  The Principle of Relativity has so far been understood as the {\it
covariance} of laws of Physics with respect to a general class of reference
frame transformations. That relativity, however, has only been expressed with
the help of {\it one single} type of mathematical entities, namely, the scalars
given by the usual continuum of the field $\mathbb{R}$ of real numbers, or by
the usual mathematical structures built upon $\mathbb{R}$, such as the scalars
given by the complex numbers $\mathbb{C}$, or the vectors in finite dimensional
Euclidean spaces $\mathbb{R}^n$, infinite dimensional Hilbert spaces, etc.
  This paper argues for {\it progressing deeper and wider} in furthering the
Principle of Relativity, not by mere covariance with respect to reference
frames, but by studying the possible covariance with respect to a {\it large
variety} of algebras of scalars which extend significantly $\mathbb{R}$ or
$\mathbb{C}$, variety of scalars in terms of which various theories of Physics
can equally well be formulated.
  First directions in this regard can be found naturally in the simple
Mathematics of Special Relativity, the Bell Inequalities in Quantum Mechanics,
or in the considerable amount of elementary Mathematics in finite dimensional
vector spaces which occurs in Quantum Computation.
  The large classes of algebras of scalars suggested, which contain
$\mathbb{R}$ and $\mathbb{C}$ as particular cases, have the important feature
of typically {\it no longer} being Archimedean, see Appendix, a feature which
can prove to be valuable when dealing with the so called "infinities" in
Physics.
  The paper has a Comment on the so called "end of time".
