Causality Violation, Gravitational Shockwaves and UV Completion

TL;DR

The paper investigates whether causality violations in low-energy effective actions involving gravity signal unphysical theories or are resolved by a UV-complete framework. By analyzing photon propagation in an Aichelburg–Sexl gravitational shockwave within QED, it derives the full energy-dependent phase shifts, showing a smooth interpolation from low-energy Shapiro time advances to high-energy causal limits where $v_{\text{ph}}(\infty)\to1$ and the coordinate shift $\Delta v(u,\omega)\to0$. The results demonstrate that apparent time-machine constructions based on the DH term are not realized in the UV-complete theory, with causality restored through vacuum polarization effects and geometry of geodesic deviation; a parallel scalar-field model confirms the robustness of this mechanism. The work also connects to Planck-scale scattering and discusses how UV completions like string-theoretic towers can resolve causality concerns, highlighting the special role of curved spacetime dispersion in reconciling IR acausalities with UV causality.

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.

Figures (15)

• Figure 1: The geodesic of the massless particle involves an instantaneous shift in the null coordinate $\Delta v_{\small\text{AS}}$ as it passes the shockwave at $u=0$ as well as a deflection in the transverse space.
• Figure 2: A closed trajectory for a massless particle made from two shockwaves moving in opposite directions with some impact parameter of the same order as the shifts $\Delta v_{\small\text{AS}}$ at each shockwave. Mirrors are placed at at the points just before and just after the photon gets close the shockwaves to direct the photon in the right direction. The right-hand picture is a side view showing the non-vanishing impact parameter.
• Figure 3: The one-loop Feynman diagram contributing to the vacuum polarization in QED in the curved background of the shockwave. The figure illustrates the gravitational tidal forces acting on the virtual electron-positron cloud screening the dressed photon.
• Figure 4: The proposed time machine consisting of two shockwaves moving in opposite directions that collide with some impact parameter $L$. The photon collides with the first at $S$, experiences a shift back to $P$ which then allows it to catch up with shockwave 2 with a jump back to $R$ in the past lightcone of $S$.
• Figure 5: The plot shows the photon and wavefront of shockwave 2 in the $(z,x_1)$ plane. The photon is behind the wavefront. When the wavefront collides with shockwave 1, it gets shifted by an amount $\Delta v_{\small\text{AS}}=\frac{1}{2}f(x_1)<0$. This corresponds to jump forward in $z$ and backwards in time. At $u=0^+$, the wavefront becomes curved as shown. Since the photon collides with shockwave 1 at some time later and for $z<0$ at $S$ it gets shifted froward to P which lies behind the wavefront of shockwave 2. If the photon receives an additional $\Delta v_{\small\text{DH}}(b)<0$ then it can then jump to point $P'$ in front of shockwave 2 and a time machine can then be constructed.