Bohm's Potential, Classical/Quantum Duality and Repulsive Gravity

Publication date: Available online 28 November 2018Source: Physics Letters BAuthor(s): Carlos Castro PerelmanAbstractWe 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.

Source: Physics Letters B - November 29, 2018 Category: Physics Source Type: research