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Present and future ultra-high-energy-cosmic-ray facilities (e.g., the PierreAuger Observatory with South and North components) and TeV-gamma-ray telescopearrays (e.g., HESS or VERITAS and CTA) have the potential to set stringentindirect bounds on the nine Lorentz-violating parameters of nonbirefringentmodified Maxwell theory minimally coupled to standard Dirac theory.Theoretically, the most interesting case is isotropic Lorentz violation, whichis described by a single parameter [taken to vanish for the standardLorentz-invariant theory]. It appears possible to obtain in the future an upper(lower) indirect bound on this single isotropic Lorentz-violating parameter atthe +10^{-21} (-10^{-17}) level. Comparison is made with existing and futuredirect bounds from laboratory experiments. The possible physics implications ofupper bounds at the 10^{-21} level are discussed.

Future limits on isotropic Lorentz violation in the photon sector from UHECRs and TeV gamma rays