Double-scale theory

Michel Gondran (1) , Alexandre Gondran (2)

1 AEIS - Académie Européenne Interdisciplinaire des Sciences
2 ENAC - Ecole Nationale de l'Aviation Civile

We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the laboratory reference frame : an external wave function and an internal one. The external wave function is the wave function of the center-of-mass, as for the dBB theory : the wave is a field that pilots the center-of-mass of the quantum system. The external wave spreads out in space over time. Mathematically, the Schrödinger equation converges to the Hamilton-Jacobi statistical equations when the Planck constant tends towards zero and the Newton trajectories are therefore approximations of the dBB trajectories. The simultaneous existence of an internal wave function, in addition to the external one, is the original element of our theory. This internal wave corresponds to the interpretation proposed by Edwin Schrödinger for whom the particle is extended. Then, the internal wave remains confined in space. Its converges, when h→0, to a Dirac distribution. Moreover, the configuration space of dimension 3N of the internal wave function can be written as the product of N individual internal wave functions of dimension 3.

Mots clés: Quantum; Bohmian mechanics; Double scale; De Broglie-Bohm

Domaines: Physique Générale [physics.gen-ph]

Michel Gondran, Alexandre Gondran. Double-scale theory. 2023. ⟨hal-03960495v1⟩