A Definition of Background Independence

Abstract

We propose a definition for background (in)/dependence in dynamical theories of the evolution of configurations that have a continuous symmetry and test this definition on particle models and on gravity. Our definition draws from Barbour's best-matching framework developed for the purpose of implementing spatial and temporal relationalism. Among other interesting theories, general relativity can be derived within this framework in novel ways. We study the detailed canonical structure of a wide range of best matching theories and show that their actions must have a local gauge symmetry. When gauge theory is derived in this way, we obtain at the same time a conceptual framework for distinguishing between background dependent and independent theories. Gauge invariant observables satisfying Kuchar's criterion are identified and, in simple cases, explicitly computed. We propose a procedure for inserting a global background time into temporally relational theories. Interestingly, using this procedure in general relativity leads to unimodular gravity.

35 pages

References in corpus (13)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Forks in the Road, on the Way to Quantum Gravity
• Relativity without relativity
• Goldstone and Pseudo-Goldstone Bosons in Nuclear, Particle and Condensed-Matter Physics
• The physical gravitational degrees of freedom
• Scale-Invariant Gravity: Particle Dynamics
• The Superspace of Geometrodynamics
• Scale-Invariant Gravity: Geometrodynamics
• New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
• Interacting vector fields in Relativity without Relativity
• Quantum Machian Time in Toy Models of Gravity
• Implementing Mach's Principle Using Gauge Theory

Cited by in corpus (8)

• Einstein gravity as a 3D conformally invariant theory
• Background-Independence
• The role of time in relational quantum theories
• Symmetry and Evolution in Quantum Gravity
• Gauge symmetry and background independence: Should the proton spin decomposition be path independent?
• Reparametrization Invariance and Some of the Key Properties of Physical Systems
• Can Bohmian Mechanics Be Made Background Independent?
• General Relativity and Background Independence