  We postulate in the present paper 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 gamma-rays colliding against photons of longer wavelengths and
converting into an electron-positron pair. For gamma-rays of energies higher
than 10 TeV, the minimum energy of the soft photons for the reaction and then
the absorption mean free path of gamma-rays are altered by orders of magnitude
from the ones conventionally estimated. Consideration is similarly applied to
high energy cosmic ray protons. The consequences may require the standard
assumptions on the maximum distance that very high energy radiation can travel
from to be revised.
