Newton and de Broglie

Jean Pierre Vigier

Nizar Hamdan

Nobody appears to have ever asked the question of how de Broglie's theroy (1) could be proven generally valid and developed from physical laws. Therefore, we will start from the classical Newton's second law (NSL) to rebuilt the therory of special relativity (SRT) (2). This enables us to derive de Broglie relations from NSL without any of the well-known contradictions between SRT and de Broglie's quantum wave..

H. Bacry, Banesh Hoffmann

Michel Gondran, Alexandre Gondran

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.

Marie-Antoinette Tonnelat

Josef Klusoň

This paper is devoted to the analysis of massive particle in general and Newton–Cartan Background in de Broglie–Bohm theory. We find classical and quantum version of Hamilton–Jacobi equations and their relations to wave equations. We also discuss fundamental difference between classical and quantum description of these two systems.