A Non-radiating Motion of a Spinning Electron

Abstract

MATHISSON¹ recently deduced the equations of motion of a spinning electron from the General Theory of Relativity. According to those equations such a particle, when free, instead of following a geodesic, performs some sort of screw motion around it. In the special case when the 'gravitational background' is the space time of the Special Theory of Relativity and the velocity is small compared to the velocity of light, this movement con sists of a uniform translation in any direction and a uniform circular motion in a plane perpendicular to the angular momentum J of the particle, the frequency v being proportional to J. The radius remains indeterminate. Assuming J = h/4π we get v = 2m₀c²/h. If this particle had the mass m⁰ and the charge —e of an electron, the radiation damping of its circular motion would be so great as to stop it almost immediately. Mathisson's attempts to establish a connexion between the Theory of Relativity and quantum mechanics would then obviously encounter unsur-mountable difficulties. In the course of a private discussion, Dr. Mathisson expressed, therefore, the view that not only the mass, charge and spin of the particle but also its magnetic moment should be taken into account. It is to be expected, then, that the electronic constants might be chosen in such a way that a free electron would not emit any radiation when moving in the above-mentioned manner. Mathisson is now completing his theory on these lines.