  Observations of the multi-TeV spectra of the nearby BL Lac objects Mkn 421
and Mkn 501 exhibit the high energy cutoffs predicted to be the result of
intergalactic annihilation interactions, primarily with IR photons having a
flux level as determined by various astronomical observations. After correcting
for such intergalactic absorption, these spectra can be explained within the
framework of synchrotron self-Compton emission models. Stecker & Glashow have
shown that the existence of this annihilation via electron-positron pair
production puts strong constraints on Lorentz violation. Such constraints have
important implications for quantum gravity models and large extra dimension
models. We also discuss the implications of observations of high energy
gamma-rays from the Crab Nebula on constraining quantum gravity models.
