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Oversights in the Respective Theorems of von Neumann and Bell are Homologous

Christian, Joy (2020) Oversights in the Respective Theorems of von Neumann and Bell are Homologous. [Preprint]

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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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Christian, Joyjjc@bu.edu
Keywords: hidden variables, von Neumann's theorem, Bell's theorem, EPR Paradox, Local Realism, Local Causality, Quantum Correlations, contextuality
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Dr. Joy Christian
Date Deposited: 29 Nov 2020 19:58
Last Modified: 29 Nov 2020 19:58
Item ID: 18461
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
Date: 25 November 2020
URI: http://philsci-archive.pitt.edu/id/eprint/18461

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