Invariance violation extends the cosmic-ray horizon?

We postulate that the energy-momentum relation is modified for very high en ergy particles to violate Lorentz invariance and the speed of photon is cha nged from the light velocity c. The violation effect is amplified in a sens itive way to detection through the modified kinematical constraints on the conservation of energy and momentum, in the absorption process of gamma-ray s colliding against photons of longer wavelengths and converting into an el ectron-positron pair. For gamma-rays of energies higher than 10(13) eV, the minimum energy of the soft photons for the reaction and then the absorptio n mean free path of gamma-rays are altered by orders of magnitude from thos e conventionally estimated. Consideration is similarly applied to high-ener gy cosmic-ray protons. The consequences may require the standard assumption s on the maximum distance from which very high energy radiation can travel to be revised.