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Oversights in the Respective Theorems of von Neumann and Bell are Homologous
Version 1
: Received: 14 January 2021 / Approved: 15 January 2021 / Online: 15 January 2021 (13:09:12 CET)
How to cite: Christian, J. Oversights in the Respective Theorems of von Neumann and Bell are Homologous. Preprints 2021, 2021010295. https://doi.org/10.20944/preprints202101.0295.v1 Christian, J. Oversights in the Respective Theorems of von Neumann and Bell are Homologous. Preprints 2021, 2021010295. https://doi.org/10.20944/preprints202101.0295.v1
Abstract
We show that the respective oversights in the von Neumann's general theorem against all hidden variable theories and Bell's theorem against their local-realistic counterparts are homologous. Both theorems unjustifiably assume the additivity of expectation values within hidden variable theories to derive their respective conclusions. However, for non-commuting observables, the equivalence of a sum of expectation values and the expectation value of the sum of measurement results, although respected within quantum mechanics, need not hold for hidden variable theories, regardless of specific characteristics such as local realism they may respect. Once this oversight is ameliorated from Bell's argument and local realism is implemented correctly, the bounds on the CHSH correlator work out to be +/-2\/2 instead of +/-2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values.
Keywords
Hidden variables; von Neumann's theorem; Bell's theorem; Local realism; Quantum correlations
Subject
Physical Sciences, Acoustics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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