Lorentz Invariance Violation: Modification of the Compton Scattering and the GZK Cutoff and Other Effects

This paper deals with the violation of Lorentz symmetry. The approach is based on Compton scattering which becomes modified due to a modified dispersion relation arising from a minimum spacetime cut off as in modern Quantum Gravity approaches. With this amendment, we find that two high-energy rays of different energies develop a time-lag. This time separation becomes prominent when the energies of the considered photons is a parts per thousand yen 1GeV. Extending our approach to gamma rays of cosmic origin we predict that they undergo innumerable such scattering processes before reaching us. Therefore, it accounts for the time-lag phenomena of gamma ray bursts (GRB)'s which have been claimed to be observed. Also, we find that resorting to the modified Snyder-Sidharth Hamiltonian it is possible to extend the GZK cut off beyond its normal limit, 10(20) eV. Some observations of ultra high energy cosmic rays support this. This extends the limits of special theory of relativity.