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A Rotational Analogy

If we compare the LORENTZ TRANSFORMATIONS with the GALILEAN TRANSFORMATIONS, several striking qualitative features are apparent: the first is the multiplicative factor  $\gamma$  which describes both TIME DILATION and LORENTZ 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.