There is more and more evidence that quantum gravity should be rather defined from the Lorentzian path integral than the Euclidean one. But there are many open questions concerning the Lorentzian path integral. Two of these are: Which configurations should be included in the Lorentzian path integral, e.g. should we include configurations that violate causality conditions? And how to compute the Lorentzian path integral?
Using Picard-Lefshetz theory to compute the Lorentzian path integral for Regge gravity, I will explain how this method can also inform on the first question. This example indicates that we can allow for causality violations to occur, but that the corresponding amplitudes are suppressed by the dynamics.