Foundations of Physics

, Volume 42, Issue 9, pp 1210–1238

The Role of Time in Relational Quantum Theories

Article

Abstract

We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical dynamics of the system and must therefore be deemed inappropriate. We propose a new strategy for consistently quantizing systems with a relational notion of time that does capture the full classical dynamics of the system and allows for evolution parametrized by an equitable internal clock. This proposal contains the minimal temporal structure necessary to retain the ordering of events required to describe classical evolution. In the context of shape dynamics (an equivalent formulation of general relativity that is locally scale invariant and free of the local problem of time) our proposal can be shown to constitute a natural methodology for describing dynamical evolution in quantum gravity and to lead to a quantum theory analogous to the Dirac quantization of unimodular gravity.

Keywords

Problem of time Relationalism Quantum gravity Constraint quantization Reparametrization invariance Internal time 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsUtrecht UniversityUtrechtNetherlands
  2. 2.Centre for Time, Department of PhilosophyUniversity of SydneySydneyAustralia

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