A numerical study of the correspondence between paths in a causal set and geodesics in the continuum

TL;DR

This study computationally investigates how the longest paths in causal sets approximate geodesics in the continuum, providing evidence for a correspondence in both flat and curved spacetimes.

Contribution

It offers the first computational evidence supporting the path-geodesic correspondence in causal set theory for various spacetime geometries.

Findings

Longest maximal chains approach continuum geodesics statistically

Evidence supports causal set-path and continuum geodesic correspondence

Applicable to flat and selected curved spacetimes

Abstract

This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.