  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]
