The Area Spectrum in Quantum Gravity

TL;DR

This paper introduces a new area operator in quantum gravity, compares it with the traditional one, and discusses their different spectra and relevance in physical contexts like black holes.

Contribution

It proposes a new area operator in quantum gravity, analyzes its spectrum, and discusses its applicability in different physical scenarios, especially black hole horizons.

Findings

The new operator's spectrum differs from the traditional one at finite spins.

Both operators are valid, with the new one being relevant for black hole horizon measurements.

The difference arises from quantum non-commutativity and fluctuations.

Abstract

We show that, apart from the usual area operator of non-perturbative quantum gravity, there exists another, closely related, operator that measures areas of surfaces. Both corresponding classical expressions yield the area. Quantum mechanically, however, the spectra of the two operators are different, coinciding only in the limit when the spins labelling the state are large. We argue that both operators are legitimate quantum operators, and which one to use depends on the context of a physical problem of interest. Thus, for example, we argue that it is the operator proposed here that is relevant in the black hole context to measure the area of black hole horizon. We show that the difference between the two operators is due to non-commutativity that is known to arise in the quantum theory. We give a heuristic picture explaining the difference between the two area spectra in terms of quantum fluctuations of the surface whose area is being measured.