  The Heisenberg uncertainty relation is known to be obtainable by a purely
mathematical argument. Based on that fact, here it is shown that the Heisenberg
uncertainty relation remains valid when Quantum Mechanics is re-formulated
within far wider frameworks of {\it scalars}, namely, within one or the other
of the infinitely many {\it reduced power algebras} which can replace the usual
real numbers $\mathbb{R}$, or complex numbers $\mathbb{C}$. A major advantage
of such a re-formulation is, among others, the disappearance of the well known
and hard to deal with problem of the so called "infinities in Physics". The use
of reduced power algebras also opens up a foundational question about the role,
and in fact, about the very meaning and existence, of fundamental constants in
Physics, such as Planck's constant $h$. A role, meaning, and existence which
may, or on the contrary, may not be so objective as to be independent of the
scalars used, be they the usual real numbers $\mathbb{R}$, complex numbers
$\mathbb{C}$, or scalars given by any of the infinitely many reduced power
algebras, algebras which can so easily be constructed and used.
