Classical theory of radiating electrons

TLDR

The Lorentz model treats the electron as a charged sphere whose mass derives from its electromagnetic field, accurately describing motion and radiation only when fields vary slowly and accelerations are modest, but it fails beyond this domain because no natural mechanism can bind the charge, and the hypothesis that all mass is electromagnetic is contradicted by the neutron and positron theories. The discovery of the neutron and the positron theory, which involve negative mass values, demonstrate that not all mass is electromagnetic, contradicting the Lorentz model’s assumption that all mass must be positive.

Abstract

The Lorentz model of the electron as a small sphere charged with electricity, possessing mass on account of the energy of the electric field around it, has proved very valuable in accounting for the motion and radiation of electrons in a certain domain of problems, in which the electromagnetic field does not vary too rapidly and the accelerations of the electrons are not too great. Beyond this domain it will not go unless supplemented by further assumptions about the forces that hold the charge on an electron together. No natural way of introducing such further assumptions has been discovered, and it seems that the Lorentz model has reached the limit of its usefulness and must be abandoned before we can make further progress. One of the most attractive ideas in the Lorentz model of the electron, the idea that all mass is of electromagnetic; origin, appears at the present time to be wrong, for two separate reasons. First, the discovery of the neutron has provided us with a form of mass which it is very hard to believe could be of electromagnetic nature. Secondly, we have the theory of the positron— a theory in agreement with experiment so far as is known—in which positive and negative values for the mass of an electron play symmetrical roles. This cannot be fitted in with the electromagnetic idea of mass, which insists on all mass being positive, even in abstract theory.