Quantization of emergent gravity

Abstract

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 far as space–time admits a symplectic structure, in other words, a microscopic space–time becomes noncommutative (NC). If gravity emerges from U(1) gauge theory on NC space–time, this picture of emergent gravity suggests a completely new quantization scheme where quantum gravity is defined by quantizing space–time itself, leading to a dynamical NC space–time. Therefore the quantization of emergent gravity 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 space–time and matter fields are equally emergent from a universal vacuum of quantum gravity.