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Causality and Superluminal Light

G. M. Shore

Abstract

The causal properties of curved spacetime, which underpin our sense of time in gravitational theories, are defined by the null cones of the spacetime metric. In classical general relativity, it is assumed that these coincide with the light cones determined by the physical propagation of light rays. However, the quantum vacuum acts as a dispersive medium for the propagation of light, since vacuum polarisation in QED induces interactions which effectively violate the strong equivalence principle (SEP). For low frequencies the phenomenon of gravitational birefringence occurs and indeed, for some metrics and polarisations, photons may acquire {\it superluminal} phase velocities. In this article, we review some of the remarkable features of SEP violating superluminal propagation in curved spacetime and discuss recent progress on the issue of dispersion, explaining why it is the high-frequency limit of the phase velocity that determines the characteristics of the effective wave equation and thus the physical causal structure.

Causality and Superluminal Light

Abstract

The causal properties of curved spacetime, which underpin our sense of time in gravitational theories, are defined by the null cones of the spacetime metric. In classical general relativity, it is assumed that these coincide with the light cones determined by the physical propagation of light rays. However, the quantum vacuum acts as a dispersive medium for the propagation of light, since vacuum polarisation in QED induces interactions which effectively violate the strong equivalence principle (SEP). For low frequencies the phenomenon of gravitational birefringence occurs and indeed, for some metrics and polarisations, photons may acquire {\it superluminal} phase velocities. In this article, we review some of the remarkable features of SEP violating superluminal propagation in curved spacetime and discuss recent progress on the issue of dispersion, explaining why it is the high-frequency limit of the phase velocity that determines the characteristics of the effective wave equation and thus the physical causal structure.

Paper Structure

This paper contains 16 sections, 57 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Causality and Superluminal Propagation
  3. Superluminal Propagation in Special and General Relativity
  4. Geometric Optics
  5. Bimetricity
  6. Stable Causality
  7. Time Machines?
  8. The Event Horizon
  9. Causality, Characteristics and the 'Speeds of Light'
  10. 'Speeds of Light'
  11. Characteristics, Wavefronts and the Phase Velocity $v_{\rm ph}(\infty)$
  12. Dispersion
  13. Effective Action for Photon-Gravity Interactions
  14. Dispersion and the Light Cone
  15. Non-Perturbative Effective Action and High-Frequency Propagation
  16. ...and 1 more sections

Figures (5)

  • Figure 1: A superluminal $(v>1)$ signal OA which is forwards in time in frame ${\cal S}$ is backwards in time in a frame ${\cal S}'$ moving relative to ${\cal S}$ with speed $u>{1\over v}$. However, the return path with the same speed in ${\cal S}$ arrives at B in the future light cone of O, independent of the frame.
  • Figure 2: A superluminal $(v>1)$ signal OC which is backwards in time in frame ${\cal S}$ is returned at the same speed to point D in the past light cone of O, creating a closed time loop.
  • Figure 3: The Dolgov-Novikov time machine proposal. A superluminal signal from $X$, described as backwards-in-time in a relevant frame, is sent towards a second gravitating source $Y$ moving relative to $X$ and returned symmetrically.
  • Figure 4: A decomposition of the paths in Fig. 3 for well-separated sources
  • Figure 5: Sketch of the behaviour of the phase, group and signal velocities with frequency in the model described by the refractive index Eq.(\ref{['eq:ca']}). The energy-transfer velocity (not shown) is always less than $c$ and becomes small near $\omega_0$. The wavefront speed is identically equal to $c$.