  It has been proposed that propagation of cosmic rays at extreme-energy may be
sensitive to Lorentz-violating metric fluctuations (``foam''). We investigate
the changes in interaction thresholds for cosmic-rays and gamma-rays
interacting on the CMB and IR backgrounds, for a class of stochastic models of
spacetime foam. The strength of the foam is characterized by the factor
(E/M_P)^a, where ``a'' is a phenomenological suppression parameter. We find
that there exists a critical value of ``a'' (dependent on the particular
reaction), below which the threshold energy can only be lowered, and above
which the threshold energy may be raised, but at most by a factor of two. Thus,
it does not appear possible in this class of models to extend cosmic-ray
spectra significantly beyond their classical absorption energies. However, the
lower thresholds resulting from foam may have signatures in the cosmic-ray
spectrum. We also find that cosmic-ray energies cannot exceed the fundamental
Planck scale, and so set a lower bound of 10^8 TeV on the context of this model
for the scale of gravity. Finally, we comment in the apparent non-conservation
of particle energy-momentum, and speculate on its re-emergence as dark energy
in the foamy vacuum.
