Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets Completed

Abstract

Temporal Relationalism (TR) is that there is no time for the universe as a whole at the primary level. Time emerges rather at a secondary level; one compelling idea for this is Mach's `time is to be abstracted from change'. TR leads to, and better explains, the well-known Frozen Formalism Problem encountered in GR at the quantum level. Indeed, abstraction from change is a type of emergent time resolution of this.Moreover, the Frozen Formalism Problem is but one of the many Problem of Time facets, which are furthermore notoriously interconnected. The other local and already classically present facets are as follows. 2) The GR Thin Sandwich involves a subcase of Best Matching, which is one particular implementation of Configurational Relationalism. 3) The Constraint Closure Problem, 4) the Problem of Observables or Beables, 5) Spacetime Relationalism, 6) the Spacetime Construction Problem, and 7) the Foliation Dependence Problem as resolved in classical GR by Refoliation Invariance. In this Article, I bring together the individual classical resolutions of these, and how these can be rendered compatible with TR. Having covered that in detail for 2) to 6) elsewhere, the rest of the current Article is dedicated to the detailed form that 7) and its TR compatible modification takes. I.e. I consider TR implementing foliations, the TR versions of Refoliation Invariance and the associated TR version of hypersurface kinematics and hypersurface deformations. These require a TR counterpart of the Arnowitt--Deser--Misner split.

arXiv comment28 pages including 13 figures

References in corpus (22)

• The Dynamics of General Relativity
• Problem of Time in Quantum Gravity
• The Problem of Time in Quantum Gravity
• The Superspace of Geometrodynamics
• The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena
• Beables/Observables in Classical and Quantum Gravity
• Foundations of Relational Particle Dynamics
• Problem of Time and Background Independence: the Individual Facets
• New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
• Conformal Superspace: the configuration space of general relativity
• Classical Machian Resolution of the Spacetime Reconstruction Problem
• Does relationalism alone control geometrodynamics with sources?
• Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
• Machian Time Is To Be Abstracted From What Change?
• Explicit partial and functional differential equations for beables or observables
• On Background Independence
• Configuration Spaces in Fundamental Physics
• TRiPoD (Temporal Relationalism incorporating Principles of Dynamics)
• Covariance and Time Regained in Canonical General Relativity
• Origin of Structure in the Universe: Quantum Cosmology Reconsidered
• Problem of Time: Facets and Machian Strategy
• Where to Apply Relationalism

Cited by in corpus (5)

• A Local Resolution of the Problem of Time
• A Local Resolution of the Problem of Time. III. The other classical facets piecemeal
• A Local Resolution of the Problem of Time. I. Introduction and Temporal Relationalism
• A Local Resolution of the Problem of Time. IV. Quantum outline and piecemeal Conclusion
• Spaces of Observables from Solving PDEs. I. Translation-Invariant Theory