Fundamental role of the retarded potential in the electrodynamics of superluminal sources: comment

The commented paper [J. Opt. Soc. Am. A 25, 543 (2008] denies the truth of a standard general formula of electrodynamics [Eq. (6.52) of Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999)]). The motivation for challenging orthodoxy is that the formula directly disproves the repeated claim of the commented authors that electromagnetic radiation, under some circumstances, can have unusually long range. The formula they challenge is for the magnetic field: B=Integral over all space of (mu0/4pi)[Curl j]/Range. Instead they advocate a (correct) formula for the vector potential: A=Integral over all space of (mu0/4pi)[j]/Range. However, as one might suppose, the former equation follows as a purely mathematical consequence of taking the curl of the latter equation. This is straightforward to make rigorous in the particular circumstances in question (confined smooth current density j). Therefore by their own formula, the standard one of electrodynamics is confirmed, and the disproof of their long range claim stands.