Stable Causality and Microcausality for Drummond-Hathrell Photons

TL;DR

This work investigates whether local DH-induced superluminality signals a breakdown of causality in curved spacetime. It uses two symmetry‑independent diagnostics: the stable causality of the optical metric and flat‑space microcausality bounds applied to a fixed Lorentz‑breaking gravitational background, tested on a Schwarzschild orbit and a two‑black‑hole geometry. Within the geometric‑optics regime $m_e^{-1} rangle ext{geq} ext{...}$, both diagnostics indicate no causal pathology: the optical metric remains stably causal and the DH dispersion relations satisfy analyticity and spectral bounds, implying microcausality is preserved in the EFT window. The results provide a controlled check that EFT superluminality in gravitational backgrounds need not imply causality violation, while noting that they do not deliver a universal curved‑space microcausality principle.

Abstract

Local superluminal photon propagation arises at $\mathcal{O}(α/m_e^2)$ in the Drummond Hathrell (DH) effective action obtained by integrating out the electron in QED coupled to gravity. Whether such superluminality implies a genuine violation of causality in curved spacetime is subtle and remains conceptually nontrivial. In this work we revisit this question using two complementary and largely symmetry-independent diagnostics. First, we analyse the global causal structure of the effective (optical) metric governing DH photon propagation and identify conditions under which it remains stably causal, thereby excluding the formation of closed causal curves. Second, from a quantum-field-theoretic perspective, we examine microcausality by treating the gravitational background as a fixed Lorentz-breaking field and applying flat-spacetime analyticity bounds to the photon commutator within the geometric-optics regime of the EFT. For two representative examples, a circular photon orbit in Schwarzschild and a linear trajectory in a two-black-hole geometry, we find that, within the regime of validity of the DH effective theory, both diagnostics indicate that the superluminal photon propagation is causally benign. Our results do not constitute a general definition of microcausality in curved spacetime, but provide a controlled and instructive check of causal consistency for EFT superluminality in gravitational backgrounds.