Quantum gravity observables: observation, algebras, and mathematical structure

TL;DR

This paper explores the structure of observables in quantum gravity, proposing a relational classification, and discusses how gravitational effects alter the algebraic framework of local quantum field theory, with implications for holography.

Contribution

It introduces a classification of relational observables in quantum gravity and connects gravitational dressings to algebraic structures like von Neumann algebras, revealing new theoretical insights.

Findings

Gravitationally dressed observables are linked to the fundamental structure of quantum gravity.

Gravitational dressings can be constructed to leading order in Newton's constant.

Gravity modifies the algebraic structure of local quantum field theory, suggesting new mathematical frameworks.

Abstract

The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables (gravitationally dressed, field relational, and more general) is outlined. Plausibly gravitationally dressed observables are particularly closely tied to the fundamental structure of the theory. These may be constructed in the quantum theory to leading order in Newton's constant, and raise important questions about localization of information. Approximate localization is given by a "standard dressing" construction of a "gravitational splitting." It is also argued that such gravitational dressings give a generalization of the crossed product construction, reducing to this and yielding type II von Neumann algebras in special cases. Gravity therefore introduces a significantly more general alteration of the algebraic structure of local quantum field theory, also with apparent connections to holography, but whose implications have not been fully understood. In particular, properties of the algebra of gravitationally dressed observables suggest a possible role for other non-algebraic structure on the Hilbert space for quantum gravity.