de Broglie’s double solution: limitations of the self-gravity approach

We present a semiclassical gravity in the framework of the double scale theory, a new interpretation of quantum mechanics which expands on the de Broglie-Bohm (dBB) theory. In this interpretation, any quantum system is associated with two wave functions, one external and one internal. The external wave function drives the center-of-mass, as in the dBB theory, and spreads with time. The internal wave function corresponds to the density of an extended particle. It remains confined in space and its average position corresponds to the center of mass of the particle. We define, for an N-body system, new semi-classical gravity equations called Einstein-de Broglie equations. The external wave function of each body depends only on the internal wave functions of the N--1 others. They are deduced from Einstein's semi-classical equation by using the internal wave functions instead of the usual wave function. If we restrict to the dBB interpretation, we find the Newton-de Broglie equations that Struyve and Lalo{ë} have recently proposed independently. We show that the Newton-de Broglie and Einstein-de Broglie equations converge to Newton's gravity when h $\rightarrow$ 0, which gives a theoretical validation.We present a semiclassical gravity in the framework of the double scale theory, a new interpretation of quantum mechanics which expands on the de Broglie-Bohm (dBB) theory. In this interpretation, any quantum system is associated with two wave functions, one external and one internal. The external wave function drives the center-of-mass, as in the dBB theory, and spreads with time. The internal wave function corresponds to the density of an extended particle. It remains confined in space and its average position corresponds to the center of mass of the particle. We define, for an N-body system, new semi-classical gravity equations called Einstein-de Broglie equations. The external wave function of each body depends only on the internal wave functions of the N--1 others. They are deduced from Einstein's semi-classical equation by using the internal wave functions instead of the usual wave function. If we restrict to the dBB interpretation, we find the Newton-de Broglie equations that Struyve and Lalo{ë} have recently proposed independently. We show that the Newton-de Broglie and Einstein-de Broglie equations converge to Newton's gravity when h $\rightarrow$ 0, which gives a theoretical validation.

arXiv:2302.10235Jan 23, 20230 citations

Resolving Inconsistencies in de Broglie's Relation

Pieter Wagner

Progress in physicsJan 1, 20100 citations

Quantum Geometrodynamics in the Bohm-de Broglie Interpretation

Eduardo Sergio Santini

In this thesis the Bohm-de Broglie interpretation of quantum mechanics is applied to canonical quantum gravity. It is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of quantum geometrodynamics is constructed, which allows the investigation of these latter structures. For instance, it is shown that any real solution of the Wheeler-De Witt equation yields a generate four-geometry compatible with the strong gravity limit of General Relativity and the Carroll group. We prove that quantum geometrodynamics in the Bohm-de Broglie interpretation is consistent for any quantum potential. As a previous step to introduce our metodology, we study the quantum theory of fields in Minkowski spacetime in the Bohm-de Broglie interpretation and exhibit a concrete example where Lorentz invariance of individual events is broken.In this thesis the Bohm-de Broglie interpretation of quantum mechanics is applied to canonical quantum gravity. It is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of quantum geometrodynamics is constructed, which allows the investigation of these latter structures. For instance, it is shown that any real solution of the Wheeler-De Witt equation yields a generate four-geometry compatible with the strong gravity limit of General Relativity and the Carroll group. We prove that quantum geometrodynamics in the Bohm-de Broglie interpretation is consistent for any quantum potential. As a previous step to introduce our metodology, we study the quantum theory of fields in Minkowski spacetime in the Bohm-de Broglie interpretation and exhibit a concrete example where Lorentz invariance of individual events is broken.

arXiv:gr-qc/0005092May 22, 20001 citation

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0, which gives a theoretical validation.