  Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning
property in Quantum Mechanics and Quantum Computation, respectively, have been
extended to versions of Quantum Mechanics and Quantum Computation which are
re-formulated using scalars in {\it reduced power algebras}, [2-9], instead of
the usual real or complex scalars. Here, the Lorentz coordinate
transformations, fundamental in Special Relativity, are extended to versions of
Special Relativity that are similarly re-formulated in terms of scalars in
reduced power algebras, instead of the usual real or complex scalars. The
interest in such re-formulations of basic theories of Physics are due to a
number of important reasons, [2-11]. Suffice to mention two of them : the
difficult problem of so called "infinities in Physics" falls easily aside due
to the presence of infinitesimal and infinitely large scalars in such reduced
power algebras, and the issue of fundamental constants in physics, like
Planck's $h$, or the velocity of light $c$, comes under a new focus which
offers rather surprising alternatives.

General Physics