Equivalence Postulate and Quantum Origin of Gravitation

TL;DR

This paper explores the idea that quantum mechanics and gravity are fundamentally connected, proposing that the quantum potential could be the origin of gravitational interaction, based on the equivalence postulate framework.

Contribution

It introduces a novel approach linking quantum potential to gravity using the quantum Hamilton-Jacobi equation and the equivalence postulate, suggesting gravity may emerge from quantum effects.

Findings

Quantum potential is always non-trivial for free particles.

Quantum potential may generate gravitational potential.

Preliminary solutions suggest a link between quantum potential and gravity.

Abstract

We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton-Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may generate the gravitational potential. The investigation, related to the formulation of quantum mechanics based on the equivalence postulate, is based on the analysis of the reduced action. A consequence of this approach is that the quantum potential is always non-trivial even in the case of the free particle. It plays the role of intrinsic energy and may in fact be at the origin of fundamental interactions. We pursue this idea, by making a preliminary investigation of whether there exists a set of solutions for which the quantum potential can be expressed with a gravitational potential leading term which alone would remain in the limit hbar \to 0. A number of questions are raised for further investigation.