The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena

Abstract

This article contains a local solution to the notorious Problem of Time in Quantum Gravity at the conceptual level and which is actually realizable for the relational triangle. The Problem of Time is that `time' in GR and `time' in ordinary quantum theory are mutually incompatible notions, which is problematic in trying to put these two theories together to form a theory of Quantum Gravity. Four frontiers to this resolution in full GR are identified, alongside three further directions not yet conquered even for the relational triangle. This article is also the definitive review on relational particle models originally due to Barbour (2003: dynamics of pure shape) and Barbour and Bertotti (1982: dynamics of shape and scale). These are exhibited as useful toy models of background independence, which I argue to be the `other half' of GR to relativistic gravitation, as well as the originator of the Problem of Time itself. Barbour's work and my localized extension of it are shown to be the classical precursor of the background independence that then manifests itself at the quantum level as the full-blown Problem of Time. In fact 7/8ths of the Isham--Kuchar Problem of Time facets are already present in classical GR; even classical mechanics in relational particle mechanics formulation exhibits 5/8ths of these! In addition to Isham, Kuchar and Barbour, the other principal authors whose works are drawn upon in building this Problem of Time approach are Kendall (relational models only: pure-shape configuration spaces), Dirac, Teitelboim and Halliwell (Problem of Time resolving components). The recommended scheme is a combination of the Machian semiclassical approach, histories theory and records theory.

This v3 is a v substantial upgrade: previous v's did not yet announce a local solution, we're up by 77 pages (to 386) & by 35 figs (to 93). It is now a quartet of Theses, the Problem of Time one of v1 splitting into cl and qm parts. I Cl RPM's. II Cl Problem of Time. III QM RPM's. IV QM Problem of Time. Contains over 100 interesting & foundational suggestions for future projects

References in corpus (1)

• Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics

Cited by in corpus (60)

• Problem of Time in Quantum Gravity
• Conceptual Problems in Quantum Gravity and Quantum Cosmology
• Beables/Observables in Classical and Quantum Gravity
• Effective relational dynamics of a nonintegrable cosmological model
• A Shape Dynamics Tutorial
• Problem of Time and Background Independence: the Individual Facets
• The role of time in relational quantum theories
• Classical Machian Resolution of the Spacetime Reconstruction Problem
• Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
• Explicit partial and functional differential equations for beables or observables
• A Local Resolution of the Problem of Time
• Machian Time Is To Be Abstracted From What Change?
• On Types of Observables in Constrained Theories
• The Smallest Shape Spaces. I. Shape Theory Posed, with Example of 3 Points on the Line
• The Smallest Shape Spaces. III. Triangles in 2- and 3-d
• 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
• On Background Independence
• TRiPoD (Temporal Relationalism incorporating Principles of Dynamics)
• Scale Anomaly as the Origin of Time
• A Local Resolution of the Problem of Time. III. The other classical facets piecemeal
• A Local Resolution of the Problem of Time. IV. Quantum outline and piecemeal Conclusion
• Alice in Triangleland: Lewis Carroll's Pillow Problem and Variants Solved on Shape Space of Triangles
• Kendall's Shape Statistics as a Classical Realization of Barbour-type Timeless Records Theory approach to Quantum Gravity
• Origin of Structure in the Universe: Quantum Cosmology Reconsidered
• A Local Resolution of the Problem of Time. I. Introduction and Temporal Relationalism
• Specific PDEs for Preserved Quantities in Geometry. I. Similarities and Subgroups
• A Local Resolution of the Problem of Time. IX. Spacetime Constructability
• A Local Resolution of the Problem of Time. V. Combining Temporal and Configurational Relationalism for Finite Theories
• Spaces of Observables from Solving PDEs. I. Translation-Invariant Theory
• Geometry from Brackets Consistency
• Two new versions of Heron's Formula
• A Local Resolution of the Problem of Time. VII. Constraint Closure
• On the Conceptual Issues Surrounding the Notion of Relational Bohmian Dynamics
• $N$-Body Problem: Minimal $N$'s for Qualitative Nontrivialities
• Monopoles of Twelve Types in 3-Body Problems
• Maximal Angle Flow on the Shape Sphere of Triangles
• Shape (In)dependent Inequalities for Triangleland's Jacobi and Democratic-Linear Ellipticity Quantitities
• Observable Equivalence between General Relativity and Shape Dynamics
• Problem of Time: Facets and Machian Strategy
• 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
• Quantum Cosmology will need to become a Numerical Subject
• Specific PDEs for Preserved Quantities in Geometry. III. 1-d Projective Transformations and Subgroups
• Relational Mechanics as a gauge theory
• Relational Quadrilateralland. Analogues of Isospin and Hypercharge
• Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets Completed
• Where to Apply Relationalism
• Topological Shape Theory
• Kerr-Newman Black Hole Thermodynamical State Space: Blockwise Coordinates
• Background Independence: ${\mathbb{S}}^1$ and $\mathbb{R}$ absolute spaces differ greatly in Shape-and-Scale Theory
• Rubber Relationalism: Smallest Graph-Theoretically Nontrivial Leibniz Spaces
• Nambu variant of Local Resolution of Problem of Time and Background Independence
• 'Shape Dynamics': Foundations Reassessed
• Quadrilaterals in Shape Theory. II. Alternative Derivations of Shape Space: Successes and Limitations
• On the Problem of Time(s) in Quantum Mechanics and Quantum Gravity: recent integrating developments and outlook
• Comparative Theory of Background Independence
• The frame of fixed stars in Relational Mechanics
• 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