On Background Independence

Abstract

This paper concerns what Background Independence itself is (as opposed to some particular physical theory that is background independent). The notions presented mostly arose from a layer-by-layer analysis of the facets of the Problem of Time in Quantum Gravity. Part of this coincides with two relational postulates which are thus identified as classical precursors of two of the facets of the Problem of Time. These are furthemore tied to the forms of each of the GR Hamiltonian and momentum constraints. Other aspects of Background Independence include the algebraic closure of these constraints, expressing physics in terms of beables, foliation independence as implemented by refoliation invariance, the reconstruction of spacetime from space. The final picture is that Background Independence - a philosophically desirable and physically implementable feature for a theory to have - has the facets of the Problem of Time among its consequences. Thus these arise naturally and are problems to be resolved, as opposed to avoided `by making one's physics background-dependent in order not to have these problems'. This serves as a selection criterion that limits the use of a number of model arenas and physical theories.

14 pages including 2 figures

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Cited by in corpus (15)

• Beables/Observables in Classical and Quantum Gravity
• Problem of Time and Background Independence: the Individual Facets
• Classical Machian Resolution of the Spacetime Reconstruction Problem
• The Smallest Shape Spaces. I. Shape Theory Posed, with Example of 3 Points on the Line
• The Smallest Shape Spaces. II. 4 Points in 1-d Suffices to have a Complex Background-Independent Theory of Inhomogeneity
• The Smallest Shape Spaces. III. Triangles in 2- and 3-d
• Kendall's Shape Statistics as a Classical Realization of Barbour-type Timeless Records Theory approach to Quantum Gravity
• $N$-Body Problem: Minimal $N$'s for Qualitative Nontrivialities
• Problem of Time: Facets and Machian Strategy
• Problem of Time: Temporal Relationalism Compatibility of Other Local Classical Facets Completed
• Where to Apply Relationalism
• Topological Shape Theory
• Background Independence: ${\mathbb{S}}^1$ and $\mathbb{R}$ absolute spaces differ greatly in Shape-and-Scale Theory
• 'Shape Dynamics': Foundations Reassessed
• Isotropy Groups and Kinematic Orbits for 1 and 2-$d$ $N$-Body Problems