Comment on "Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?" by B. Dittrich and T. Thiemann

TL;DR

This paper defends the view that physical spectra in Loop Quantum Gravity are discrete at the Planck scale, countering recent arguments and clarifying interpretative frameworks, emphasizing the robustness of the discreteness prediction.

Contribution

It provides a rebuttal to recent counter-arguments against spectral discreteness in Loop Quantum Gravity and clarifies interpretative issues related to gauge invariance.

Findings

Discreteness prediction remains valid despite counter-arguments.

A common interpretative confusion is clarified, supporting the discreteness conclusion.

Counter-example by Dittrich and Thiemann does not apply to gravity.

Abstract

I argue that the prediction of physical discreteness at the Planck scale in loop gravity is a reasonable conclusion that derives from a sensible ensemble of hypotheses, in spite of some contrary arguments considered in an interesting recent paper by Dittrich and Thiemann. The counter-example presented by Dittrich and Thiemann illustrates a pathology which does not seem to be present in gravity. I also point out a common confusion between two distinct frameworks for the interpretation of general-covariant quantum theory, and observe that within one of these, the derivation of physical discreteness is immediate, and not in contradiction with gauge invariance.