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Emergent Geometry and Quantum Gravity · Around

2010

Emergent Geometry and Quantum Gravity

Yang, Hyun Seok

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We explain how quantum gravity can be defined by quantizing spacetime itself.

A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P.
The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of symplectic structure \omega in terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g.
This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.

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