A classical approach to the electron g-factor

TL;DR

This paper presents a classical, relativistic model of the electron as a spinning Gaussian body, explaining the g-factor and its slight deviation from 2 without relying solely on quantum mechanics.

Contribution

It introduces a classical relativistic model of the electron that accounts for the g-factor and its small correction, challenging the notion that g=2 is purely quantum.

Findings

The classical model reproduces the standard g-factor value of 2.

The model predicts a corrected g-factor of approximately 2.0021.

Relativistic effects and electromagnetic angular momentum explain the g-factor.

Abstract

According to a prevailing opinion, the electron g-factor ge = 2 is exclusively a quantum feature. Here we demonstrate it could be explained classically only in relativistic terms. The electron is treated as an extended, continuous, but rigid Gaussian body (RGB) spinning at finite angular frequency. In contrast to expectations, the mechanical energy and spin angular momentum of the particle are not diverging but standard values are reproduced. The g-factor value ge = 2 immediately follows from the ratio of non-relativistic and relativistic angular momenta which can be both attributed to a spinning electron of known rest mass. A detailed analysis of the inertia tensor and limit, torque-free precession reveals a multiplication factor of -2 between the external and internal precession angular frequency which might resemble the spin-1/2 appearance of the particle. Furthermore, the theory of Li\'enard and Wiechert is used to derive a static electromagnetic field. A continuous form of Gaussian charge density ensures an absence of infinities in electromagnetic energy and angular momentum. Introducing the associated electromagnetic angular momentum as a small correction to the mechanical spin angular momentum, we obtain a modified g-factor ge* = 2.0021 which is close to the measured value ge = 2.0023.