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Discreteness without symmetry breaking: a theorem
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This paper concerns sprinklings into Minkowski space (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to ``Lorentz breaking'' effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.
Forward citations
Cited by 2 Pith papers
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Link degree distribution, symmetrized Hasse diagram Laplacian eigenvalues, and causal interval abundance distinguish nine classes of causal sets.
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Causal sets can approximate black hole horizons via discrete timelike curves and ladders tracing null geodesics, with a discrete expansion changing sign across the horizon in a 1+1D toy model.
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