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 $v=1\pm p^2/{\Lambda }^2$, which typically bound $\Lambda >{10}^{21}\mathrm{G}\mathrm{e}\mathrm{V}$, well above the Planck scale. For ($CPT$ violating) dispersion correction of the form $v=1+p/\Lambda$, the bounds are up to 15 orders of magnitude beyond the Planck scale.

• Received 30 April 2004

DOI:https://doi.org/10.1103/PhysRevD.70.065002