A Classical Sequential Growth Dynamics for Causal Sets

TL;DR

This paper develops a broad class of classical stochastic models for causal set growth, offering insights into potential pathways toward quantum gravity and matter emergence from fundamental discrete structures.

Contribution

It introduces a general family of sequential growth dynamics for causal sets based on causality and covariance, linking classical models to quantum gravity concepts.

Findings

Provides a new class of growth models for causal sets

Demonstrates matter can emerge dynamically from causal relations

Connects classical causal set dynamics to quantum gravity ideas

Abstract

Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively accessible ``half way house'' to full quantum gravity that possibly contains the latter's classical limit (general relativity). Because they can be expressed in terms of state models for an assembly of Ising spins living on the relations of the causal set, these theories also illustrate how non-gravitational matter can arise dynamically from the causal set without having to be built in at the fundamental level. Additionally, our results bring into focus some interpretive issues of importance for causal set dynamics, and for quantum gravity more generally.