Quantum Theory of Non-Relativistic Particles Interacting with Gravity

TL;DR

This paper develops a quantum mechanical model for non-relativistic particles interacting with gravity, deriving a master equation that reveals non-local, non-Markovian effects and discusses implications for decoherence and gravity-induced collapse.

Contribution

It introduces a first-order gravitational interaction model for quantum particles using the influence functional, highlighting non-local, non-Markovian dynamics and their effects on decoherence.

Findings

Gravitational self-interaction does not cause decoherence in microscopic particles.

For macroscopic particles, gravity leads to energy eigenstate diagonalization.

The model predicts non-local, non-Markovian behavior in quantum-gravity interactions.

Abstract

We investigate the effects of the gravitational field on the quantum dynamics of non-relativistic particles. We consider N non-relativistic particles, interacting with the linearized gravitational field. Using the Feynman - Vernon influence functional technique, we trace out the graviton field, to obtain a master equation for the system of particles to first order in $G$. The effective interaction between the particles, as well as the self-interaction is non-local in time and in general non-markovian. We show that the gravitational self-interaction cannot be held responsible for decoherence of microscopic particles due to the fast vanishing of the diffusion function. For macroscopic particles though, it leads to diagonalization to the energy eigenstate basis, a desirable feature in gravity induced collapse models. We finally comment on possible applications.