Time in quantum gravity by weakening the Hamiltonian constraint

TL;DR

This paper proposes a modified quantum gravity framework where the Hamiltonian constraint is weakened, enabling a time-dependent Schrödinger equation and addressing the problem of time without extra degrees of freedom.

Contribution

It introduces a new approach to quantum gravity by replacing the Hamiltonian constraint with a weaker condition, allowing for a consistent notion of time.

Findings

The theory has the correct classical limit.

It provides a viable solution to the problem of time.

Wave function phase remains time-independent in general.

Abstract

We replace the usual Hamiltonian constraint of quantum gravity H|psi>=0 by a weaker one <psi|H|psi>=0. This allows |psi> to satisfy the time-dependent functional Schrodinger equation. In general, only the phase of the wave function appears to be time independent. The resulting quantum theory has the correct classical limit and thus provides a viable theory of quantum gravity that solves the problem of time without introducing additional nongravitational degrees of freedom.