Could we observe the discreteness of Quantum-Gravity length and area operators ?

TL;DR

This paper examines whether the discrete eigenvalues of length and area operators in Quantum Gravity can be observed in practice, suggesting that such discreteness might not be experimentally detectable.

Contribution

It analyzes measurement procedures for quantum length and area operators, questioning the observability of their discreteness and exploring connections with $$ deformations of Poincaré symmetries.

Findings

Discreteness of quantum length and area may not be observable in simple measurement procedures.

The analysis suggests limitations in detecting quantum geometric discreteness.

Potential links between quantum geometric operators and $$-deformed symmetries are discussed.

Abstract

Several proposals for Quantum Gravity involve length and area operators with discrete eigenvalues. I show that the analyses of some simple procedures for the measurement of areas and lengths suggest that this discreteness characterizing the formalism might not be observable. I also discuss a possible relation with the so-called $\kappa$ deformations of Poincare' symmetries.