  In papers on primary state diffusion (Percival 1994, 1995), numerical
estimates suggested that fluctuations in the space-time metric on the scale of
the Planck time (10^-44s) could be detected using atom interferometers. In this
paper we first specify a stochastic metric obtained from fluctuations that
propagate with the velocity of light, and then develop the non-Markovian
quantum state diffusion theory required to estimate the resulting decoherence
effects on a model matter interferometer. Both commuting and non-commuting
fluctuations are considered. The effects of the latter are so large that if
they applied to some real atom interferometry experiments they would have
suppressed the observed interference. The model is too crude to conclude that
such fluctuations do not exist, but it does demonstrate that the small
numerical value of the Planck time does not alone prevent experimental access
to Planck-scale phenomena in the laboratory.
