Emergent Spacetime and Quantum Gravity

Emergent gravity is based on a novel form of the equivalence principle known as the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as fas as spacetime admits a symplectic structure, namely, a microscopic spacetime becomes noncommutative (NC). If gravity is emergent from U(1) gauge theory on NC spacetime, this picture of emergent gravity suggests a completely new quantization scheme where quantum gravity is defined by quantizing spacetime itself, leading to a dynamical NC spacetime, which is radically different from the conventional approach trying to quantize a phase space of metric fields. 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.