Invariance Violation Extends the Cosmic-Ray Horizon?

We postulate that the energy-momentum relation is modified for very high energy particles to violate Lorentz invariance and the speed of photon is changed from the light velocity c . The violation effect is amplified in a sensitive way to detection through the modified kinematical constraints on the conservation of energy and momentum, in the absorption process of γ-rays colliding against photons of longer wavelengths and converting into an electron-positron pair. For γ-rays of energies higher than 10 13 eV, the minimum energy of the soft photons for the reaction and then the absorption mean free path of γ-rays are altered by orders of magnitude from those conventionally estimated. Consideration is similarly applied to high-energy cosmic-ray protons. The consequences may require the standard assumptions on the maximum distance from which very high energy radiation can travel to be revised.