  Multi-TeV spectra of Mkn 501 and other BL Lac objects exhibit the high energy
cutoffs predicted to be the result of intergalactic annihilation interactions,
primarily with IR photons having the flux level determined by various
astrophysical observations. After correcting for such intergalactic absorption,
these spectra can be explained within the framework of synchrotron self-Compton
emission models. Stecker and Glashow have shown that the existence of this
annihilation via electron-positron pair production puts strong constriants on
Lorentz invariance violation. Such constriants have important implications for
some quantum gravity and large extra dimension models. A much smaller amount of
Lorentz invariance violation has potential implications for understanding the
spectra of ultrahigh energy cosmic rays.
