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

Published online by Cambridge University Press:  01 April 2022

Miklós Rédei
Miklós Rédei*
Affiliation:
Loránd Eötvös University
*
‡Send reprint requests to the author, Loránd Eötvös University, Budapest, Rákóczi út 5, H–1088, HUNGARY.
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Abstract

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.

Type
Research Article
Information
Philosophy of Science , Volume 58 , Issue 4 , December 1991 , pp. 628 - 638
Copyright
Copyright © 1991 The Philosophy of Science Association

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Footnotes

†

This work was done while I was holding a courtesy appointment in the Department of Physics, University of Florida. I wish to thank Professor D. B. Tanner for his support.

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