Surprisingly Long Length Scales for Semiclassical Loop Quantum Gravity and Their Physical Consequences

TL;DR

This paper investigates the implications of unexpectedly large length scales in semiclassical loop quantum gravity, revealing their effects on space-time fluctuations, regularization issues, and potential experimental observability.

Contribution

It introduces a new proper distance scale in LQG, explores its physical consequences, and links it to collective coherent states and experimental measurements.

Findings

Earth surface length scale between 100 μm and 0.7 m

Space-time strain amplitude below current detection limits

Large length scale impacts photon dispersion relations

Abstract

When gauge field theory coherent states for loop quantum gravity (LQG) were introduced, an optimized semiclassical proper length emerged, corresponding to the edge length $\epsilon$ of a graph embedded in a given classical geometry. Here $\epsilon$ is explored in more detail. $\epsilon$ at the Earth's surface is found to lie between 100 $\mu $m and 0.7 m. The implied quantum fluctuating space-time strain amplitude and noise spectrum are estimated to be $4\; 1/2$ orders smaller than the current experimental detectability. However, such a macroscopic $\epsilon $ makes regularization of the semiclassical electromagnetic Hamiltonian problematic for photon wavelengths shorter than $\epsilon$. The origin of a large $\epsilon$ is traced to an edge-wise tensor product of independent edge-based coherent states for the whole graph state. This provides physical grounds for recently proposed collective coherent states, where $\epsilon$ acquires the interpretation of a sliding scale. A new proper distance $\xi$ emerges as the characteristic length of semiclassical LQG. $\xi$ will affect the LQG photon vacuum dispersion relations, and is also accessible to current measurements of space-time strain. Matter interactions may also affect $\xi$.