  The propagation of photons, electrons and positrons at ultra-high energies
above 10^{19} eV can be changed considerably if the dispersion relations of
these particles are modified by terms suppressed by powers of the Planck scale.
We recently pointed out that the current non-observation of photons in the
ultra-high energy cosmic ray flux at such energies can put strong constraints
on such modified dispersion relations. In the present work we generalize these
constraints to all three Lorentz invariance breaking parameters that can occur
in the dispersion relations for photons, electrons and positrons at first and
second order suppression with the Planck scale. We also show how the excluded
regions in these three-dimensional parameter ranges would be extended if
ultra-high energy photons were detected in the future.
