  We apply Lie algebra deformation theory to the problem of identifying the
stable form of the quantum relativistic kinematical algebra. As a warm up,
given Galileo's conception of spacetime as input, some modest computer code we
wrote zeroes in on the Poincare-plus-Heisenberg algebra in about a minute.
Further ahead, along the same path, lies a three dimensional deformation space,
with an instability double cone through its origin. We give physical as well as
geometrical arguments supporting our view that moment, rather than position
operators, should enter as generators in the Lie algebra. With this
identification, the deformation parameters give rise to invariant length and
mass scales. Moreover, standard quantum relativistic kinematics of massive,
spinless particles corresponds to non-commuting moment operators, a purely
quantum effect that bears no relation to spacetime non-commutativity, in sharp
contrast to earlier interpretations.
