Constructing an interval of Minkowski space from a causal set

TL;DR

This paper presents a computational method to embed small manifoldlike causal sets into Minkowski space, aiding in identifying manifoldlike structures and their scales within causal set quantum gravity.

Contribution

It introduces a practical algorithm for embedding causal sets into Minkowski space and assessing their manifoldlikeness, addressing a key challenge in causal set quantum gravity.

Findings

Method successfully tested in 2D case

Can determine manifoldlikeness of causal sets

Defines scales of manifoldlikeness

Abstract

A criticism sometimes made of the causal set quantum gravity program is that there is no practical scheme for identifying manifoldlike causal sets and finding embeddings of them into manifolds. A computational method for constructing an approximate embedding of a small manifoldlike causal set into Minkowski space (or any spacetime that is approximately flat at short scales) is given, and tested in the 2 dimensional case. This method can also be used to determine how manifoldlike a causal set is, and conversely to define scales of manifoldlikeness.