The Dispersion of Newton's Constant: A Transfer Matrix Formulation of Quantum Gravity

TL;DR

This paper introduces a transfer matrix approach to quantum gravity, revealing that the universe's non-stationary state implies Newton's constant varies, with the Planck mass linked to eigenvalues of an evolution operator.

Contribution

It proposes a novel transfer matrix formalism for reparametrization invariant theories like quantum gravity, connecting stationary states to eigenvalues of an evolution operator.

Findings

Stationary states satisfy Wheeler-DeWitt equations with varying Planck mass.

The Planck mass squared is proportional to the eigenvalue of the evolution operator.

The universe's non-stationarity indicates Newton's constant is not fixed.

Abstract

A transfer matrix formalism applicable to certain reparametrization invariant theories, including quantum gravity, is proposed. In this formulation it is found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt equation, but each with a different value of the Planck mass; the value $m_{Planck}^4$ turns out to be proportional to the eigenvalue of the evolution operator. As a consequence, the fact that the Universe is non-stationary implies that it is not in an eigenstate of Newton's constant.