Problem of Time and Background Independence: the Individual Facets

Abstract

I lay out the problem of time facets as arising piecemeal from a number of aspects of background independence. Almost all of these already have simpler classical counterparts. This approach can be viewed as a facet by facet completion of the observation that Barbour-type relationalism is a background independent precursor to 2 of the 9 facets. That completion proceeds in an order dictated by the additional layers of mathematical structure required to support each. Moreover, the `nonlinear nature' of the interactions between the Problem of Time facets renders a joint study of them mandatory. The current article is none the less a useful prequel via gaining a conceptual understanding of each facet, prior to embarking on rendering some combinations of facets consistent and what further obstructions arise in attempting such joint considerations. See [20, 21, 26] for up to date studies of this more complicated joint version. I also identify new facets (threading based), subfacets (of observables and of reconstructions) and further source of variety from how far down the levels of mathematical structure these facets extend.

40 pages including 13 Figures

References in corpus (29)

• The Confrontation between General Relativity and Experiment
• The Dynamics of General Relativity
• Background Independent Quantum Gravity: A Status Report
• Quantum Gravity: a Progress Report
• Problem of Time in Quantum Gravity
• Relativity without relativity
• Some remarks on the notions of general covariance and background independence
• Continuous Histories and the History Group in Generalised Quantum Theory
• The Problem of Time in Quantum Gravity
• Prima Facie Questions in Quantum Gravity
• The physical gravitational degrees of freedom
• Somewhere in the Universe: Where is the Information Stored When Histories Decohere?
• The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena
• Proof of the Thin Sandwich Conjecture
• Scale-Invariant Gravity: Geometrodynamics
• Probabilities in Quantum Cosmological Models: A Decoherent Histories Analysis Using a Complex Potential
• Beables/Observables in Classical and Quantum Gravity
• A Shape Dynamics Tutorial
• New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
• General relativity histories theory I: The spacetime character of the canonical description
• Classical Machian Resolution of the Spacetime Reconstruction Problem
• Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
• Machian Time Is To Be Abstracted From What Change?
• On Background Independence
• Covariance and Time Regained in Canonical General Relativity
• A loop quantum multiverse?
• Challenges for Emergent Gravity
• Problem of Time: Facets and Machian Strategy
• A New Approach to Quantising Space-Time: I. Quantising on a General Category

Cited by in corpus (35)

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• The Smallest Shape Spaces. II. 4 Points in 1-d Suffices to have a Complex Background-Independent Theory of Inhomogeneity
• Configuration Spaces in Fundamental Physics
• TRiPoD (Temporal Relationalism incorporating Principles of Dynamics)
• A Local Resolution of the Problem of Time. III. The other classical facets piecemeal
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• A Local Resolution of the Problem of Time. VII. Constraint Closure
• Geometry from Brackets Consistency
• $N$-Body Problem: Minimal $N$'s for Qualitative Nontrivialities
• Problem of Time and Background Independence: classical version's higher Lie Theory
• Specific PDEs for Preserved Quantities in Geometry. III. 1-d Projective Transformations and Subgroups
• Specific PDEs for Preserved Quantities in Geometry. II. Affine Transformations and Subgroups
• A Local Resolution of the Problem of Time. XIV. Grounding on Lie's Mathematics
• Where to Apply Relationalism
• Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets Completed
• Topological Shape Theory
• Background Independence: ${\mathbb{S}}^1$ and $\mathbb{R}$ absolute spaces differ greatly in Shape-and-Scale Theory
• We have time because we shall never know
• Quadrilaterals in Shape Theory. II. Alternative Derivations of Shape Space: Successes and Limitations
• 'Shape Dynamics': Foundations Reassessed
• Isotropy Groups and Kinematic Orbits for 1 and 2-$d$ $N$-Body Problems
• A Local Resolution of the Problem of Time. VIII. Assignment of Observables
• A different perspective on the problem of time in quantum gravity