Bohm's potential, classical/quantum duality and repulsive gravity

Abstract:

We propose the notion of a classical/quantum duality in the gravitational case (it can be extended to other interactions). By this one means exchanging Bohm's quantum potential for the classical potential VQ↔V in the stationary quantum Hamilton–Jacobi equation (QHJE) so that VQ+V=−V0 (ground state energy). Despite that the corresponding Schrödinger equations, and their solutions differ, their associated quantum Hamilton–Jacobi equation, and ground state energy remains the same. This is how the classical/quantum duality is implemented. In this scenario Bohm's quantum potential (which coincides with the attractive Newtonian potential) is now correlated to a classical repulsive gravitational potential (plus a constant). These results suggest that there might be a quantum origin to the classical repulsive gravitational behavior (of the accelerated expansion) of the universe which is based on this notion of classical/quantum duality. We hope that the notion of classical/quantum duality raised in this work in connection to the QHJE may cast further light into the deep interplay between gravity and quantum mechanics.

Año de publicación:

2019

Keywords:

• (Repulsive) gravity
• quantum mechanics
• Bohm's potential

Fuente:

scopus