  A satisfactory theory of quantum gravity will very likely require
modification of our classical perception of space-time, perhaps by giving it a
'foamy' structure at scales of order the Planck length. This is expected to
modify the propagation of photons and other relativistic particles such as
neutrinos, such that they will experience a non-trivial refractive index even
in vacuo. The implied spontaneous violation of Lorentz invariance may also
result in alterations of kinematical thresholds for key astrophysical processes
involving high energy cosmic radiation. We discuss experimental probes of these
possible manifestations of the fundamental quantum nature of space-time using
observations of distant astrophysical sources such as gamma-ray bursts and
active galactic nuclei.
