Derivation of the Lorentz–Dirac Equation

Two problems are woven together in this debate: one is the question of whether there should be radiation from uniformly accelerating charges in flat spacetime with no gravitational effects (not even non-tidal ones) and the other is the question of whether there should be radiation from charges that are stationary relative to coordinates in curved spacetimes (or even flat spacetimes in which we consider that there is an SHGF to be treated by general relativity) in which the metric is static. The first question spawns others, as we have seen. The aim of this section is to consider one of these in more detail, viz., if uniformly accelerating charges in flat spacetime (without gravitational effects) do radiate, how is it that the radiation reaction derived from energy–momentum conservation turns out to be zero?

One is inclined to look at the derivation of the Lorentz-Dirac equation, because the radiation reaction terms turn up there.We begin with Parrott’s derivation in [13] and compare it with Dirac’s original 1938 derivation in [14].