  The stabilized Poincare-Heisenberg algebra (SPHA) is the Lie algebra of
quantum relativistic kinematics generated by fifteen generators. It is obtained
from imposing stability conditions after attempting to combine the Lie algebras
of quantum mechanics and relativity which by themselves are stable, however not
when combined. In this paper we show how the sixteen dimensional Clifford
algebra CL(1,3) can be used to generate the SPHA. The Clifford algebra path to
the SPHA avoids the traditional stability considerations, relying instead on
the fact that CL(1,3) is a semi-simple algebra and therefore stable. It is
therefore conceptually easier and more straightforward to work with a Clifford
algebra. The Clifford algebra path suggests the next evolutionary step toward a
theory of physics at the interface of GR and QM might be to depart from working
in space-time and instead to work in space-time-momentum.
