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Equivalence Postulate and Quantum Origin of Gravitation
Authors:Marco Matone
Institution:(1) Department of Physics ldquoG. Galilei,rdquo Istituto Nazionale di Fisica Nucleare, University of Padova, Via Marzolo, 8, 35131 Padova, Italy
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 hstrokrarr0. A number of questions are raised for further investigation.
Keywords:quantum Hamilton–  Jacobi equation  quantum potential  classical limit  gravity
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