Scale Dependent Metric and Minimal Length in QEG

TL;DR

This paper explores the concept of a minimal length in quantum gravity within the asymptotic safety framework, demonstrating that certain quantum spacetimes exhibit a fundamental limit to how closely points can be distinguished.

Contribution

It introduces a mathematical model showing that QEG spacetimes have a minimal resolvable length, indicating a fundamental limit to spatial resolution in quantum gravity.

Findings

QEG spacetimes are 'fuzzy' with a minimal coordinate separation

A specific measurement model ('COM microscope') is used to demonstrate minimal length

Quantum Einstein Gravity trajectories imply a fundamental length scale

Abstract

The possibility of a minimal physical length in quantum gravity is discussed within the asymptotic safety approach. Using a specific mathematical model for length measurements ("COM microscope") it is shown that the spacetimes of Quantum Einstein Gravity (QEG) based upon a special class of renormalization group trajectories are "fuzzy" in the sense that there is a minimal coordinate separation below which two points cannot be resolved.