Propagation Velocity of Electromagnetic Signals

Abstract

The propagation velocity of electromagnetic signals has been a vexing problem for about a century. The often-mentioned group velocity fails on two accounts, one being that it is generally larger than the velocity of light for waves in the atmosphere; the other that its derivation implies a transmission rate of information equal to zero. The reason why this problem has resisted a solution for so long is that Maxwell's equations fail for signals propagating in a lossy medium. The propagation velocity is of interest only in a lossy medium, since its value in a loss-free medium has been known since d'Alembert's solution of the wave equation. For infinite signal-to-noise ratios and ideal receivers, the propagation velocity of signals in media with ohmic losses equals the velocity of light; it decreases with decreasing signal-to-noise ratio and eventually approaches zero.