Electron Spin or "Classically Non-Describable Two-Valuedness"

TL;DR

This paper investigates whether classical models of the electron can reproduce its quantum properties without conflicting with Special Relativity, emphasizing the importance of surface stresses and the need for exact solutions.

Contribution

It provides a detailed analysis of classical electron models within Special Relativity, highlighting the role of surface stresses and presenting the necessity of exact solutions.

Findings

Surface stresses are crucial in classical electron models.

Exact solutions are necessary to assess compatibility with Special Relativity.

Classical models face significant challenges in replicating quantum electron properties.

Abstract

In December 1924 Wolfgang Pauli proposed the idea of an inner degree of freedom of the electron, which he insisted should be thought of as genuinely quantum mechanical in nature. Shortly thereafter Ralph Kronig and, independently, Samuel Goudsmit and George Uhlenbeck took up a less radical stance by suggesting that this degree of freedom somehow corresponded to an inner rotational motion, though it was unclear from the very beginning how literal one was actually supposed to take this picture, since it was immediately recognised (already by Goudsmit and Uhlenbeck) that it would very likely lead to serious problems with Special Relativity if the model were to reproduce the electron's values for mass, charge, angular momentum, and magnetic moment. However, probably due to the then overwhelming impression that classical concepts were generally insufficient for the proper description of microscopic phenomena, a more detailed reasoning was never given. In this contribution I shall investigate in some detail what the restrictions on the physical quantities just mentioned are, if they are to be reproduced by rather simple classical models of the electron within the framework of Special Relativity. It turns out that surface stresses play a decisive role and that the question of whether a classical model for the electron does indeed contradict Special Relativity can only be answered on the basis of an \emph{exact} solution, which has hitherto not been given.