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Physics Letters A

The Bell inequalities and their irrelevance to the problem of locality in quantum mechanics

Willem M. de Muynck

Published Feb 1, 1986• 51 citations
Publisher
DOI
10.1016/0375-9601(86)90480-9

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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.
According to quantum mechanics in its current form, quantum randomness is an intrinsic property of the physical world. The legitimacy of such interpretation is the essence of the Einstein-Bohr debate. Bell’s theorem implies that local realism should be responsible for the experimental invalidation of Bell inequalities. In this paper, it is shown that quantum randomness is due to the unattainability of precise space and time coordinates, and the failure of Bell inequalities is irrelevant to local realism. Furthermore, by reconsidering Bell’s theorem in the context of the mathematical setting for quantum physics, namely, Hilbert space, it is shown that, whether a measurement is performed on a system or not, the logical relation between orthogonal vectors corresponding to mutually exclusive properties of the system must be disjunction (“or”) rather than conjunction (“and”). Moreover, if the unattainability of precise space and time coordinates is taken into account, and if disjunction is used to serve as the logical relation between the orthogonal vectors, then it is possible to render quantum mechanics complete in the sense considered by Einstein while not essentially modifying the mathematical setting for quantum physics.