Emergent Geometry and Quantum Gravity

TL;DR

This paper proposes a background-independent approach to quantum gravity by quantizing spacetime's symplectic structure, leading to emergent geometry and matter fields from a universal quantum vacuum.

Contribution

It introduces a novel framework linking symplectic and Riemannian geometry to describe quantum gravity without background dependence.

Findings

Spacetime becomes noncommutative at the Planck scale.

Deformations of symplectic structure relate to electromagnetic fields.

Spacetime and matter emerge from a universal quantum vacuum.

Abstract

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.