Emergent geometry and quantum gravity

Abstract

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = LP 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 LP. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ω 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. © 2010 World Scientific Publishing Company.