Bell's Theorem Begs the Question

Joy Christian

doi:10.20944/preprints202301.0023.v3

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preprints.org > physical sciences > quantum science and technology > doi: 10.20944/preprints202301.0023.v3

Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

Bell's Theorem Begs the Question

Joy Christian

Version 1 : 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)
Version 3 : Received: 5 January 2023 / Approved: 6 January 2023 / Online: 6 January 2023 (02:16:05 CET)
Version 4 : Received: 16 January 2023 / Approved: 16 January 2023 / Online: 16 January 2023 (07:28:20 CET)
Version 5 : Received: 19 January 2023 / Approved: 20 January 2023 / Online: 20 January 2023 (02:03:44 CET)
Version 6 : Received: 23 January 2023 / Approved: 24 January 2023 / Online: 24 January 2023 (13:15:45 CET)
Version 7 : Received: 1 February 2023 / Approved: 1 February 2023 / Online: 1 February 2023 (07:17:00 CET)
Version 8 : Received: 7 February 2023 / Approved: 8 February 2023 / Online: 8 February 2023 (01:52:13 CET)
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)
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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)

How to cite: Christian, J. Bell's Theorem Begs the Question. Preprints 2023, 2023010023. https://doi.org/10.20944/preprints202301.0023.v3 Christian, J. Bell's Theorem Begs the Question. Preprints 2023, 2023010023. https://doi.org/10.20944/preprints202301.0023.v3

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MDPI and ACS Style

Christian, J. Bell's Theorem Begs the Question. Preprints 2023, 2023010023. https://doi.org/10.20944/preprints202301.0023.v3

APA Style

Christian, J. (2023). Bell's Theorem Begs the Question. Preprints. https://doi.org/10.20944/preprints202301.0023.v3

Chicago/Turabian Style

Christian, J. 2023 "Bell's Theorem Begs the Question" Preprints. https://doi.org/10.20944/preprints202301.0023.v3

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. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

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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Comments (4)

Comment 1

Received: 6 January 2023
Commenter: Joy Christian
Commenter's Conflict of Interests: Author

Comment: I have had to make some minor corrections again.

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Comment 2

Received: 6 January 2023
Commenter:

Thomas Howard Ray

The commenter has declared there is no conflict of interests.

Comment: The circularity of Bell's Theorem results from the mathematical proof method of double negation. I.e., one proves A by proving not-not-A. So while Joy says in the RSOS paper that BT is not a theorem in the mathematical sense, I take issueit is mathematically correct. Double negation is an acceptable mathematical technique.

BT cannot be converted to a physical theorem, however, and in this, Joy Christian is absolutely correct. Karl Popper had an ingenious way of demonstrating the difference between scientific verifiability and falsifiability, by reformulating two yet unproven mathematical conjecturesthe Twin Primes conjecture and Goldbach conjecture. I give an account of this in my 2006 NECSI conference paper "Self Organization in Real and Complex Analysis." Popper details in "Realism and the Aim of Science", Routledge 1983.

In short, no physical theorem can be verified using infinite additivity, as Joy notes correctly. A mathematical proof does not imply physical reality.

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Comment 3

Received: 13 January 2023
Commenter:

Richard Gill

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The commenter has declared there is no conflict of interests.

Comment: The problem raised by this author has been raised many times in the past, and in my opinion answered perfectly adequately many years ago, by Bell himself. See J.S. Bell (1975) "Locality in quantum mechanics: reply to critics", CERN preprint, https://cds.cern.ch/record/980330/files/CM-P00061609.pdf; reprinted as chapter 8 in "Speakable and Unspeakable" https://www.cambridge.org/core/books/abs/speakable-and-unspeakable-in-quantum-mechanics/locality-in-quantum-mechanics-reply-to-critics/9812C555B5317FED53A34CDC4D9EA616. Since then it has been repeatedly recurring and will no doubt remain a minority opinion as long as foundational debates on quantum mechanics continue.

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Comment 4

Received: 14 January 2023
Commenter:

Richard David Gill

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The commenter has declared there is no conflict of interests.

Comment: I think that this paper actually falls into another circularity trap. The author seems to suggest that the hidden variables used in a possible completion of quantum mechanics should actually be modelled as quantum "observables", ie operators on a Hilbert space (or their state should be modelled as a quantum state, ie an operator on a Hilbert space). Bell's aim was to show that there could not exist a *classical* physical explanation for quantum randomness.

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