(ABRIDGED) The Gamma-ray Large Area Space Telescope (GLAST) will measure the
spectra of distant extragalactic sources of high energy gamma-rays. GLAST can
look for energy dependent propagation effects from such sources as a signal of
Lorentz invariance violation (LIV). Such sources should also exhibit high
energy spectral cutoffs from pair production interactions with low energy
photons. The properties of such cutoffs can also be used to test LIV. Detectors
to measure gamma-ray polarization can look for the depolarizing effect of
space-time birefingence predicted by loop quantum gravity. A spaceborne
detector array looking down on Earth to study extensive air showers produced by
ultrahigh energy cosmic rays can study their spectral properties and look for a
possible deviation from the predicted GZK effect as another signal of LIV.Comment: 14 pages, Text of invitated talk presented at the "From Quantum to
Cosmos: Fundamental Physics Studies from Space" meeting. More references
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