A new spin on the hole argument

Abstract

This paper shows how an exact analog of the hole argument can be constructed in the loop representation of quantum gravity. The new argument is based on the embedding of spin-networks in a manifold along with the action of the diffeomorphism constraint on them. I will then briefly discuss the implications of this result vis-à-vis the ontological debate about the nature of space. I argue that the conclusions of many physicists working on loop quantum gravity (e.g., Rovelli and Smolin) that the loop representation uniquely supports relationalism are unfounded, as is the claim of Belot and Earman that quantum gravity might serve to settle the debate one way or the other.