  Galilean Relativity and Einstein's Special and General Relativity showed that
the Laws of Physics go deeper than their representations in any given reference
frame. Thus covariance, or independence of Laws of Physics with respect to
changes of reference frames became a fundamental principle. So far, all of that
has only been expressed within one single mathematical model, namely, the
traditional one built upon the usual continuum of the field $\mathbb{R}$ of
real numbers, since complex numbers, finite dimensional Euclidean spaces, or
infinite dimensional Hilbert spaces, etc., are built upon the real numbers.
Here, following [55], we give one example of how one can go beyond that
situation and study what stays the same and what changes in the Laws of
Physics, when one models them within an infinitely large variety of algebras of
scalars constructed rather naturally. Specifically, it is shown that the
Special Relativistic addition of velocities can naturally be considered in any
of infinitely many reduced power algebras, each of them containing the usual
field of real numbers and which, unlike the latter, are non-Archimedean. The
nonstandard reals are but one case of such reduced power algebras, and are as
well non-Archimedean. Two surprising and strange effects of such a study of the
Special Relativistic addition of velocities are that one can easily go beyond
the velocity of light, and rather dually, one can as easily end up frozen in
immobility, with zero velocity. Both of these situations, together with many
other ones, are as naturally available, as the usual one within real numbers.
