Causal Set Dynamics and The Problem of Time
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Abstract: (submitter)
Causal Set Theory is an approach to Quantum Gravity that takes spacetime tobe a discrete collection of events that is given its structure by their causal order. In thiswork we discuss the impossibility of having CPT-invariance (as order-reversal symmetry)in a CSG dynamics for causal sets and explore some possible alternatives that may satisfythis symmetry. We discuss the Alternating Dynamics (AD), generalising it to allow forany pattern, and show that any AD must correspond to Transitive Percolation (TP) inorder to be generally covariant. This leads us to introduce the Atemporal CSG (ACSG)models, by dropping internal temporality in the CSG models. We find again that TP isthe only generally covariant such model and that it leads to an order-reversal symmetricdynamics. Finally we discuss whether a dynamics that allows for past infinite causetsmust be deterministic and whether a dynamics where Time is finite may be the solutionto make CSG models CPT-invariant. We try to approach these problems using a recentproposal for causal set dynamics, the Covariant Tree (Covtree).- causal set
- covariance
- space-time
- causality
- percolation
- set theory
- quantum gravity
- structure
- time: emergence
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