Causal Set Dynamics: A Toy Model

TL;DR

This paper introduces a quantum model for causal set dynamics inspired by directed percolation, revealing unique quantum interference effects and multiple crossover points, unlike classical percolation.

Contribution

It develops a quantum measure on directed graphs, demonstrating novel phenomena such as dual crossover points and indeterminate spacetime properties.

Findings

Quantum interference causes non-classical properties.

The model exhibits two crossover points instead of one.

Spacetime percolation becomes indeterminate between these points.

Abstract

We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from 1-dimensional directed percolation. Quantum interference patterns lead to properties which do not appear to have any analogue in classical percolation. Most notably, instead of the single phase transition of classical percolation, the quantum model displays two distinct crossover points. Between these two points, spacetime questions such as "does the network percolate" have no definite or probabilistic answer.