Quantum mechanics versus equivalence principle

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 $\theta$ for a photon passing by the sun is evaluated afterward and the likelihood of detecting $\frac{\Delta \theta }{{\theta }_E}\equiv \frac{\theta -{\theta }_E}{{\theta }_E}$ (where ${\theta }_E$ is the value predicted by Einstein’s geometrical theory for the light bending) in the foreseeable future, is discussed.

Figure 1

Feynman graph for photon scattering by an external gravitational field; $|\mathbf{p}|=|{\mathbf{p}}^{\prime }|$.

Figure 2

Second order Feynman graphs for photon scattering by an external gravitational field; $|\mathbf{p}|=|{\mathbf{p}}^{\prime }|$.