Polarization precession in photon-photon encounters

We calculate the rate of precession of the direction of polarization of a photon traversing a sea of plane-polarized photons moving in the opposed direction, where the interaction is the one-loop "vacuum" Heisenberg-Euler coupling of four fields. Substantial precession can take place in a distance many orders of magnitude shorter than the free path for photon-photon scattering, mediated by the same interaction. We consider briefly the possibility of some interesting collective effects in the case in which instead of a particle and a sea, two seas are caused to collide.