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where C and $\xi$ are constants fixed by the microscopic couplings and d(x,y) is the distance between the two sites on the lattice [ 1 ] . Outside the cone, where d(x,y) exceeds $c_{\mathrm{LR}}$ t , the right-hand side collapses toward zero; inside it, the inequality simply has nothing to say. The velocity $c_{\mathrm{LR}}$ plays exactly the causal role the vacuum speed c plays in relativity, with one difference that matters for everything that follows: it is a property of the material, not of empty space, and it changes from one lattice to the next.

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