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Spin Helicity

Bryan Sanctuary

Published Jun 17, 2024• 3 citations
Publisher

Abstract

Under the quaternion group, $Q_8$, 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.

DOI
10.20944/preprints202301.0571.v3

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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 present an analysis of the local singlet state and compare its correlation to that of a separated pair of spins devoid of entanglement. In addition to polarization, we include its hyper-helicity, and this quantum coherence is shown to account for the quantum correlation that leads to the apparent violation of Bell's inequalities. Upon separation, particles conserve linear momentum, angular momentum, helicity and correlation. In order to agree with experimental coincidence data, both polarization and coherence, incompatible elements of reality, must simultaneously exist.
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.
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.
Changing the symmetry of spin from SU(2) to the quaternion group, Q8, introduces Q-spin which has a number of ramifications. We first summarize the properties of Q-spin and then discuss some of those resulting changes. Many are counter to well-established ideas which change our view of the microscopic. Dirac’s matter-antimatter pair is challenged, being replaced by a 2D structured spin. His negative energy issue and the baryon asymmetry problem are resolved; parity is not violated in beta decay, and the existence of neutrinos is questioned. Bell’s theorem is disproven by counter example, restoring Local Realism to Nature. The singlet state is an approximation; teleportation is not feasible, quantum computing must change to remove teleportation and focus on the qubit form of Q-spin which gives deterministic outcomes of ±1. This impinges on the Foundations of Quantum Mechanics, and we discuss the reasons for the failure of Bell’s theorem; the use of Hidden Variables, wave function collapse and explain the violation of Bell’s Inequalities by showing Q-spin is a boson of odd parity in free flight, and a fermion of even parity in a polarizing field. The violation of Bell’s Inequalities is due to an anyon transition between a boson and a fermion, formulating wave-particle duality. These changes are a result of compexifying the Dirac field.