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Version 20
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Bell's Theorem Begs the Question
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: Received: 2 January 2023 / Approved: 3 January 2023 / Online: 3 January 2023 (08:52:26 CET)
Version 2 : Received: 4 January 2023 / Approved: 5 January 2023 / Online: 5 January 2023 (02:41:00 CET)
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Version 2 : Received: 4 January 2023 / Approved: 5 January 2023 / Online: 5 January 2023 (02:41:00 CET)
Version 3 : Received: 5 January 2023 / Approved: 6 January 2023 / Online: 6 January 2023 (02:16:05 CET)
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Version 6 : Received: 23 January 2023 / Approved: 24 January 2023 / Online: 24 January 2023 (13:15:45 CET)
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Version 9 : Received: 28 March 2023 / Approved: 28 March 2023 / Online: 28 March 2023 (05:39:30 CEST)
Version 10 : Received: 9 May 2023 / Approved: 9 May 2023 / Online: 9 May 2023 (10:30:49 CEST)
Version 11 : Received: 13 June 2023 / Approved: 13 June 2023 / Online: 13 June 2023 (07:21:21 CEST)
Version 12 : Received: 2 August 2023 / Approved: 3 August 2023 / Online: 3 August 2023 (07:22:51 CEST)
Version 13 : Received: 22 September 2023 / Approved: 22 September 2023 / Online: 25 September 2023 (04:03:31 CEST)
Version 14 : Received: 28 November 2023 / Approved: 28 November 2023 / Online: 28 November 2023 (10:12:21 CET)
Version 15 : Received: 26 December 2023 / Approved: 27 December 2023 / Online: 27 December 2023 (04:58:31 CET)
Version 16 : Received: 25 January 2024 / Approved: 25 January 2024 / Online: 26 January 2024 (01:57:51 CET)
Version 17 : Received: 10 February 2024 / Approved: 12 February 2024 / Online: 12 February 2024 (14:54:15 CET)
Version 18 : Received: 23 July 2024 / Approved: 24 July 2024 / Online: 24 July 2024 (07:59:49 CEST)
Version 19 : Received: 6 August 2024 / Approved: 6 August 2024 / Online: 7 August 2024 (03:03:04 CEST)
Version 20 : Received: 27 August 2024 / Approved: 27 August 2024 / Online: 29 August 2024 (09:53:51 CEST)
How to cite: Christian, J. Bell's Theorem Begs the Question. Preprints 2023, 2023010023. https://doi.org/10.20944/preprints202301.0023.v20 Christian, J. Bell's Theorem Begs the Question. Preprints 2023, 2023010023. https://doi.org/10.20944/preprints202301.0023.v20
Abstract
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von~Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s.
Keywords
Bell’s theorem; local realism; Bell-CHSH inequalities; quantum correlations; Bell-test experimentsexperiments
Subject
Physical Sciences, Quantum Science and Technology
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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