Causality constraints and the lightcone

Abstract

It is an attractive idea that effective theories admitting a consistent UV completion require quanta to propagate sub-luminally in non-trivial backgrounds. However, there is a counter example to this proposition in the form of QED in a curved geometry, a theory that is certainly causal. Nevertheless, Drummond and Hathrell showed that there is always at least one choice of polarization for which low frequency photons propagate super-luminally. Conventional arguments involving dispersion relations would then normally imply that the high frequency phase velocity would also exceed c yielding a contradiction with the UV completion. We show how the contradiction is avoided by a mechanism that relies on the subtle behaviour of the lightcones in the geometry and that, in the end, super-luminal low frequency propagation is perfectly consistent with causality. In particular, time machines cannot be constructed using the effect. The lesson is that causality constraints in low energy effective theories need to be treated with some caution.