Photons propagating in curved spacetime may, depending on their direction and polarisation, have velocities exceeding the "speed of light" c. This phenomenon arises through vacuum polarisation in QED and is a tidal gravitational effect depending on the local curvature. It implies that the Principle of Equivalence does not hold for interacting quantum field theories in curved spacetime and reflects a quantum violation of local Lorentz invariance. These results are illustrated for the propagation of photons in the ReissnerNordström spacetime characterising a charged black hole. A general analysis of electromagnetic as well as gravitational birefringence is presented.SWAT 93/9
The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation of these constraints implies superluminal propagation, in the sense that the low-frequency limit of the phase velocity v ph (0) exceeds c. It is explained why causality is related not to v ph (0) but to the high-frequency limit v ph (∞) and how these are related by the Kramers-Kronig dispersion relation, depending on the sign of the imaginary part of the refractive index Im n(ω) which is normally assumed positive. Superluminal propagation and its relation to UV completion is investigated in detail in three theories: QED in a background electromagnetic field, where the full dispersion relation for n(ω) is evaluated numerically for the first time and the role of the null energy condition T µν k µ k ν ≥ 0 is highlighted; QED in a background gravitational field, where examples of superluminal low-frequency phase velocities arise in violation of the positivity constraints; and light propagation in coupled laser-atom Λ-systems exhibiting Raman gain lines with Im n(ω) < 0. The possibility that a negative Im n(ω) must occur in quantum field theories involving gravity to avoid causality violation, and the implications for the relation of IR effective field theories to their UV completion, are carefully analysed.
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