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arXiv:1004.3240 · AIP conference proceedings

Geometrizing the Quantum—A Toy Model

Benjamin Koch, Jerzy Kowalski-Glikman, R. Durka, M. Szczachor

Published Jan 1, 2009• 5 citations
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Abstract

It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally “curved” space‐time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.

DOI
10.1063/1.3284379

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It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally “curved” space‐time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.
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The de Broglie–Bohm theory allows us to have got a satisfactory geometrodynamic interpretation of quantum mechanics. The fundamental element, which creates a geometrodynamic picture of the quantum world in the non-relativistic domain, a relativistic curved space-time background, and the quantum gravity domain, is the quantum potential. It is shown that, in the non-relativistic domain, the geometrodynamic nature of the quantum potential followsfrom the fact that it is an information potential containing a space-like active information on the environment; the geometric properties of the space expressed by the quantum potential determine non-local correlations between subatomic particles. Moreover, in the de Broglie–Bohm theory in a curved space-time, it is shown that the quantum, as well as the gravitational, effects of matter have geometric nature and are highly related: the quantum potential can be interpreted as the conformal degree of freedom of the space-time metric, and its presence is equivalent to the curved space-time. It is shown on the basis of some recent research that, in quantum gravity, we have a generalized geometric unification of gravitational and quantum effects of matter; Bohm's interpretation shows that the form of a quantum potential and its relation to the conformal degree of freedom of the space-time metric can be derived from the equations of motion.