Mass and Spin Renormalization in Lorentz Electrodynamics

Abstract

Lorentz' objection to the Uhlenbeck–Goudsmit proposal of a spin magnetic moment of the electron, namely that the electron's equatorial rotation speed would exceed the speed of light by a factor ≈10, mutated into an objection against Lorentz electrodynamics (LED) itself when the spin magnetic moment became established. However, Lorentz' renormalization calculation, based on the early 20th century's notion of a purely electromagnetic electron, does not qualify as proper from a modern perspective. This paper shows that renormalization treated properly does lead to a mathematically consistent and physically viable LED. A new, relativistically covariant massive LED is presented in which the bare particle has a finite positive bare rest mass and moment of inertia. The particle's electromagnetic self-interaction renormalizes its mass and spin. Most crucially, the renormalized particle is a soliton: after any scattering process its rest mass and spin magnitude are dynamically restored to their pre-scattering values. This guarantees that “an electron remains an electron,” poetically speaking. A renormalization flow study of the limit of vanishing bare rest mass is conducted for this model. This limit yields a purely electromagnetic classical field theory with ultra-violet cutoff at about the electron's Compton wavelength! The renormalized limit model matches the empirical electron data as orderly as one can hope for at the level of Lorentz theory. In particular, no superluminal equatorial speeds occur.