Solving the problem of time in mini-superspace: Measurement of Dirac observables

2009/02/09 by Donald Marolf
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc #quant-ph

paper · pdf · doi:10.1103/physrevd.79.084016

published as Phys.Rev.D79:084016,2009 · 12 pages, ReVTeX

arxiv created 2009/02/09 · openalex publication_date 2009/04/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One solution to the so-called problem of time is to construct certain Dirac observables, sometimes called evolving constants of motion. There has been some discussion in the literature about the interpretation of such observables, and, in particular, whether single Dirac observables can be measured. Here we clarify the situation by describing a class of interactions that can be said to implement measurements of such observables. Along the way, we describe a useful notion of perturbation theory for the rigging map \ensuremathη of group averaging (sometimes loosely called the physical state ``projector''), which maps states from the auxiliary Hilbert space to the physical Hilbert space.

Citations

• The semiclassical approximation to quantum gravity
• Refined Algebraic Quantization of Constrained Systems with Structure Functions
• Semiclassical Gravity and the Problem of Time
• Loss of entanglement in quantum mechanics due to the use of realistic measuring rods
• Fundamental decoherence from quantum gravity: a pedagogical review
• A uniqueness theorem for constraint quantization
• Observables in effective gravity
• Time in quantum gravity: An hypothesis
• Partial and Complete Observables for Canonical General Relativity
• Refined Algebraic Quantization: Systems with a single constraint