Equivalence Postulate and Quantum Origin of Gravitation

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 hbar \to 0. A number of questions are raised for further investigation.

1+19 pages, minor changes and typos corrected, to appear in Found. Phys. Lett

References in corpus (2)

• Equivalence Principle, Higher Dimensional Moebius Group and the Hidden Antisymmetric Tensor of Quantum Mechanics
• About Some Problems Raised by the Relativistic Form of De-Broglie--Bohm Theory of Pilot Wave

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• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
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