  Contrary to what is often stated, a fundamental spacetime discreteness need
not contradict Lorentz invariance. A causal set's discreteness is in fact
locally Lorentz invariant, and we recall the reasons why. For illustration, we
introduce a phenomenological model of massive particles propagating in a
Minkowski spacetime which arises from an underlying causal set. The particles
undergo a Lorentz invariant diffusion in phase space, and we speculate on
whether this could have any bearing on the origin of high energy cosmic rays.
