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Nonbirefringent modified-Maxwell theory, coupled to standard Dirac particles, involves nine dimensionless parameters, which can be bounded by the inferred absence of vacuum Cherenkov radiation for ultrahigh-energy cosmic rays (UHECRs). With selected UHECR events, two-sided bounds on the eight nonisotropic parameters are obtained at the 10^-18 level, together with an improved one-sided bound on the single isotropic parameter at the 10^-19 level.
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Klinkhamer et al. (2008) studied this question.
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