If we compare the Lorentz transformations with the
Galilean transformations, several striking qualitative features
are apparent: the first is the multiplicative factor
which
describes both time dilationLorentz contraction;
the second is the fact that time and space
get mixed together by the Lorentz transformation --
a blasphemy in the paradigm of classical Physics.
The latter weirdness is going to be confusing no matter what we do; is there any way to at least make it look familiar? What we need is an analogy with something that does ``make sense'' and is still intact. Fortunately there is a precedent for a transformation that mixes coordinates, namely the rotation. Unfortunately, the analogy has severe limitations, as we shall see; but even its breakdown is instructive, so I will lead you a little way down a path that will ultimately turn out to be a dead end....