Non-Local EPR Correlations using Quaternion Spin

Bryan Sanctuary

doi:10.20944/preprints202301.0570.v6

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preprints.org > physical sciences > quantum science and technology > doi: 10.20944/preprints202301.0570.v6

Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed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)
Version 8 : Received: 12 July 2024 / Approved: 15 July 2024 / Online: 17 July 2024 (04:27:06 CEST)

A peer-reviewed article of this Preprint also exists.

Sanctuary, B. EPR Correlations Using Quaternion Spin. Quantum Reports 2024, 6, 409–425, doi:10.3390/quantum6030026. Sanctuary, B. EPR Correlations Using Quaternion Spin. Quantum Reports 2024, 6, 409–425, doi:10.3390/quantum6030026.

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 as an attribute which is anti-symmetric and generates the helicity. This spin has structure formed from two orthogonal magnetic moments of spin $1/2$ each. These couple in free flight to form a spin 1, a boson. Upon encountering a filter, the spin 1 decouples into its two independent spins axes of $\frac{1}{2}$, with one aligning with the filter and the other randomizing. The process of decoupling from a free-flight boson to a measured fermion 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 3, more than from an entangled state which is $2\sqrt{2}$. Coherence can only be formulated by the existence of a bivector which gives a spin the same geometric structure as a photon. The only variable in this work is the angle that orients a spin on the Bloch sphere, first identified in the 1920's. The new features introduced here result from changing the spin symmetry from SU(2) to the quaternion group, $Q_8$. This introduces a bivector into the Dirac equation giving 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 (1)

Comment 1

Received: 18 October 2023
Commenter: Bryan Sanctuary
Commenter's Conflict of Interests: Author

Comment: Improved presentation and claity.
Corrected errors in the section Determining the Correlation
Improved the description of the CHSH correlation

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