If time had no beginning: growth dynamics for past-infinite causal sets

TL;DR

This paper investigates extending Causal Set Theory's growth dynamics to include past-infinite causal sets, proposing new models and observables to accommodate this broader framework.

Contribution

It introduces a modified growth dynamics model for past-infinite causal sets and proposes convex-suborders as physical observables in this context.

Findings

Modified classical sequential growth dynamics for past-infinite sets

Introduction of convex-suborders as physical observables

A covariant framework for growth models of past-infinite causal sets

Abstract

We explore whether the growth dynamics paradigm of Causal Set Theory is compatible with past-infinite causal sets. We modify the Classical Sequential Growth dynamics of Rideout and Sorkin to accommodate growth "into the past" and discuss what form physical constraints such as causality could take in this new framework. We propose convex-suborders as the "observables" or "physical properties" in a theory in which causal sets can be past-infinite and use this proposal to construct a manifestly covariant framework for dynamical models of growth for past-infinite causal sets.