Emergent Continuum Spacetime from a Random, Discrete, Partial Order

TL;DR

This paper investigates how a fundamentally discrete, random causal set can give rise to continuum spacetime geometry, including distances and curves, bridging discrete quantum gravity models with classical spacetime structures.

Contribution

It demonstrates how to derive geometrical information like distances and curve lengths from causal sets approximating Minkowski and curved spacetimes.

Findings

Timelike and spacelike distances can be reconstructed from causal sets.

Geometrical quantities such as curve lengths can be obtained from causal set structures.

The approach provides a link between discrete causal sets and continuum spacetime geometry.

Abstract

There are several indications (from different approaches) that Spacetime at the Plank Scale could be discrete. One approach to Quantum Gravity that takes this most seriously is the Causal Sets Approach. In this approach spacetime is fundamentally a discrete, random, partially ordered set (where the partial order is the causal relation). In this contribution, we examine how timelike and spacelike distances arise from a causal set (in the case that the causal set is approximated by Minkowski spacetime), and how one can use this to obtain geometrical information (such as lengths of curves) for the general case, where the causal set could be approximated by some curved spacetime.