## 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 |
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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 2月 6 → 2012 2月 9 |

### 出版系列

名字 | 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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國家/地區 | Taiwan |

城市 | Taipei |

期間 | 12-02-06 → 12-02-09 |

## All Science Journal Classification (ASJC) codes

- 空間與行星科學
- 物理與天文學 (全部)