Semiclassical gravity in the de Broglie-Bohm theory and the double scale theory

TL;DR

This paper introduces a new semiclassical gravity framework within a double scale interpretation of quantum mechanics, involving dual wave functions per particle, and derives equations that unify quantum and classical gravitational descriptions.

Contribution

It develops the Einstein-de Broglie equations for semiclassical gravity based on a novel double scale quantum interpretation, extending the de Broglie-Bohm theory with internal and external wave functions.

Findings

The Einstein-de Broglie equations generalize semiclassical gravity with dual wave functions.

The equations reduce to Newtonian gravity as Planck's constant approaches zero.

The framework provides a theoretical validation for the Newton-de Broglie equations.

Abstract

We present a semiclassical gravity in the framework of the double scale theory, a new interpretation of quantum mechanics which expands on the de Broglie-Bohm (dBB) theory. In this interpretation, any quantum system is associated with two wave functions, one external and one internal. The external wave function drives the center-of-mass, as in the dBB theory, and spreads with time. The internal wave function corresponds to the density of an extended particle. It remains confined in space and its average position corresponds to the center of mass of the particle. We define, for an N-body system, new semi-classical gravity equations called Einstein-de Broglie equations. The external wave function of each body depends only on the internal wave functions of the N--1 others. They are deduced from Einstein's semi-classical equation by using the internal wave functions instead of the usual wave function. If we restrict to the dBB interpretation, we find the Newton-de Broglie equations that Struyve and Lalo{\"e} have recently proposed independently. We show that the Newton-de Broglie and Einstein-de Broglie equations converge to Newton's gravity when h $\rightarrow$ 0, which gives a theoretical validation.