F. Rohrlich: The dynamics of a charged sphere and the electron Am J Phys 65 (11) p. 1051 (1997)[permanent dead link]. "The dynamics of point charges is an excellent example of the importance of obeying the validity limits of a physical theory. When these limits are exceeded the predictions of the theory may be incorrect or even patently absurd. In the present case, the classical equations of motion have their validity limits where quantum mechanics becomes important: they can no longer be trusted at distances of the order of (or below) the Compton wavelength…Only when all distances involved are in the classical domain is classical dynamics acceptable for electrons."
