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

We show how 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).Comment: 10 pages, 1 figure, more details in the conclusio

The algebraic origin of the Doppler factor in the Lienard-Wiechert potentials

After reviewing the algebraic derivation of the Doppler factor in the Lienard-Wiechert potentials of an electrically charged point particle, we conclude that the Dirac delta function used in electrodynamics must be the one obeying the weak definition, non-zero in an infinitesimal neighborhood, and not the one obeying the strong definition, non-zero in a point. This conclusion emerges from our analysis of a) the derivation of an important Dirac delta function identity, which generates the Doppler factor, b) the linear superposition principle implicitly used by the Green function method, and c) the two equivalent formulations of the Schwarzschild-Tetrode-Fokker action. As a consequence, in full agreement with our previous discussion of the geometrical origin of the Doppler factor, we conclude that the electromagnetic interaction takes place not between points in Minkowski space, but between corresponding infinitesimal segments along the worldlines of the particles.Comment: 15 pages, no figure