Perspectives of Bohm's Quantum Potential Towards a Geometrodynamic Interpretation of Quantum Physics. A Critical Survey

In virtue of its features, Bohm's quantum potential introduces relevant perspectives towards a satisfactory geometrodynamic picture of quantum processes. In this paper the geometry subtended by the quantum potential is explored, both in the non-relativistic domain and in the relativistic domain and in the quantum gravity domain and in canonical quantum cosmology. As regards the non-relativistic domain, the geometrodynamic nature of the quantum potential corresponding with its space-like, non-local, active information on the environment is analysed. As regards the relativistic de Broglie-Bohm theory in a curved space-time, the geometrical features of the quantum as well as the gravitational effects of matter and their link are examined on the basis of some recent results. As regards the quantum gravity domain, a generalized geometrical unification of gravitational and quantum effects of matter obtained by means of the quantum potential is explored. Then, some considerations about the geometrodynamic features of the quantum potential in canonical quantum cosmology are made. In the second part of the paper, it is shown that, on the basis of some current research, Bohm's quantum potential and its geometry can receive a new suggestive interpretation. In particular, the following interesting perspectives are analysed. On one hand, that the geometrodynamic features of the quantum potential can be seen as a consequence of a more fundamental entity called "quantum entropy." On the other hand, that the geometrodynamic features of the quantum potential lead to a three-dimensional space as a fundamental arena of physical processes in the context of a symmetrized quantum potential: in the quantum domain three-dimensional space acts as an immediate information medium between subatomic particles.