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 [Formula: see text] 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, 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.