### 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 language | English |
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Title of host publication | 1st LeCosPA Symposium |

Subtitle of host publication | Towards Ultimate Understanding of the Universe, LeCosPA 2012 |

Editors | Pisin Chen |

Publisher | World Scientific Publishing Co. Pte Ltd |

Pages | 76-87 |

Number of pages | 12 |

ISBN (Electronic) | 9789814449366 |

Publication status | Published - 2013 Jan 1 |

Event | 1st Leung Center for Cosmology and Particle Astrophysics Symposium, LeCosPA 2012 - Taipei, Taiwan Duration: 2012 Feb 6 → 2012 Feb 9 |

### Publication series

Name | 1st LeCosPA Symposium: Towards Ultimate Understanding of the Universe, LeCosPA 2012 |
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### Other

Other | 1st Leung Center for Cosmology and Particle Astrophysics Symposium, LeCosPA 2012 |
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Country | Taiwan |

City | Taipei |

Period | 12-02-06 → 12-02-09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*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.

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference 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.

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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 -