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

2026/05/21 by Álvaro Mozota Frauca · 1 voice · 1 citation
Physics and Astronomy · #physics.hist-ph #gr-qc

paper · pdf · doi:10.1086/741910

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.

Citations

• Does Quantum Cosmology Predict the Age of the Universe?
• Relational Dynamics with Periodic Clocks
• First-Class Constraints, Gauge Transformations, de-Ockhamization, and Triviality: Replies to Critics, Or, How (Not) to Get a Gauge Transformation from a Second-Class Primary Constraint
• Philosophical Foundations of Loop Quantum Gravity
• First-class constraints generate gauge transformations in electromagnetism (reply to Pitts)
• Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings
• Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity
• Can chaos be observed in quantum gravity?
• Chaos, Dirac observables and constraint quantization
• Time Remains
• Change in Hamiltonian General Relativity from the Lack of a Time-like Killing Vector Field
• A First Class Constraint Generates Not a Gauge Transformation, But a Bad Physical Change: The Case of Electromagnetism
• TIME AND INTERPRETATIONS OF QUANTUM GRAVITY
• "Forget time"
• Constraints and gauge transformations: Dirac's theorem is not always valid
• Jacobi's Principle and the Disappearance of Time
• GPS observables in general relativity
• Quantization of Gauge Systems
• Canonical Quantum Gravity and the Problem of Time
• Time in quantum gravity: An hypothesis

Discussions

• \'Alvaro Mozota Frauca: The Limitations of the Notion of `Observable' in Diffeomorphism-Invariant Models https://arxiv.org/abs/2605.22260 https://arxiv.org/pdf/2605.22260 https://arxiv.org/html/2605.2 [bsky, 0 points, 0 comments]

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