I shall not discuss the order of differentiability postulated, which varies with the theory being defined. In the mathematical
literature, smoothness is often postulated, i.e., differentiability to all orders. But in physical theories defined by hyperbolic
systems of partial differential equations, it is precisely the existence of non-smooth solutions that allows for the transmission of
information. Indeed, the characteristic hypersurfaces of such a system may be defined as those hypersurfaces, along which
discontinuities may propagate.