Disordered locality and Lorentz dispersion relations: an explicit model of quantum foam

TL;DR

This paper models quantum foam with non-local links in spacetime using Quantum Graphity, analyzing how these links affect Lorentz invariance and dispersion relations, and exploring specific distributions of non-local link lengths.

Contribution

It provides an explicit quantum foam model with non-local links and examines their impact on Lorentz invariance and dispersion relations, including specific distribution cases.

Findings

Non-local links suppress superpositions of spacetimes.

Corrections to Lorentz dispersion relations are derived.

Different distributions of link lengths affect Lorentz invariance.

Abstract

Using the framework of Quantum Graphity, we construct an explicit model of a quantum foam, a quantum spacetime with spatial non-local links. The states depend on two parameters: the minimal size of the link and their density with respect to this length. Macroscopic Lorentz invariance requires that the quantum superposition of spacetimes is suppressed by the length of these non-local links. We parametrize this suppression by the distribution of non-local links lengths in the quantum foam. We discuss the general case and then analyze two specific natural distributions. Corrections to the Lorentz dispersion relations are calculated using techniques developed in previous work.