The Self-Oscillations of a Charged Particle

It is found that certain rigid charge distributions can oscillate without radiation even when no forces are present, other than their own retarded fields. The periods are of the order of the time required for light to cross the particle. The energy of these oscillations is always positive, and there are therefore no exponentially increasing unstable motions of the type possessed by the Dirac classical electron.

The frequencies of these oscillations are such, that when quantized, the energy of the first excited state is of the order of the meson self-energy. Hence, it is suggested that some kinds of mesons may be electrons in such an excited state of self-oscillation.

It is indicated that the principle of causality may have to be reformulated in terms of causal connections over finite intervals of time if one wishes to regard the electron plus its associated electromagnetic field as a single system.