  Many quantum gravity theories imply that the vacuum is filled with virtual
black holes. This paper explores the process in which high energy photons
interact with virtual black holes and decay into gravitons and photons of lower
energy. The effect requires violation (or modification) of Lorentz invariance
and implies that high energy photons cannot propagate over arbitrarily large
distances. For the standard Planck mass and the likely form for the interaction
cross section, this quantum foam limit becomes $\dist < 450$ Mpc $(\egam/10^7
{\rm GeV})^{-5}$. For quantum gravity theories that posit a lower Planck scale,
the interaction rate is larger and the limit is stronger. This paper uses
extant observations of gamma rays from cosmological sources to constrain this
process for varying values of the Planck mass and a range of forms for the
interaction cross sections.
