Emergence of spatial structure from causal sets

TL;DR

This paper proposes a method to derive spatial distances from causal sets, addressing a key challenge in emergent spacetime models within quantum gravity, and offers criteria to assess their continuum embedding fidelity.

Contribution

It introduces a novel approach to extract spatial distances from causal sets and suggests a way to evaluate their continuum correspondence.

Findings

Method to deduce spatial distances from causal sets

Criteria to assess causal set embedding into continuum spacetime

Addresses the challenge of spatial distance in causal set theory

Abstract

There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying discreteness. The causal set approach, in which the fundamental relation is based upon causality, finds it easy to reproduce timelike distances, but has a more difficult time with spatial distance, due to the unique combination of Lorentz invariance and discreteness within that approach. We describe a method to deduce spatial distances from a causal set. In addition, we sketch how one might use an important ingredient in deducing spatial distance, the `$n$-link', to deduce whether a given causal set is likely to faithfully embed into a continuum spacetime.