Wave mechanics for gravity with point-particles

TL;DR

This paper develops a quantum framework for gravity coupled with point particles, deriving a quantum version of Einstein's equations and exploring implications for semiclassical and quantum corrections in general relativity.

Contribution

It introduces a quantum geometrodynamics approach for point particles coupled to gravity, extending Einstein's equations with quantum contributions to the energy-momentum tensor.

Findings

Quantum Einstein equations include quantum contributions to energy-momentum tensor

Guided evolution of particles and 3-metric by the wave function

Potential for deriving semiclassical and quantum corrections

Abstract

We consider non-relativistic point-particles coupled to Einstein gravity and their canonical quantization. From the resulting Wheeler-DeWitt wave equation we determine a quantum version of geometrodynamics, where the coupled evolution of particle positions and 3-metric is guided by the wave function. We find that this quantum dynamics implies a quantum extension of the Einstein equations. The conserved energy-momentum tensor now contains a quantum contribution. This conceptually-simple set up is promising both for deriving semiclassical and weak field approximations to the quantum Einstein equations and is thus important for the development of quantum corrections to computational general relativity.