All our physical models are described by local partial differential equations. Given the data on an (n-1) dimensional slice (including derivatives, of course), we can propagate that to cover the whole space.
In that generality, this is false. Not all differential equations are causal in all directions. I doubt that it’s true of most physical examples. In particular, everyone I’ve ever heard talk about reconstruction in GR mentioned space-like hypersurfaces.
In that generality, this is false. Not all differential equations are causal in all directions. I doubt that it’s true of most physical examples. In particular, everyone I’ve ever heard talk about reconstruction in GR mentioned space-like hypersurfaces.