2004/08/16 by Rodolfo Gambini, Rafael A. Porto, Rafael Porto +1 · 2 citations
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.1103/physrevd.70.124001
published as Phys.Rev. D70 (2004) 124001 · 10 pages, RevTex
arxiv created 2004/08/16 · openalex publication_date 2004/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.