Bell's inequalities, relativistic quantum field theory and the problem of hidden variables

Philosophy of Science 58 (4):628-638 (1991)
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
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DOI 10.1086/289644
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Jeremy Butterfield (2007). Stochastic Einstein Locality Revisited. British Journal for the Philosophy of Science 58 (4):805 - 867.
Gábor Hofer-Szabó (2015). On the Relation Between the Probabilistic Characterization of the Common Cause and Bell׳s Notion of Local Causality. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49:32-41.

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