The Lorentz Transformation for Photons in Dispersive Media and in Gravitational Fields

Abstract

It is pointed out that the traditional explanation for the observation of a non-zero energy h nu for light in free space does not apply for the analogous situation in dispersive media. Because the speed of light u is no longer equal to c in this case, the key quantity, gamma = (1-u2/c2)-0.5, is finite as a result. Since the rest energy of photons is believed to always be equal to zero, multiplying it with gamma in analogy to the usual procedure employed in the special theory of relativity (STR) does not produce a nonzero result for photons in dispersive media. The experimental evidence of the Fizeau light-drag and Cerenkov radiation phenomena indicate that the Lorentz transformation in free space is nonetheless valid for light in dispersive media. Instead, the energy and momentum of photons in transparent media can be obtained from observations of the frequency, wavelength and index of refraction of the light. A modification of the Lorentz transformation in which the observed speed of light does appear explicitly is required, however, in order to accurately predict the results of measurements made when the observer is at a different gravitational potential than the object.