MICHEL JANSSEN AND MATTHEW MECKLENBURG FROM CLASSICAL TO RELATIVISTIC MECHANICS: ELECTROMAGNETIC MODELS OF THE ELECTRON 1. INTRODUCTION “Special relativity killed the classical dream of using the energy-momentum- velocity relations as a means of probing

“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. There were actually two such dreams in the years surrounding the advent of special relativity. Like Einstein’s theory, both dreams originated in the electrodynamics of moving bodies developed in the 1890s by the Dutch physicist Hendrik Antoon Lorentz. Both took the form of concrete models of the electron. Even these models were similar. Yet they were part of fundamentally different programs competing with one another in the years around 1905. One model, due to the German theoretician Max Abraham (1902a), was part of a revolutionary effort to substitute the laws of electrodynamics for those of Newtonian mechanics as the fundamental laws of physics. The other model, adapted from Abraham’s by Lorentz (1904b) and fixed up by the French mathematician Henri Poincaré (1906), was part of the attempt to provide a general explanation for the absence of any sign of the earth’s motion through the ether, the elusive 19th-century medium thought to carry light waves and electromagnetic fields. A choice had to be made between the objectives of Lorentz and Abraham. One could not eliminate all signs of ether drift and reduce all physics to electrodynamics at the same time. Special relativity was initially conflated with Lorentz’s theory because it too seemed to focus on the undetectability of motion at the expense of electromagnetic purity. The theories of Lorentz and Einstein agreed in all their empirical predictions, including those for the velocity-dependence of electron mass, even though special relativity was not wedded to any particular model of the electron. For a while there was a third electron model, a variant on Lorentz’s proposed independently by Alfred Bucherer (1904, 57–60; 1905) and Paul Langevin (1905). At the time, the acknowledged arbiter between these models and the broader theories (perceived to be) attached to them was a series of experiments by Walter Kaufmann and others on the deflection of high-speed