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This paper concerns sprinklings into Minkowski space (Poisson processes). Itproves that there exists no equivariant measurable map from sprinklings tospacetime directions (even locally). Therefore, if a discrete structure isassociated to a sprinkling in an intrinsic manner, then the structure will notpick out a preferred frame, locally or globally. This implies that thediscreteness of a sprinkled causal set will not give rise to ``Lorentzbreaking'' effects like modified dispersion relations. Another consequence isthat there is no way to associate a finite-valency graph to a sprinklingconsistently with Lorentz invariance.Comment: 7 pages, laTe

DISCRETENESS WITHOUT SYMMETRY BREAKING: A THEOREM