Scharnhorst effect at oblique incidence - art. no. 085003

We consider the Scharnhorst effect (anomalous photon propagation in the Cas imir vacuum) at oblique incidence, calculating both photon speed and polari zation states as functions of angle. The analysis is performed in the frame work of nonlinear electrodynamics and we show that many features of the sit uation can be extracted solely on the basis of symmetry considerations. Alt hough birefringence is common in nonlinear electrodynamics it is not univer sal; in particular, we verify that the Casimir vacuum is not birefringent a t any incidence angle. On the other hand, the group velocity is typically n ot equal to the phase velocity, though the distinction vanishes for special directions or if one is only working to second order in the fine structure constant. We obtain an "effective metric'' that is subtly different from p revious results. The disagreement is due to the way that "polarization sums " are implemented in the extant literature, and we demonstrate that a fully consistent polarization sum must be implemented via a bootstrap procedure using the effective metric one is attempting to define. Furthermore, in the case of birefringence, we show that the polarization sum technique is intr insically an approximation.