Physical meaning of electromagnetic mass and 4/3-problem

TL;DR

This paper clarifies the physical interpretation of electromagnetic mass and the 4/3-problem in classical electron models, emphasizing the distinction between different definitions of electromagnetic mass and their physical meanings.

Contribution

It demonstrates that the two common definitions of electromagnetic mass have different physical meanings, resolving ambiguities in the 4/3-problem.

Findings

The relativistic EM mass is the ratio of field energy to c^2.

The Thomson EM mass is related to the electron's self-inductance.

The two definitions of EM mass are physically distinct and cannot be equated.

Abstract

In this article one aspect of the so-called '4/3-problem' is analyzed, namely definitions of the electromagnetic mass of the classical electron. It is shown that if the special relativity definition of the electromagnetic (EM) mass as the ratio of the electromagnetic field energy to the square of the speed of light is correctly treated by the scientists who considered this probem, the second definition, which originated with Thomson, i.e. a coefficient of proportionality of the EM momentum of the particle and its velocity has another physical meaning. This meaning was explained by Frenkel in his textbook on clssical electrodynamics. According to this scientist, the second EM mass is actualy a self-inductance of the classical electron or the reaction of its magnetic field to a change in the velocity of this particle. Consequently, these two physical quantities have different meanings, and attempts to reduce the expression for one mass to an expression for the second mass have always been unsuccessful.