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Physical Review Letters

Bell's Theorem: Does the Clauser-Horne Inequality Hold for All Local Theories?

Thomas D. Angelidis

Published Nov 14, 1983• 21 citations
Publisher

Abstract

The claim that the Clauser-Horne inequality $S(\ensuremath{\phi})<~1$ is valid for all local theories is criticized. The criticism is based on the author's proof that this universality claim is incompatible with the conservation law of angular momentum. There exists an infinity of counterexamples to the universality claim made for $S(\ensuremath{\phi})<~1$. So Clauser and Horne offer no valid proof of the nonlocality of the quantum formalism; consequently experiments like Aspect's cannot be said to refute Einsteinian locality.

DOI
10.1103/physrevlett.51.1819

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Comment on "Bell's Theorem: Does the Clauser-Horne Inequality Hold for All Local Theories?"

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An Exchange on Local Beables

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a) Bell tries to formulate more explicitly a notion of “local causality”: correlations between physical events in different space-time regions should be explicable in terms of physical events in the overlap of the backward light cones. It is shown that ordinary relativistic quantum field theory is not locally causal in this sense, and cannot be embedded in a locally causal theory. b) Clauser, Home and Shimony criticize several steps in Bell's argument that any theory of local “beables” is incompatible with quantum mechanics. It is contended that the Clauser-Horne derivation of a Bell-type inequality circumvents his weak steps. The Clauser-Horne derivation must assume that there are no undetected correlations between choices of controllable variables in two space-like separated regions. Methodological considerations support this assumption. c) In response to criticism by Shimony, Home, and Clauser, Bell tries to clarify the argument of “The theory of local beables”, and to defend as permissible the hypothesis of free variables. d) Bell's reply to an earlier criticism by Shimony, Clauser, and Home is answered. The convergence of Bell's position towards theirs is noted.

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Clauser-Horne-Shimony-Holt correlation and Clauser-Horne correlation do not lead to the largest violations of Bell’s inequality

M. Ardehali

An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment that can actually be performed with present technology to test local realism. Quantum mechanics violates this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities [for example, those of J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969); S. J. Freedman and I. F. Clauser ibid. 28, 938 (1972); and J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974)] by a factor of $\sqrt{2}.$ Thus the magnitude of violation of the inequality derived in this paper is approximately 20.7% larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.

arXiv:quant-ph/9701032•Physical Review A•Jan 1, 1998•5 citations
The claim that the Clauser-Horne inequality S(\ensuremathϕ)< 1S(\ensuremath{\phi})<~1S(\ensuremathϕ)< 1 is valid for all local theories is criticized. The criticism is based on the author's proof that this universality claim is incompatible with the conservation law of angular momentum. There exists an infinity of counterexamples to the universality claim made for S(\ensuremathϕ)< 1S(\ensuremath{\phi})<~1S(\ensuremathϕ)< 1. So Clauser and Horne offer no valid proof of the nonlocality of the quantum formalism; consequently experiments like Aspect's cannot be said to refute Einsteinian locality.
a) Bell tries to formulate more explicitly a notion of “local causality”: correlations between physical events in different space-time regions should be explicable in terms of physical events in the overlap of the backward light cones. It is shown that ordinary relativistic quantum field theory is not locally causal in this sense, and cannot be embedded in a locally causal theory. b) Clauser, Home and Shimony criticize several steps in Bell's argument that any theory of local “beables” is incompatible with quantum mechanics. It is contended that the Clauser-Horne derivation of a Bell-type inequality circumvents his weak steps. The Clauser-Horne derivation must assume that there are no undetected correlations between choices of controllable variables in two space-like separated regions. Methodological considerations support this assumption. c) In response to criticism by Shimony, Home, and Clauser, Bell tries to clarify the argument of “The theory of local beables”, and to defend as permissible the hypothesis of free variables. d) Bell's reply to an earlier criticism by Shimony, Clauser, and Home is answered. The convergence of Bell's position towards theirs is noted.
An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment that can actually be performed with present technology to test local realism. Quantum mechanics violates this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities [for example, those of J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969); S. J. Freedman and I. F. Clauser ibid. 28, 938 (1972); and J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974)] by a factor of 2.\sqrt{2}.2​. Thus the magnitude of violation of the inequality derived in this paper is approximately 20.7% larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.