  We show that excitations of interacting quantum particles in lattice models
always propagate with a finite speed of sound. Our argument is simple yet
general and shows that by focusing on the physically relevant observables one
can generally expect a bounded speed of information propagation. The argument
applies equally to quantum spins, bosons such as in the Bose-Hubbard model,
fermions, anyons, and general mixtures thereof, on arbitrary lattices of any
dimension. It also pertains to dissipative dynamics on the lattice, and
generalizes to the continuum for quantum fields. Our result can be seen as a
meaningful analogue of the Lieb-Robinson bound for strongly correlated models.
