Examples of uniformly moving charge distributions that possess conserved electromagnetic stress tensors are exhibited. These constitute stable systems with covariantly characterized electromagnetic mass. This note, on a topic to which Paul Dirac made a significant contribution in 1938, is dedicated to him for his 80th birthday.

“Special relativity killed the classical dream of using the energy-momentumvelocity relations as a means of probing the dynamical origins of [the mass of the electron]. The relations are purely kinematical” (Pais, 1982, 159). This perceptive comment comes from a section on the pre-relativistic notion of electromagnetic mass in ‘Subtle is the Lord . . . ’, Abraham Pais’ highly acclaimed biography of Albert Einstein. ‘Kinematical’ in this context means ‘independent of the details of the dynamics’. In this paper we examine (...) the classical dream referred to by Pais from the vantage point of relativistic continuum mechanics. (shrink)