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

摘要

We propose the notion of a classical/quantumdualityin the gravitational case (it can be extended to other interactions). By this one meansexchangingBohm's quantum potential for the classical potentialVQ?Vin the stationary quantum Hamilton–Jacobi equation (QHJE) so thatVQ+V=?V0(ground state energy). Despite that the corresponding Schr?dinger equations, and their solutions differ, their associated quantum Hamilton–Jacobi equation, andgroundstate energy remains thesame. 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 classicalrepulsivegravitational potential (plus a constant). These results suggest that there might be aquantumorigin to the classicalrepulsivegravitational behavior (of the accelerated expansion) of the universe which is based on this notion of classical/quantumduality. 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.