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International Journal of Apllied Mathematics

THE PHYSICAL MOTION OF INTRINSIC SPIN AND THE EXPERIMENTAL IMPLICATION

Gregory L. Light

Published Aug 24, 2017• 1 citation
Publisher

Abstract

We propose a revised Stern-Gerlach experiment of setting up two perpendicular magnetic fields B(1) and B(2); we predict that half of the electrons will be observed to align with B(1) and the other half, B(2), so that any electron, left (right) -handed, has four spin states, up (down), left (right), down (up), and right (left), in a 720 • -cycle, altering the basis for quantum computing.

DOI
10.12732/ijam.v30i4.3

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The Stern–Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. However, that theory is based on mathematical errors in the way it (mis)treats spinors and group theory. We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry. Contrary to what Pauli has been reading into the Stern–Gerlach experiment, the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured. Surprisingly, this leads to only two energy states, which should be qualified as precession-up and precession-down rather than spin-up and spin-down. Indeed, despite the presence of the many different possible angles θ between the spin axis s and the magnetic field B, the fermions can only have two possible energies m0c2±μB. The values ±μB thus do not correspond to the continuum of values −μ·B Einstein and Ehrenfest had conjectured. The energy term V=−μ·B is a macroscopic quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies ±μB, and as such not valid for individual fermions. The two fermion states with energy ±μB are not potential-energy states. We also explain the mathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clear and understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle.
It is well known that electron spin is quantized, and is measured to be either spin up or spin down in a magnetic field, as was first demonstrated in the classic Stern-Gerlach experiment almost 100 years ago. However, it is also believed that a quantum spin may be indeterminate until it is measured, being in a quantum superposition of the two quantum states. On the contrary, I propose (based on a locally realistic spin-quantized picture of quantum waves) that an electron quantum state is always either spin up or spin down, but is never in a superposition of the two. This concept should be directly testable using a two-stage Stern-Gerlach experiment, similar to that presented in standard quantum textbooks, but apparently never carried out experimentally. This experiment should be straightforward using modern atomic beam laboratory equipment. If successful, this could lead to a serious review of quantum foundations, as well as a new set of practical applications. In particular, a binary storage or logic element based on quantum spin should continue to work down to the atomic scale. This should enable computer memories with orders of magnitude greater density than those based on conventional magnetic memories. 2
The Stern-Gerlach experiment has played an important role in our understanding of quantum behavior. We propose and analyze a modified version of this experiment where the magnetic field of the detector is in a quantum superposition, which may be experimentally realized using a superconducting flux qubit. We show that if incident spin-1/2 particles couple with the two-state magnetic field, a discrete target distribution results that resembles the distribution in the classical Stern-Gerlach experiment. As an application of the general result, we compute the distribution for a Gaussian waveform of the incident fermion. This analysis allows us to demonstrate theoretically: (1) the quantization of the intrinsic angular momentum of a spin-1/2 particle, and (2) a correlation between EPR pairs leading to nonlocality, without necessarily collapsing the particle’s spin wavefunction.
The nature of electron spin has presented an enigma right from the beginning of quantum mechanics. We suggest that a simple realistic picture of a real coherently rotating vector field can account for both the Schrodinger equation and electron spin in a consistent manner. Such a rotating field carries distributed angular momentum and energy in the same way as a circularly polarized electromagnetic wave. We derive the Schrodinger equation from the relativistic Klein-Gordon Equation, where the complex wave function maps onto a fixed-axis real rotating vector. Such a realistic picture can also explain the Stern-Gerlach experiment which first identified electron spin. Remarkably, the predictions of a two-stage Stern-Gerlach experiment within this realistic picture differ from those of the orthodox quantum superposition approach. This two-stage experiment has not actually been done, and could provide insights into the limits of realistic models. This realistic picture also avoids quantum paradoxes and enables realistic explanations for a variety of quantum phenomena.