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Geometrodynamics of spinning light | Nature Photonics
Volume Article Contents. Free Hamiltonian. Asymptotic behavior of the Hamiltonian at early and late intrinsic times. Early universe and Cotton—York dominance.
Initial state of the universe and Penrose's Weyl curvature hypothesis. Emergence of Einstein—Hilbert gravity. Quantum geometrodynamics redux.
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Hoi-Lai Yu. Cite Citation. Permissions Icon Permissions. Abstract Quantum geometrodynamics with intrinsic time development and momentric variables is presented. A century after the birth of Einstein's general relativity GR , successful quantization of the gravitational field remains the preeminent challenge. Geometrodynamics with a positive definite spatial metric is the simplest consistent framework to implement fundamental canonical commutation relations CR predicated on the existence of spacelike hypersurfaces.
"Geometrodynamics: The Nonlinear Dynamics of Warped Spacetime" by Kip Thorne (CalTech)
Perturbative renormalizability of GR can be attained by adding higher-derivative terms, but 4-covariance locks higher temporal and spatial derivatives to the same order, compromising the stability and unitarity of the theory [ 7 ]. Ricci curvature terms become increasingly important in the potential after the initial era of Cotton—York dominance.
They can be introduced in a manner which preserves the underlying structure which regulates the Hamiltonian by extending the Chern—Simons action with 3dDI invariants of the spatial metric. To wit, only the Einstein—Hilbert action in three dimensions and the Chern—Simons functional are relevant, i. On account of the quadratic dependence on momenta and ordering ambiguities of the Hamiltonian, which also depends on the intrinsic time, this formulation can reproduce the physics of the usual Wheeler—DeWitt WDW equation only at the classical limit, and certainly not at the quantum level.
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