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Relativistic causality constrains the $S$-matrix both through itsanalyticity, and by imposing lower bounds on the scattering time delay. Thesebounds are easiest to determine for spacetimes which admit either a timelike ornull Killing vector. We revisit a class of pp-wave spacetimes and carefullydetermine the scattering time delay for arbitrary incoming states in theeikonal, semi-classical, and Born approximations. We apply this to the EFT ofgravity in arbitrary dimensions. It is well-known that higher-dimensionoperators such as the Gauss-Bonnet term, when treated perturbatively at lowenergies, can appear to make both positive and negative contributions to thetime delays of the background geometry. We show that even when multipleshockwaves are stacked, the corrections to the scattering time delay relativeto the background are generically unresolvable within the regime of validity ofthe effective field theory so long as the Wilson coefficients are of orderunity. This is in agreement with previously derived positivity/bootstrap boundsand the requirement that infrared causality be maintained in consistentlow-energy effective theories, irrespective of the UV completion.

Surfin' pp-waves with Good Vibrations: Causality in the presence of stacked shockwaves