  The quantum lightcone fluctuations in flat spacetimes with compactified
spatial dimensions or with boundaries are examined. The discussion is based
upon a model in which the source of the underlying metric fluctuations is taken
to be quantized linear perturbations of the gravitational field. General
expressions are derived, in the transverse trace-free gauge, for the summation
of graviton polarization tensors, and for vacuum graviton two-point functions.
Because of the fluctuating light cone, the flight time of photons between a
source and a detector may be either longer or shorter than the light
propagation time in the background classical spacetime. We calculate the mean
deviations from the classical propagation time of photons due to the changes in
the topology of the flat spacetime. These deviations are in general larger in
the directions in which topology changes occur and are typically of the order
of the Planck time, but they can get larger as the travel distance increases.
