Fundamental decoherence from relational time in discrete quantum gravity: Galilean covariance

Rodolfo Gambini, Rafael A. Porto, and Jorge Pullin
Phys. Rev. D 70, 124001 – Published 1 December 2004

Abstract

We have recently argued that if one introduces a relational time in quantum mechanics and quantum gravity, the resulting quantum theory is such that pure states evolve into mixed states. The rate at which states decohere depends on the energy of the states. There is therefore the question of how this can be reconciled with Galilean invariance. More generally, since the relational description is based on objects that are not Dirac observables, the issue of covariance is of importance in the formalism as a whole. In this note we work out an explicit example of a totally constrained, generally covariant system of nonrelativistic particles that shows that the formula for the relational conditional probability is a Galilean scalar and therefore the decoherence rate is invariant.

  • Received 16 August 2004

DOI:https://doi.org/10.1103/PhysRevD.70.124001

©2004 American Physical Society

Authors & Affiliations

Rodolfo Gambini1, Rafael A. Porto2, and Jorge Pullin3

  • 1Instituto de Física, Facultad de Ciencias, Iguá 4225, esq. Mataojo, Montevideo, Uruguay
  • 2Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
  • 3Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA

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Issue

Vol. 70, Iss. 12 — 15 December 2004

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