On magnetic monopoles, the anomalous g-factor of the electron and the spin-orbit coupling in the Dirac theory

TL;DR

This paper critically examines the Dirac theory's explanations for magnetic phenomena, revealing errors in traditional interpretations of spin-orbit coupling and magnetic monopoles, and proposes symmetry-respecting alternatives and deeper insights.

Contribution

It provides an alternative, symmetry-respecting interpretation of the anomalous Zeeman effect, clarifies the distinction between magnetic monopoles and charge quantization, and corrects errors in the traditional understanding of spin-orbit coupling.

Findings

The algebra for the anomalous Zeeman effect aligns with experiments.

Traditional spin-orbit coupling theory is flawed and cannot account for Thomas precession.

Thomas precession is better understood via Berry phase in velocity space.

Abstract

We discuss the algebra and the interpretation of the anomalous Zeeman effect and the spin-orbit coupling within the Dirac theory. Whereas the algebra for the anomalous Zeeman effect is impeccable and therefore in excellent agreement with experiment, the physical interpretation of that algebra uses images that are based on macroscopic intuition but do not correspond to the meaning of this algebra. The interpretation violates the Lorentz symmetry. We give an alternative intuitive description of the meaning of this effect, which respects the symmetry and is exact. It can be summarized by stating that a magnetic field makes any charged particle spin. We show also that the traditional discussion about magnetic monopoles confuses two issues, viz. the symmetry of the Maxwell equations and the quantization of charge. These two issues define each a different concept of magnetic monopole. They cannot be merged together into a unique all-encompassing issue. We also generalize the minimal substitution for a charged particle, and provide some intuition for the magnetic vector potential. We finally explore the algebra of the spin-orbit coupling, which turns out to be badly wrong. The traditional theory that is claimed to reproduce the Thomas half is based on a number of errors. An error-free application of the Dirac theory cannot account for the Thomas precession, because it only accounts for the instantaneous local boosts, not for the rotational component of the Lorentz transformation. This runs contrary to established beliefs, but Thomas precession can be understood in terms of the Berry phase on a path through the velocity space of the Lorentz group manifold. These results clearly reveal the limitations of the prevailing working philosophy to "shut up and calculate".