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arXiv · gr-qc/0605006

Discreteness without symmetry breaking: a theorem

Luca Bombelli·Joe Henson·Rafael D. Sorkin
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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.

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Luca Bombelli, Joe Henson, Rafael D. Sorkin. 2006-05-01. Discreteness without symmetry breaking: a theorem. https://doi.org/10.1142/s0217732309031958

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