Dispersion of Newton’s constant: A transfer matrix formulation of quantum gravity

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 ${\mathit{M}}_{\mathrm{Planck}}^4$ turns out to be proportional to the eigenvalue of the evolution operator. As a consequence, the fact that the Universe is nonstationary implies that it is not in an eigenstate of Newton’s constant.