  It is demonstrated that any two reference frames (RFs), which are uniformly
and rectilinearly moving relative to each other, can be adjusted via (possibly
anisotropic) rescaling and re-synchronization so that the resulting pair of RFs
is Lorentzian; this statement remains true if the word "Lorentzian" is replaced
by "Galilean" or "Riemannian", i.e., if a finite positive value of $c^2$ is
replaced by $\infty$ or by a negative real number. In this particular sense,
the Lorentzian, as well as Galilean or Riemannian, phenomenon turns out to be
merely a matter of an arbitrary choice of appropriate rescaling and
re-synchronization of any given pair of RFs. Generalizations and refinements of
this result are obtained, including universal generalized Lorentzian adjustment
via rescaling and re-synchronization of arbitrarily large families of RFs.
Alternatively, the generalized Lorentzian property of a pair of RFs is shown to
be a consequence of reciprocity and isotropy, with no adjustment needed in this
case. The universality of light and of the corresponding Lorentzian property of
the spacetime is questioned. Waves of transformation of spacetime are
introduced, which have in a certain sense a more universal character than
electromagnetic or gravitational waves.
