  The quantum fluctuations of the geodesic deviation equation in a flat
background spacetime are discussed. We calculate the resulting mean squared
fluctuations in the relative velocity and separation of test particles. The
effect of these quantum fluctuations of the spacetime geometry is given in
terms of the Riemann tensor correlation function. Three different sources of
the Riemann tensor fluctuations are considered: a thermal bath of gravitons,
gravitons in a squeezed state, and the graviton vacuum state.
