1201.3164 (Chopin Soo et al.)

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

Chopin Soo, Hoi-Lai Yu

The framework of a theory of gravity from quantum to classical regimes is presented. The paradigm shift from full space-time covariance to spatial diffeomorphism invariance, together with master constraint formulation and clean decomposition of the canonical structure, yield transparent physical dynamics and a resolution of the problem of time. All Kuchar observables become physical. The deep divide between quantum mechanics and conventional canonical formulations with Klein-Gordon type Wheeler-DeWitt equations is overcome with a Schrodinger equation with positive semi-definite probability density at any instant of intrinsic time. Not only is time-ordering possible, complete formulation in the Heisenberg picture with unitary and diffeomorphism invariant evolution operator is also viable. The Hamilton-Jacobi equation is also first order in intrinsic time, with the implication of completeness. Classical space-time with direct correlation between its proper times and intrinsic time intervals emerges from constructive interference. The framework not only yields a physical Hamiltonian for Einstein's theory, but also prompts natural extensions and improvements towards a well-behaved quantum theory of gravity.

View original: http://arxiv.org/abs/1201.3164