The New Classical Electrodynamics

Abstract

EXCEPT for a gauge-fixing condition, Dirac's recent theory1–3 corresponds to the natural form of Maxwell–Lorentz electrodynamics for very fine-grained streams of charged corpuscles all with the same constant mass μ and charge e; the velocity field in the stream is supposed to be continuous and differentiable. The ratio μ′/e is written k; here μ′ is the measure of μ in energy units: μ′ ≡ μc2. (We call this first special form of the theory the superconductive theory, since its equations will be seen to be entirely equivalent to those of the relativistic form of the Maxwell–London theory when only supercurrents are present. As not all electrodynamics is superconductive, this theory is insufficiently general.) It is evident intuitively that in the uniform stream theory3, where μ and e are everywhere constant, a non-trivial electrostatics is impossible; for example, it is not possible to describe as a static situation a charged dielectric, or any system with a space-charge which appears at rest macroscopically. For this and other reasons, connected with the existence of more than one kind of elementary particle, one is led to generalize the prequantum theory by allowing the mass μ and charge e to be variable in space-time. Such a theory may be called the general stream theory, and will be considered elsewhere. Here we confine ourselves to discussing some characteristic physical consequences of (a) the equations of motion, and (b) the gauge condition of the uniform stream theory. These follow from the assumption of: