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Computational nanotechnology

Bell-Inequality and Two Slit Experiments: Comparing Misapplication of Classical Probability by Feynman and Bell

Andrei Yu. Khrennikov

Published Sep 15, 2021• 0 citations
Publisher

Abstract

10.33693/2313-223X-2021-8-3-19-22, Khrennikov A.., (2021), BELL-INEQUALITY AND TWO SLIT EXPERIMENTS: COMPARING MISAPPLICATION OF CLASSICAL PROBABILITY BY FEYNMAN AND BELL. Computational Nanotechnology, 3: 19-22.
DOI
10.33693/2313-223x-2021-8-3-19-22

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We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.
From the early days of quantum mechanics, there has been a discussion on the concept of reality, exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell inequality. Yet, there remains considerable evidence that this inequality can be violated even by classical systems, so that experiments showing quantum behavior and the violation of the inequality must be questioned. Here, we demonstrate that classical optical polarization experiments can be shown to violate the Bell inequality. Hence, such experiments cannot be used to distinguish between classical and quantum theories.