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Non-Local EPR Correlations using Quaternion Spin

B. C. Sanctuary

Published Apr 11, 2023• 0 citations
Publisher

Abstract

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 ½, 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, Q8, 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. March 28, 2023

DOI
10.21203/rs.3.rs-2795917/v1

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The two dimensional spin and its resonance fringe

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Violation of Bell's Inequalities gives experimental evidence for the existence of a spin 1/2 which has two simultaneous axes of spin quantization rather than one. These couple to form a resonance state, called the spin fringe, and this quantum effect is solely responsible for violation of Bell's Inequalities within this model. The Bell states can be represented by products of these spin states and leads to the intuitive concept that as entangled states decompose they form biparticles that are not entangled. In EPR coincidence experiments filter settings for both the Bell and CHSH forms of Bell's Inequalities are rationalized in terms of the correlation between biparticles.

arXiv:0707.1763•Jul 12, 2007•6 citations
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 ½, 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, Q8, 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. March 28, 2023
A statistical simulation is presented which reproduces the correlation obtained from EPR coincidence experiments without non-local connectivity. Defining spin under the quaternion group reveals hyper-helicity, a hitherto missed attribute of spin. Including this in the treatment, reveals two complementary properties: spin polarization and spin coherence. The former has a CHSH value of 2, and spin coherence has a CHSH = 1 giving CHSH = 3 for an EPR pair. The simulation here gives 2.995. We suggest that Nature has CHSH=3 being considerable more than predicted from quantum mechanics of 222\sqrt{2}22​. There are no Local Hidden Variables. We suggest that quaternion spin is more fundamental than Dirac spin. A computer program which performs the simulation without non-local connectivity is described.
Under the quaternion group, Q8Q_8Q8​, spin helicity emerges as an element of reality, and complementary to spin polarization. Here we show that the correlation in EPR coincidence experiments is conserved upon separation from a singlet, being divided between polarization and coherence. Including helicity accounts for the violation of Bell's Inequalities without non-locality.
We extend our description of the electron’s quaternion spin (Q–spin) as a geometric rotor. This follows from incorporating both the symmetric polarization and the antisymmetric coherence into the theory. Polarization is observed only through the local process we call contextual instantiation. For an EPR pair the observed correlation is reconstructed statistically from the coincidence populations and follows from the scalar invariant of the quaternion rotor, yielding the observed correlation. Numerical simulations reproduce this correlation using only local detector events, and show the same data retain complementary polarization and coherence structure producing a lemniscate rotor portrait. Because spin observables are not jointly definable on a single Kolmogorov probability space, the CHSH quadruple cannot be formed and Bell’s theorem is therefore not applicable. The results provide a unified geometric description of spin, measurement, and Bell correlations, contributing to the foundations of quantum mechanics.
This comment examines the mathematical framework developed by Bryan Sanctuary across a series of papers and preprints (2023–2025) concerning bivector and quaternion representations of spin and claims regarding Bell correlations. We focus on the internal algebraic structure, the treatment of measurement correlations, and the use of linear combinations of projections from a single global bivector. We find that the framework is internally consistent, preserves positivity of expectation values, and produces correlations resembling the quantum correlation −a·b. These correlations are generated using a shared global algebraic object rather than from ±1-valued random variables satisfying the locality and factorization hypotheses of Bell’s non-existence theorem. Consequently, the results are best understood as describing a non-trivial classical geometric framework that lies outside the scope of Bell’s theorem, rather than as a contradiction of it. The analysis is restricted to mathematical and probabilistic considerations, without reference to physical or experimental interpretations.
Violation of Bell's Inequalities gives experimental evidence for the existence of a spin 1/2 which has two simultaneous axes of spin quantization rather than one. These couple to form a resonance state, called the spin fringe, and this quantum effect is solely responsible for violation of Bell's Inequalities within this model. The Bell states can be represented by products of these spin states and leads to the intuitive concept that as entangled states decompose they form biparticles that are not entangled. In EPR coincidence experiments filter settings for both the Bell and CHSH forms of Bell's Inequalities are rationalized in terms of the correlation between biparticles.