Derivation of Photon Mass using Generalized Special Relativity

Abstract

Some recent experiments shows that the photon has a rest mass. Special relativity says that the photon is rest massless which is in conflict with some recent observations and the common sense. There is also no well defined theory which predict the photon wave function and photon localization. In this work generalized special relativity is utilized to develop a quantum theory for the photon and to explain some phenomena associated with the nature of the photon. The Planck famous energy relation is obtained by treating the photon as electromagnetic wave packet. The photon rest mass is found by finding the potential at which the energy is minimum and then finding the minimum energy. If one relates vacuum energy to photon rest mass energy, the rest mass energy is found to be equal to . But if one relates the photon rest mass with the plasma frequency which is related to photon dispersion, its value becomes , which is in conformity with some experiments. It was also shown that the photon can be amplified if the external and internal fields are coherent. This new condition can be utilized to predict new lasing mechanisms and may lead to new lasing system. Treating the photon as a harmonic oscillator, quantum generalized special relativity (GSR) theory predicts the well known photon energy and momentum, beside particle nature of the photon. It is also found that the photon has a wave function and it is highly localized. The photon wave equation is shown also correspond to the complex operator method which quantize electromagnetic field.