EMERGENT GEOMETRY AND QUANTUM GRAVITY

We explain how quantum gravity can be defined by quantizing spacetime itself. A pin-point 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.