Quantum Geometrodynamics I: Quantum-Driven Many-Fingered Time

TL;DR

This paper introduces a novel approach to quantum gravity that derives the concept of time from expectation-value constraints, leading to different predictions and resolving interpretational issues in quantum gravity.

Contribution

It presents a new quantization method for gravity based on expectation-value equations, addressing the problem of time and anisotropy in quantum gravity.

Findings

Different predictions from Dirac and ADM quantizations

Avoids interpretational issues of the problem of time

Applied to two examples illustrating the approach

Abstract

The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the constraints as expectation-value equations over the true dynamical degrees of freedom of the gravitational field -- a representation of the underlying anisotropy of space. This self-consistent approach leads to qualitatively different predictions than the Dirac and the ADM quantizations, and in addition, our theory avoids the interpretational conundrums associated with the problem of time in quantum gravity. We briefly describe the structure of our functional equations, and apply our quantization technique to two examples so as to illustrate the basic ideas of our approach.