Spacetime discreteness, Lorentz invariance and locality

If spacetime is fundamentally discrete, as many workers on quantum gravity suspect, then continuum symmetries such as Lorentz invariance are imperilled. Lorentz symmetry can nevertheless be compatible with spacetime atomicity but the price is locality. Indeed, causal sets are discrete and Lorentz invariant but highly nonlocal. The question becomes: can the nonlocality be tamed far enough to allow known local physics to emerge at large distances? We give evidence that the answer to this question is yes.