A novel quantum-mechanical interpretation of the Dirac equation

TL;DR

This paper offers a new quantum-mechanical interpretation of the Dirac equation, viewing electrons and positrons as different topological states of a single particle, supported by general relativity structures, and explores implications for atomic spectra.

Contribution

It introduces a topological spin-based interpretation of the Dirac equation, unifying electrons and positrons as states of one particle, and formulates a related bi-particle Dirac equation.

Findings

Electron and positron are topological states of a single particle.

Spectral analysis links the magnetic moment to the ring structure.

Zero-G Kerr-Newman model aligns with the electron's anomalous magnetic moment.

Abstract

A novel interpretation is given of Dirac's "wave equation for the relativistic electron" as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different "topological spin" states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such bi-particle structures in general relativity, in particular the ring singularity present in any spacelike section of the maximal analytically extended, topologically non-trivial, electromagnetic Kerr-Newman spacetime in the zero-gravity limit (here, "zero-gravity" means the limit $G\to 0$, where $G$ is Newton's constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac's wave equation seems to be capable of describing both the electron and the positron in "external" fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two - as it should if it were a two-particle equation! A Dirac equation is formulated for a ring-like bi-particle which interacts with a static point charges located elsewhere in the topologically non-trivial physical space associated with the moving ring bi-particle, the motion being governed by a de-Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity Hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-$G$ Kerr-Newman magnetic moment be identified with the so-called "anomalous magnetic moment of the physical electron," not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron's Compton wave length.