Time symmetric electrodynamics, electric charge conservation, and the Lorenz gauge

Abstract

We reveal a new way in which the Lorenz gauge condition is related to the electric charge conservation, in a universe where electrically charged point particles are created and annihilated. We derive our results using time symmetric electrodynamics, relying on observations made by Jacov Frenkel (in 1925) and John Archibald Wheeler (in 1940). Both the Lorenz gauge condition and the electric charge conservation are expressed as closed path integrals in Minkowski space. The integration path is the same, it is the sum of all "Wheeler electrons".