Symmetry-breaking and zero-one laws

TL;DR

This paper demonstrates that the inherent discreteness in causal sets does not break fundamental symmetries of spacetime, such as Poincaré invariance, through rigorous proofs and zero-one law analysis.

Contribution

It provides a rigorous proof that Poisson sprinkling in Minkowski spacetime cannot break key spacetime symmetries, supporting the invariance of causal set models.

Findings

Poisson sprinkling preserves Poincaré invariance

Discreteness does not induce preferred directions or points

Zero-one law is established from first principles

Abstract

We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincar{\'e} invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based.