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Optics and Spectroscopy

Objective Reality and the Paradox of Wigner Friends

Aleksandr V. Belinsky

Published Sep 1, 2020• 2 citations
Publisher

Abstract

Abstract Using the experiment described at https://arxiv.org/pdf/1902.05080.pdf as an example, it has been shown that the absence of the objective existence of the results of quantum measurements cannot be rigorously proved based on the registration of the violation of the Bell inequality in the form of Clauser–Horne–Shimony–Holt. Universal arguments are also presented to generalize this inference.

DOI
10.1134/s0030400x20090039

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Abstract Using the experiment described at https://arxiv.org/pdf/1902.05080.pdf as an example, it has been shown that the absence of the objective existence of the results of quantum measurements cannot be rigorously proved based on the registration of the violation of the Bell inequality in the form of Clauser–Horne–Shimony–Holt. Universal arguments are also presented to generalize this inference.
Abstract Bell’s theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein–Rosen–Podolsky argument occurs if there exists an ‘element of reality’ but nevertheless addition of complementary results is impossible because they are represented by elements from different arithmetics. A naive mixing of arithmetics leads to contradictions at a much more elementary level than the Clauser–Horne–Shimony–Holt inequality.
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.