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 $ V_Q \leftrightarrow V $ in the stationary quantum Hamilton-Jacobi equation (QHJE) so that $ V_Q + V = - V_0$ ($V_0$ is the ground state energy). Despite that the corresponding Schr\{o}dinger 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 $duality$.
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