On the Classical Limit of Spin Network Gravity: Two Conjectures

TL;DR

This paper discusses the classical limit of spin network gravity, estimating wave packet spreading times and conjecturing suppression of certain Hamiltonian terms in the classical regime.

Contribution

It introduces two conjectures about the behavior of spin network gravity in the classical limit, focusing on wave packet spreading and Hamiltonian term suppression.

Findings

Spreading of coherent state wave packets is small for large angular momentum.

Terms adding new vertices in the Hamiltonian are conjectured to be suppressed in the classical limit.

Estimates are based on dimensional analysis of time scales.

Abstract

Estimates are given of the time scales which govern spreading of a coherent state wave packet. The estimates, based on dimensional analysis, suggest that spreading should be small for coherent states with average angular momentum of order 100 or larger. It is conjectured that in the classical limit, terms in the Hamiltonian which add a new vertex will be suppressed, compared to terms which modify the existing spin network without changing the number of vertices.