Discreteness without symmetry breaking: a theorem

Abstract

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.

7 pages, laTeX

References in corpus (3)

• Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness
• Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
• Semiclassical Quantum Gravity: Statistics of Combinatorial Riemannian Geometries

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