Causality is one the most fundamental and essential notions of physics. Causal efficacy cannot propagate faster than light. Otherwise, reference coordinate systems could be constructed (using the
Lorentz transform of
special relativity) in which an observer would see an effect precede its cause (i.e. the postulate of causality would be violated).
Causal notions appear in the context of the flow of mass-energy. For example, it is commonplace to argue that causal efficacy can be propagated by waves (such as electromagnetic waves) only if they propagate no faster than light. Wave packets have
group velocity and
phase velocity. For waves that propagate causal efficacy, both of these must travel no faster than light. Thus light waves often propagate causal efficacy but
de Broglie waves often have phase velocity faster than light and consequently cannot be propagating causal efficacy.
Causal notions are important in general relativity to the extent that the existence of an arrow of time demands that the universe’s semi-Riemannian manifold be orientable, so that “future” and “past” are globally definable quantities.