Superluminal motions (and microwave propagation) in Special Relativity: Solution of the causal paradoxes

Abstract

Some recent experiments, performed at Berkeley, Cologne, Florence and Vienna led to the claim that something seems to travel with a speed larger than the speed c of light in vacuum. Various other experimental results seem to point in the same direction: For instance, localized wavelet-type solutions of Maxwell equations have been found, both theoretically and experimentally, that travel with Superluminal speed. Even muonic and electronic neutrinos --it has been proposed-- might be "tachyons", since their square mass appears to be negative; not to mention the apparent Superluminal expansions observed in the core of quasars and, recently, in the so-called galactic microquasars. In the first part of this paper we verify, on the basis of the numerical solution of Maxwell equations, that waves propagating down a microwave guide can travel with Superluminal group velocity, just confirming some of the previously mentioned experimental results. Then, we have to face the question of Superluminal motions within the theory of Special Relativity. It is not widely recognized that all such theoretical and experimental results do not place relativistic causality in jeopardy. For instance, it is possible (at least in microphysics) to solve also the known causal paradoxes, devised for "faster than light" motion. Here we show, in detail and rigorously, how to solve the oldest causal paradox, originally proposed by Tolman, which is the kernel of many further tachyon paradoxes. The key to the solution is a careful application of tachyon mechanics, as it unambiguously follows from Special Relativity. [Subj-classes: Classical Physics, Special Relativity, Optics, General Physics, Microwaves, Evanescent Waves, Tunnelling Photons]