Lightcone fluctuations in flat spacetimes with nontrivial topology

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.