Non-Local EPR Correlations using Quaternion Spin

Bryan Sanctuary

doi:10.20944/preprints202301.0570.v4

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preprints.org > physical sciences > quantum science and technology > doi: 10.20944/preprints202301.0570.v4

Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

Non-Local EPR Correlations using Quaternion Spin

Bryan Sanctuary

Version 1 : Received: 16 January 2023 / Approved: 31 January 2023 / Online: 31 January 2023 (04:19:48 CET)
Version 2 : Received: 3 February 2023 / Approved: 6 February 2023 / Online: 6 February 2023 (02:04:35 CET)
Version 3 : Received: 31 March 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (04:12:41 CEST)
Version 4 : Received: 3 April 2023 / Approved: 4 April 2023 / Online: 4 April 2023 (03:54:28 CEST)
Version 5 : Received: 29 July 2023 / Approved: 31 July 2023 / Online: 1 August 2023 (10:03:11 CEST)
Version 6 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 18 October 2023 (10:08:48 CEST)
Version 7 : Received: 26 January 2024 / Approved: 28 January 2024 / Online: 29 January 2024 (04:18:41 CET)

How to cite: Sanctuary, B. Non-Local EPR Correlations using Quaternion Spin. Preprints 2023, 2023010570. https://doi.org/10.20944/preprints202301.0570.v4 Sanctuary, B. Non-Local EPR Correlations using Quaternion Spin. Preprints 2023, 2023010570. https://doi.org/10.20944/preprints202301.0570.v4

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MDPI and ACS Style

Sanctuary, B. Non-Local EPR Correlations using Quaternion Spin. Preprints 2023, 2023010570. https://doi.org/10.20944/preprints202301.0570.v4

APA Style

Sanctuary, B. (2023). Non-Local EPR Correlations using Quaternion Spin. Preprints. https://doi.org/10.20944/preprints202301.0570.v4

Chicago/Turabian Style

Sanctuary, B. 2023 "Non-Local EPR Correlations using Quaternion Spin" Preprints. https://doi.org/10.20944/preprints202301.0570.v4

Abstract

A statistical simulation is presented which reproduces the correlation obtained from EPR coincidence experiments without non-local connectivity. We suggest that spin carries two complementary properties. In addition to the spin polarization, we identify spin coherence. This spin attribute is anti-symmetric and generates the helicity. In addition this spin has structure formed from two orthogonal magnetic moments. From these, a resonance spin results from their coupling in free flight. Upon encountering a filter, the resonance spin 1 decouples back into two independent spins of $\frac{1}{2}$, with one aligning with the filter and the other randomizing. The process of decoupling the resonance spin is responsible for the quantum correlation which results in the observe violation of Bell's Inequalities. The polarized states give a CHSH value of 2 while the resonance spin give a CHSH value of 1. Coherence can only be formulated by the existence of a bivector which gives a spin the same geometric structure as a photon. Although this work is not about Bell's theorem, we note that there are no hidden variables (HV). The only local variable is the angle that orients a spin on the Bloch sphere, first identified in the 1920's. The new features introduced are changing the spin symmetry from SU(2) to the quaternion group, $Q_8$, and the introduction of a bivector into spin which leads to an element of reality which is anti-Hermitian. The calculations use standard spin algebra, and properties of quaternions.

Keywords

Foundations of physics; Dirac equation; Spin; Quantum Theory; non-locality; helicity

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 (2)

Comment 1

Received: 4 April 2023
Commenter: Bryan Sanctuary
Commenter's Conflict of Interests: Author

Comment: I had the references to PrePrints with the volume number which took readers to the earlier versions. I have changed that only

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Comment 2

Received: 7 April 2023
Commenter: Richard David Gill
The commenter has declared there is no conflict of interests.

Comment: According to formula (32) and some other remarks in the paper, the correlation which is predicted by this model is actually a 75:25 mixture of the famous saw-tooth or triangular wave, and the "French mustache" curve, which the author associates with polarization and coherence respectively. Neither curve violates Bell-CHSH inequalities so their mixture does not either, and hence cannot be anywhere near the negative cosine predicted by the conventional QM EPR-B model. The author writes that his work has nothing to do with Bell's theorem but actually it has everything to do with that theorem, since his two "submodels" (polarization, coherence) are local hidden variable models in Bell's mathematical sense of that phrase. NB. "hidden" means, hidden with respect to conventional QM; "local" means that the measurement functions only depend on the local setting.

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