# Echoes of Asymptotic Silence in Causal Set Quantum Gravity

## TL;DR

This paper investigates asymptotic silence in causal set quantum gravity, demonstrating dimensional reduction at small scales and convergence to continuum behavior at larger scales through numerical simulations.

## Contribution

It introduces an intrinsic spatial distance measure in causal sets and shows how it reveals asymptotic silence and dimensional reduction in quantum gravity models.

## Key findings

- Discrete distance converges to continuum distance at larger scales.
- Effective dimension shows ultraviolet dimensional reduction.
- Causal sets exhibit asymptotic silence behavior.

## Abstract

We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behaviour akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between causal set elements in the discrete analogue of a spatial hypersurface. Using numerical simulations for causal sets approximated by D=2,3 and 4 dimensional Minkowski spacetime, we show that while the discrete distance rapidly converges to the continuum distance at a scale roughly an order of magnitude larger than the discreteness scale, it is significantly larger on small scales. This allows us to define an effective dimension which exhibits dimensional reduction in the ultraviolet, while monotonically increasing to the continuum dimension with increasing continuum distance. We interpret these findings as manifestations of asymptotic silence in causal set theory.