  Lorentz symmetry breaking at very high energies may lead to photon dispersion
relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed
by a power n of the Planck mass M_Pl. We show that first and second order terms
of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a
photon component in cosmic rays above 10^(19) eV that should already have been
detected, if corresponding terms for electrons and positrons are significantly
smaller. This suggests that Lorentz invariance breakings suppressed up to
second order in the Planck scale are unlikely to be phenomenologically viable
for photons.
