Limits on Lorentz violation from the highest energy cosmic rays

We place several new limits on Lorentz violating effects, which can modify particles' dispersion relations, by considering the highest energy cosmic rays observed. Since these are hadrons, this involves considering the partonic content of such cosmic rays. We get a number of bounds on differences in maximum propagation speeds, which are typically bounded at the 10^-21 level, and on momentum dependent dispersion corrections of the form v=1±p²/Λ², which typically bound Λ>10²¹ GeV, well above the Planck scale. For ($CPT$ violating) dispersion correction of the form v=1+p/Λ, the bounds are up to 15 orders of magnitude beyond the Planck scale.