Causality Violation, Gravitational Shockwaves and UV Completion

TL;DR

This paper investigates causality violations in low-energy effective actions involving gravity, analyzing photon scattering in shockwave backgrounds to understand how UV completion resolves these issues and maintains causality at high energies.

Contribution

It provides a detailed analysis of causality violations in gravitational effective actions and demonstrates how UV completion ensures causality is preserved at high energies.

Findings

Phase shifts interpolate smoothly from low to high energies.

Causality violations at low energies are resolved at high energies.

Implications for Planck-scale scattering are discussed.

Abstract

The effective actions describing the low-energy dynamics of QFTs involving gravity generically exhibit causality violations. These may take the form of superluminal propagation or Shapiro time advances and allow the construction of "time machines", i.e. spacetimes admitting closed non-spacelike curves. Here, we discuss critically whether such causality violations may be used as a criterion to identify unphysical effective actions or whether, and how, causality problems may be resolved by embedding the action in a fundamental, UV complete QFT. We study in detail the case of photon scattering in an Aichelburg-Sexl gravitational shockwave background and calculate the phase shifts in QED for all energies, demonstrating their smooth interpolation from the causality-violating effective action values at low-energy to their manifestly causal high-energy limits. At low energies, these phase shifts may be interpreted as backwards-in-time coordinate jumps as the photon encounters the shock wavefront, and we illustrate how the resulting causality problems emerge and are resolved in a two-shockwave time machine scenario. The implications of our results for ultra-high (Planck) energy scattering, in which graviton exchange is modelled by the shockwave background, are highlighted.