The Limitations of the Notion of `Observable' in Diffeomorphism-Invariant Models

TL;DR

This paper critically examines the concept of 'observable' in diffeomorphism-invariant theories like general relativity, highlighting conceptual limitations and clarifying the distinction between local and global gauge transformations.

Contribution

It clarifies the distinction between local and global gauge transformations and argues that the notion of observable is only meaningful in the local sense, challenging common claims.

Findings

Observable concept is more natural in local gauge transformations.

Diffeomorphism invariance is a gauge symmetry only from a global perspective.

Claims that correlations encode all physical content are unfounded.

Abstract

The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with this symmetry and building quantum versions of them. In this article I distinguish between two senses of gauge transformation: local and global, and I argue that the notion of observable appears more naturally in the local sense of gauge transformation. Then, I argue that diffeomorphism invariance can be understood as a gauge symmetry only from a global point of view, and hence, that the concept of observable applies only in a restricted manner. This has the consequence that some popular claims in the literature, such as the claim that the physical content of diffeomorphism-invariant models is encoded in correlations, are unfounded.