General Relativity without paradigm of space-time covariance: sensible quantum gravity and resolution of the "problem of time"

Details General Relativity without paradigm of space-time covariance: sensible quantum gravity and resolution of the "problem of time" General Relativity without paradigm of space-time covariance: sensible quantum gravity and resolution of the "problem of time"

2012-01-16

arxiv.org/abs/1201.3164v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

Covariance of space and time in General Relativity (GR) entails a number of technical and conceptual difficulties. These can be resolved by a paradigm shift from full 4-dimensional general coordinate invariance to invariance only with respect to spatial diffeomorphisms. 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, and the consequent baggage of multi-fingered evolution with arbitrary lapse functions is absent. The Dirac algebra, with 4-dimensional diffeomorphism symmetry 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 clean separation of the canonical variables. The classical content of GR can be captured with a Hamiltonian constraint linear in the trace of the momentum; with the quantum theory 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 completeness; and gauge-invariant 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 content 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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