The Classical Charged Photon

Abstract

BONNOR^1,2 has given a solution of Maxwell's equations which can be interpreted as a radiative field caused by a source moving at the speed of light. Because the world-line of the source is therefore a null curve Γ, the current four-vector Jⁱ is everywhere tangent to it. Hence where g_ik is the metric tensor in local coordinates. In Bonnor's solution Lⁱ is always parallel to Jⁱ , that is where Q is a scalar field. It will be shown below that in Minkowski space, for a null (or radiative) solution of Maxwell's equations satisfying equations (1) and (2) only, the radiation is propagated along a family of null straight lines which is, in general, shear-free, expanding and twisting. Further, in the absence of twisting, Q in these solutions vanished at every point of Γ. Bonnor's rather strange solution arises as the singular solution of equation (10) below, which gives zero expansion and twist.