General relativity without paradigm of space-time covariance

Sensible quantum gravity and resolution of the “problem of time”

Cho-Pin Soo, Hoi Lai Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publication1st LeCosPA Symposium
Subtitle of host publicationTowards Ultimate Understanding of the Universe, LeCosPA 2012
EditorsPisin Chen
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages76-87
Number of pages12
ISBN (Electronic)9789814449366
Publication statusPublished - 2013 Jan 1
Event1st Leung Center for Cosmology and Particle Astrophysics Symposium, LeCosPA 2012 - Taipei, Taiwan
Duration: 2012 Feb 62012 Feb 9

Publication series

Name1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012

Other

Other1st Leung Center for Cosmology and Particle Astrophysics Symposium, LeCosPA 2012
CountryTaiwan
CityTaipei
Period12-02-0612-02-09

Fingerprint

relativity
gravity
gravitation
symmetry
paradigm shift
gauge
invariance
algebra
shell
Hamilton-Jacobi equation
commuting
shift
determinants
quantum theory
momentum
decomposition
intervals
interference

All Science Journal Classification (ASJC) codes

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

Cite this

Soo, C-P., & Yu, H. L. (2013). General relativity without paradigm of space-time covariance: Sensible quantum gravity and resolution of the “problem of time”. In P. Chen (Ed.), 1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012 (pp. 76-87). (1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012). World Scientific Publishing Co. Pte Ltd.
Soo, Cho-Pin ; Yu, Hoi Lai. / General relativity without paradigm of space-time covariance : Sensible quantum gravity and resolution of the “problem of time”. 1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012. editor / Pisin Chen. World Scientific Publishing Co. Pte Ltd, 2013. pp. 76-87 (1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012).
@inproceedings{dc9ec8a0f74a4274845d6a5b176f707c,
title = "General relativity without paradigm of space-time covariance: Sensible quantum gravity and resolution of the “problem of time”",
abstract = "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.",
author = "Cho-Pin Soo and Yu, {Hoi Lai}",
year = "2013",
month = "1",
day = "1",
language = "English",
series = "1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012",
publisher = "World Scientific Publishing Co. Pte Ltd",
pages = "76--87",
editor = "Pisin Chen",
booktitle = "1st LeCosPA Symposium",
address = "Singapore",

}

Soo, C-P & Yu, HL 2013, General relativity without paradigm of space-time covariance: Sensible quantum gravity and resolution of the “problem of time”. in P Chen (ed.), 1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012. 1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012, World Scientific Publishing Co. Pte Ltd, pp. 76-87, 1st Leung Center for Cosmology and Particle Astrophysics Symposium, LeCosPA 2012, Taipei, Taiwan, 12-02-06.

General relativity without paradigm of space-time covariance : Sensible quantum gravity and resolution of the “problem of time”. / Soo, Cho-Pin; Yu, Hoi Lai.

1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012. ed. / Pisin Chen. World Scientific Publishing Co. Pte Ltd, 2013. p. 76-87 (1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - General relativity without paradigm of space-time covariance

T2 - Sensible quantum gravity and resolution of the “problem of time”

AU - Soo, Cho-Pin

AU - Yu, Hoi Lai

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85032569018&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032569018&partnerID=8YFLogxK

M3 - Conference contribution

T3 - 1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012

SP - 76

EP - 87

BT - 1st LeCosPA Symposium

A2 - Chen, Pisin

PB - World Scientific Publishing Co. Pte Ltd

ER -

Soo C-P, Yu HL. General relativity without paradigm of space-time covariance: Sensible quantum gravity and resolution of the “problem of time”. In Chen P, editor, 1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012. World Scientific Publishing Co. Pte Ltd. 2013. p. 76-87. (1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012).