Quantum mechanics versus equivalence principle

Abstract

We consider the scattering of a photon by a weak gravitational field, treated as an external field, up to second order of the perturbation expansion. The resulting cross section is energy dependent which indicates a violation of Galileo's equivalence principle (universality of free fall) and, consequently, of the classical equivalence principle. The deflection angle $\ensuremath{\theta}$ for a photon passing by the sun is evaluated afterward and the likelihood of detecting $\frac{\ensuremath{\Delta}\ensuremath{\theta}}{{\ensuremath{\theta}}_{E}}\ensuremath{\equiv}\frac{\ensuremath{\theta}\ensuremath{-}{\ensuremath{\theta}}_{E}}{{\ensuremath{\theta}}_{E}}$ (where ${\ensuremath{\theta}}_{E}$ is the value predicted by Einstein's geometrical theory for the light bending) in the foreseeable future, is discussed.