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The requirement that particles propagate causally on non-trivial backgroundsimplies interesting constraints on higher-derivative operators. This work ispart of a systematic study of the positivity bounds derivable from time delayson shockwave backgrounds. First, we discuss shockwaves in field theory, whichare infinitely boosted Coulomb-like field configurations. We show how apositive time delay implies positivity of four-derivative operators in scalarfield theory and electromagnetism, consistent with the results derived usingdispersion relations, and we comment on how additional higher-derivativeoperators could be included.  We then turn to gravitational shockwave backgrounds. We compute the infiniteboost limit of Reissner-Nordstr\"om black holes to derive charged shockwavebackgrounds. We consider photons traveling on these backgrounds and interactingthrough four-derivative corrections to Einstein-Maxwell theory. The inclusionof gravity introduces a logarithmic term into the time delay that interfereswith the straightforward bounds derivable in pure field theory, a factconsistent with CEMZ and with recent results from dispersion relations. Wediscuss two ways to extract a physically meaningful quantity from thelogarithmic time delay -- by introducing an IR cutoff, or by considering thederivative of the time delay -- and comment on the bounds implied in each case.Finally, we review a number of additional shockwave backgrounds which might beof use in future applications, including spinning shockwaves, those in higherdimensions or with a cosmological constant, and shockwaves from boostedextended objects.

Electric shocks: bounding Einstein-Maxwell theory with time delays on boosted RN backgrounds