General relativity without paradigm of space-time covariance: Sensible quantum gravity and resolution of the “problem of time”

Chopin Soo, Hoi Lai Yu

研究成果: Conference contribution

摘要

Covariance of space and time in General Relativity (GR) entails a number of technical and conceptual difficulties. Remarkably, these can be resolved by a paradigm shift from full 4-dimensional general coordinate invariance to invariance only with respect to spatial diffeomorphisms. The framework for a theory of gravity with this paradigm shift, from quantum to classical regimes, is presented; GR is contained as a special case. Appositely formulated as a master constraint, the Hamiltonian constraint now determines only dynamics; and is relieved of its dual role of generating symmetry transformations. The Dirac algebra, in which 4-dimensional diffeomorphism symmetry is only realized on-shell, is replaced by the master constraint algebra which possesses only spatial diffeomorphism gauge symmetry, both on- and off-shell. Decomposition of the spatial metric into unimodular and determinant, q, factors results in mutually commuting pairs of canonical variables. The classical content of GR can be captured with a Hamiltonian constraint linear in the trace of the momentum. This implies a theory of quantum gravity can be described by a Schrodinger equation first order in intrinsic time ln q accompanied with positive semi-definite probability density. The semi-classical Hamilton-Jacobi equation is also first order in intrinsic time, with the implication of being complete; and gauge- invariant physical observables can be constructed from integration constants of its complete integral solution. Classical space-time, with direct correlation of its proper times and intrinsic time intervals, emerges from constructive interference; and the physical con- tent of GR can be regained from a theory with a true Hamiltonian generating intrinsic time translations, but with only spatial diffeomorphism symmetry. The framework also prompts natural extensions towards a well-behaved quantum theory of gravity.

原文English
主出版物標題1st LeCosPA Symposium
主出版物子標題Towards Ultimate Understanding of the Universe, LeCosPA 2012
編輯Pisin Chen
發行者World Scientific Publishing Co. Pte Ltd
頁面76-87
頁數12
ISBN(電子)9789814449366
DOIs
出版狀態Published - 2013
事件1st Leung Center for Cosmology and Particle Astrophysics Symposium, LeCosPA 2012 - Taipei, Taiwan
持續時間: 2012 二月 62012 二月 9

出版系列

名字1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012

Other

Other1st Leung Center for Cosmology and Particle Astrophysics Symposium, LeCosPA 2012
國家Taiwan
城市Taipei
期間12-02-0612-02-09

All Science Journal Classification (ASJC) codes

  • Space and Planetary Science
  • Physics and Astronomy(all)

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