  The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg)
is unstable. Stabilization by deformation leads to a new deformation parameter
$\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The
implications of the deformed algebras for the uncertainty principle and the
density of states are worked out and compared with the results of past analysis
following from gravity and string theory.
