  Quantum decoherence can arise due to classical fluctuations in the parameters
which define the dynamics of the system. In this case decoherence, and
complementary noise, is manifest when data from repeated measurement trials are
combined. Recently a number of authors have suggested that fluctuations in the
space-time metric arising from quantum gravity effects would correspond to a
source of intrinsic noise, which would necessarily be accompanied by intrinsic
decoherence. This work extends a previous heuristic modification of
Schr\"{o}dinger dynamics based on discrete time intervals with an intrinsic
uncertainty. The extension uses unital semigroup representations of space and
time translations rather than the more usual unitary representation, and does
the least violence to physically important invariance principles. Physical
consequences include a modification of the uncertainty principle and a
modification of field dispersion relations, in a way consistent with other
modifications suggested by quantum gravity and string theory .
