  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.
