Abstract

A system of nonlinear integro-differential equations is derived for the motion of the classical electron with a rigid and spherically symmetric 3D gaussian distribution of charge. The equations are analyzed for stability around the state of rest and of uniform rectilinear motion with velocity small with respect to the velocity of light. The extremely high-frequency and radiationless micro-oscillations that the electron executes when disturbed from the equilibrium states show the inconsistency of the Abraham-Lorentz equation and of all concepts associated with this equation, like the notion that the electron may have a mass of electromagnetic origin