Relational Particle Models. II. Use as toy models for quantum geometrodynamics

Abstract

Relational particle models are employed as toy models for the study of the Problem of Time in quantum geometrodynamics. These models' analogue of the thin sandwich is resolved. It is argued that the relative configuration space and shape space of these models are close analogues from various perspectives of superspace and conformal superspace respectively. The geometry of these spaces and quantization thereupon is presented. A quantity that is frozen in the scale invariant relational particle model is demonstrated to be an internal time in a certain portion of the relational particle reformulation of Newtonian mechanics. The semiclassical approach for these models is studied as an emergent time resolution for these models, as are consistent records approaches.

Replaced with published version. Minor changes only; 1 reference corrected

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Cited by in corpus (21)

• Foundations of Relational Particle Dynamics
• Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
• New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
• Schrodinger Evolution for the Universe: Reparametrization
• Triangleland. I. Classical dynamics with exchange of relative angular momentum
• Relational Particle Models. I. Reconciliation with standard classical and quantum theory
• Records Theory
• The equivalent emergence of time dependence in classical and quantum mechanics
• Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
• Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace Examples
• Triangleland. II. Quantum Mechanics of Pure Shape
• Classical dynamics on triangleland
• Jacobi's Principle and the Disappearance of Time
• Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics
• Quantum Machian Time in Toy Models of Gravity
• Relational Motivation for Conformal Operator Ordering in Quantum Cosmology
• Quantum Cosmological Metroland Model
• Shape Space Methods for Quantum Cosmological Triangleland
• Quantum Cosmological Relational Model of Shape and Scale in 1-d
• On the recovery of geometrodynamics from two different sets of first principles
• Relational Quadrilateralland. II. The Quantum Theory