The Theory of Magnetic Poles

Abstract

If one supposes that a particle with a single magnetic pole can exist and that it interacts with charged particles, the laws of quantum mechanics lead to the requirement that the electric charges shall be quantized---all charges must be integral multiples of a unit charge $e$ connected with the pole strength $g$ by the formula $eg=\frac{1}{2}\ensuremath{\hbar}c$. Since electric charges are known to be quantized and no reason for this has yet been proposed apart from the existence of magnetic poles, we have here a reason for taking magnetic poles seriously. The fact that they have not yet been observed may be ascribed to the large value of the quantum of pole.In 1931 I gave a primitive theory which described the motion of a pole in the field of a charged particle whose motion is given, or the motion of a charged particle in the field of a pole whose motion is given. The present paper sets up a general theory of charged particles and poles in interaction through the medium of the electromagnetic field. The idea which makes this generalization possible consists in supposing each pole to be at the end of an observable string, which is the line along which the electromagnetic potentials are singular, and introducing dynamical coordinates and momenta to describe the motion of the strings. The whole theory then comes out by the application of standard methods. There are unsolved difficulties, concerned with the interaction of a point charge or a point pole with the field it produces itself, such as occur in all dynamical theories of fields and particles in interaction.