Toward a Background Independent Quantum Theory of Gravity

TL;DR

This paper proposes a background independent, non-perturbative geometric framework for quantum gravity, integrating statistical and symplectic geometries as dynamical entities, and offers insights into fundamental issues like observables and the cosmological constant.

Contribution

It introduces a novel geometric formulation of quantum gravity that treats statistical and symplectic geometries as dynamical, advancing understanding of key quantum gravity problems.

Findings

Provides a background independent formulation of quantum gravity.

Offers a new perspective on the problem of time and observables.

Suggests a rationale for the smallness of the cosmological constant.

Abstract

Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a novel, background independent non-perturbative formulation of quantum gravity. We invoke a quantum version of the equivalence principle, which requires both the statistical and symplectic geometries of canonical quantum theory to be fully dynamical quantities. Our approach sheds new light on such basic issues of quantum gravity as the nature of observables, the problem of time, and the physics of the vacuum. In particular, the observed numerical smallness of the cosmological constant can be rationalized in this approach.