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

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.