Do we live in an eigenstate of the fundamental constants operators?

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Title: Do we live in an eigenstate of the fundamental constants operators?
Authors: Barrow, JD
Magueijo, J
Item Type: Journal Article
Abstract: We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the treatment given to classical parameters in quantum information theory, at least if we were to inhabit a constants’ eigenstate. Noncommutativity introduces novelties, due to its associated uncertainty and complementarity principles, and it may even preclude Hamiltonian evolution. The system typically evolves as a quantum superposition of hamiltonian evolutions resulting from a diagonalization process, and these are usually quite distinct from the original one (defined in terms of the noncommuting constants). We present several examples targeting G, c, and Λ, and the dynamics of homogeneous and isotropic Universes. If we base our construction on the Heisenberg algebra and the quantum harmonic oscillator, the alternative dynamics tends to silence matter (effectively setting G to zero), and make curvature and the cosmological constant act as if their signs are reversed. Thus, the early Universe expands as a quantum superposition of different Milne or de Sitter expansions for all material equations of state, even though matter nominally dominates the density, ρ, because of the negligible influence of Gρ on the dynamics. A superposition of Einstein static universes can also be obtained. We also investigate the results of basing our construction on the algebra of SU(2), into which we insert information about the sign of a constant of Nature, or whether its action is switched on or off. In this case we find examples displaying quantum superpositions of bounces at the initial state for the Universe.
Issue Date: 15-Jan-2019
Date of Acceptance: 1-Jan-2019
ISSN: 2470-0010
Publisher: American Physical Society
Journal / Book Title: Physical Review D
Volume: 99
Issue: 2
Copyright Statement: © 2019 American Physical Society.
Keywords: Science & Technology
Physical Sciences
Astronomy & Astrophysics
Physics, Particles & Fields
Publication Status: Published
Article Number: 023509
Online Publication Date: 2019-01-04
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences

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