 14, 1993• 1 citation
arXivHTMLPDF

Abstract

Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The expectation values defined through path integrals obey Bell's inequalities in Euclidean time, but not in Minkowski time. This observation allows us to pinpoint the origin of violation of Bell's inequalities in quantum mechanics. % This article is not precise enough for mathematicians and not vague % enough for philosophers, but it should be interesting for physicists. % Contributed to the XVI International Symposium on Lepton-Photon % Interactions, Cornell University, August 10-15, 1993.

DOI
10.48550/arxiv.hep-th/9309077

Related papers

On how to Produce Entangled States Violating Bell's Inequalities in Quantum Theory

Apoorva Patel

Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The time evolution kernel is unitary in Minkowski time, but generically it becomes real and non-negative in Euclidean time. It follows that the entangled state correlations, that violate Bell's inequalities in Minkowski time, obey the inequalities in Euclidean time. This observation emphasises the link between violation of Bell's inequalities in quantum mechanics and unitarity of the theory. Search for an evolution kernel that cannot be conveniently made non-negative leads to effective interactions that violate time reversal invariance. Interactions giving rise to geometric phases in the effective description of the theory, such as the anomalous Wess-Zumino interactions, have this feature. I infer that they must be present in any set-up that produces entangled states violating Bell's inequalities. Such interactions would be a crucial ingredient in a quantum computer.

arXiv:quant-ph/9810071•Oct 23, 1998•0 citations

Local Hidden Variable Theory of Quantum Mechanics that Violates Bell's Inequality

Henok Tadesse

In this paper the mystery of local hidden variable theory of quantum mechanics that violates Bell’s inequality is proposed. These ‘hidden variables’ are fundamentally inaccessible to physical experiments. It is not something physicists ever dreamed of.

•Jan 26, 2023•0 citations

Bell inequalities and hidden variables over all possible paths in a quantum system

Leffler, Warren

Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the other, of an experiment involving two entangled particles traveling in opposite directions from a source. The parameter lambda (the set of "hidden variables") represents a more complete description of the joint state of the two particles. Because of lambda, the joint probability of detection is now dependent only on lambda and the local measurement setting of alpha; similarly for the other side and the setting beta. From this equation John Bell derived a simple inequality that is violated by the predictions of quantum mechanics, which is generally taken to imply that quantum mechanics is a nonlocal theory. But, by combining Richard Feynman's formulation of quantum mechanics with a model of particle interaction described by David Deutsch, we develop a system (the "space of all paths," SP) that (1) is immediately seen to replicate the predictions of quantum mechanics, (2) has a single outcome for each quantum event (unlike MWI on which it is partly based), and (3) contains the set lambda of hidden variables consisting of all possible paths from the source to the detectors on each side of the two-particle experiment. However, the set lambda is nonmeasurable, and therefore the above equation is meaningless in SP.

arXiv:1207.6352•Jul 26, 2012•0 citations

Expectation Value in Bell's Theorem

Zheng-Chuan Wang

We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theory. Considering the difference of their expectation values, a generalized Bell's inequality is presented, which is coincided with the prediction of quantum mechanics.

arXiv:quant-ph/0604194•Apr 26, 2006•0 citations

The Violation of Bell-CHSH Inequalities Leads to Different Conclusions Depending on the Description Used

Aldo F. G. Solis-Labastida, Melina Gastélum Vargas, Jorge G. Hirsch

Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. However, the hypothesis from which Bell's inequalities are derived differ according to the probability space used to write them. The violation of Bell's inequalities can, alternatively, be explained by assuming that the hidden variables do not exist at all, that they exist but their values cannot be simultaneously assigned, that the values can be assigned but joint probabilities cannot be properly defined, or that averages taken in different contexts cannot be combined. All of the above are valid options, selected by different communities to provide support to their particular research program.

arXiv:2107.02808•Entropy•Jul 8, 2021•3 citations

Bell's Inequalities, Relativistic Quantum Field Theory and the Problem of Hidden Variables

Miklós Rédei

Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a–c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle.

Philosophy of Science•Dec 1, 1991•10 citations
Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The expectation values defined through path integrals obey Bell's inequalities in Euclidean time, but not in Minkowski time. This observation allows us to pinpoint the origin of violation of Bell's inequalities in quantum mechanics. % This article is not precise enough for mathematicians and not vague % enough for philosophers, but it should be interesting for physicists. % Contributed to the XVI International Symposium on Lepton-Photon % Interactions, Cornell University, August 10-15, 1993.
Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The time evolution kernel is unitary in Minkowski time, but generically it becomes real and non-negative in Euclidean time. It follows that the entangled state correlations, that violate Bell's inequalities in Minkowski time, obey the inequalities in Euclidean time. This observation emphasises the link between violation of Bell's inequalities in quantum mechanics and unitarity of the theory. Search for an evolution kernel that cannot be conveniently made non-negative leads to effective interactions that violate time reversal invariance. Interactions giving rise to geometric phases in the effective description of the theory, such as the anomalous Wess-Zumino interactions, have this feature. I infer that they must be present in any set-up that produces entangled states violating Bell's inequalities. Such interactions would be a crucial ingredient in a quantum computer.
Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the other, of an experiment involving two entangled particles traveling in opposite directions from a source. The parameter lambda (the set of "hidden variables") represents a more complete description of the joint state of the two particles. Because of lambda, the joint probability of detection is now dependent only on lambda and the local measurement setting of alpha; similarly for the other side and the setting beta. From this equation John Bell derived a simple inequality that is violated by the predictions of quantum mechanics, which is generally taken to imply that quantum mechanics is a nonlocal theory. But, by combining Richard Feynman's formulation of quantum mechanics with a model of particle interaction described by David Deutsch, we develop a system (the "space of all paths," SP) that (1) is immediately seen to replicate the predictions of quantum mechanics, (2) has a single outcome for each quantum event (unlike MWI on which it is partly based), and (3) contains the set lambda of hidden variables consisting of all possible paths from the source to the detectors on each side of the two-particle experiment. However, the set lambda is nonmeasurable, and therefore the above equation is meaningless in SP.
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theory. Considering the difference of their expectation values, a generalized Bell's inequality is presented, which is coincided with the prediction of quantum mechanics.
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. However, the hypothesis from which Bell's inequalities are derived differ according to the probability space used to write them. The violation of Bell's inequalities can, alternatively, be explained by assuming that the hidden variables do not exist at all, that they exist but their values cannot be simultaneously assigned, that the values can be assigned but joint probabilities cannot be properly defined, or that averages taken in different contexts cannot be combined. All of the above are valid options, selected by different communities to provide support to their particular research program.
Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a–c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle.