Photon pairing instabilities: A microscopic origin for gravitation?

We show that general phase-space considerations permit the scattering amplitude for two interacting massless particles to develop a weak-coupling singularity in the ladder approximation. In the case of photon-photon scattering induced by electron vacuum polarization, spin factors prevent such singularities from actually occurring in unaccelerated flat spacetime. However, in the case of conformally flat Riemannian spacetimes, which can be studied using Feynman rules similar to those in the Minkowski-space case, a reevaluation of the photon-photon scattering ladder sum shows that weak-coupling singularities do occur. We conjecture that such instabilities are a general feature of the non-Minkowski case and may provide a microscopic basis for gravitation, with the gravitational fields identified with photon pairing amplitudes of a superconductive type. According to this conjecture, the "graviton" would not be described by a conventional local quantum field.