Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables

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 eta of group averaging (sometimes loosely called the physical state "projector"), which maps states from the auxiliary Hilbert space to the physical Hilbert space.

12 pages, ReVTeX

References in corpus (10)

• Observables in effective gravity
• Conditional probabilities with Dirac observables and the problem of time in quantum gravity
• Fundamental decoherence from quantum gravity: a pedagogical review
• A perturbative approach to Dirac observables and their space-time algebra
• A global picture of quantum de Sitter space
• Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
• Group averaging, positive definiteness and superselection sectors
• The Conditional Probability Interpretation of the Hamiltonian Constraint
• Loss of entanglement in quantum mechanics due to the use of realistic measuring rods
• Partial Observables in Extended Systems

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• Chaos, Dirac observables and constraint quantization
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Weyl Symmetry in Stochastic Quantum Gravity
• Unitary and non-unitary transitions around a cosmological bounce
• Emergence of General Relativity from Loop Quantum Gravity
• Quantum Cauchy Surfaces in Canonical Quantum Gravity
• Emergence of General Relativity from Loop Quantum Gravity: A Summary
• Quantum Reference Frames via Transition Amplitudes in Timeless Quantum Gravity
• A Quantum Informational Approach to the Problem of Time