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The Two-Scale Interpretation: de Broglie and Schrödinger’s External and Internal Wave Functions

Abstract : We propose an interpretative framework for quantum mechanics inspired by Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions: an external wave function corresponding to the evolution of its center of mass along with other macroscopic degrees of freedom, and an internal wave function corresponding to the evolution of its internal variables in the center-of-mass system. These two wave functions will have different meanings and interpretations. The external wave function ``pilots'' the center of mass of the quantum system: it corresponds to the de Broglie pilot wave. For the internal wave function, we argue in favor of the interpretation proposed by Erwin Schrödinger at the Solvay Congress in 1927: the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
Keywords : quantum interpretation
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Submitted on : Thursday, March 4, 2021 - 4:26:23 PM
Last modification on : Thursday, March 11, 2021 - 6:48:17 PM

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Michel Gondran, Alexandre Gondran, Camille Noûs. The Two-Scale Interpretation: de Broglie and Schrödinger’s External and Internal Wave Functions. Annales de la Fondation Louis de Broglie, Fondation Louis de Broglie, In press. ⟨hal-02435248v2⟩

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