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  1. Quantum Solitodynamics: Non-linear Wave Mechanics and Pilot-Wave Theory.Aurélien Drezet - 2023 - Foundations of Physics 53 (1):1-45.
    In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandoned. Here we propose a nonlinear scalar field theory able (...)
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  • The effect of localization on interference. II. Bearing on locality violation and the interpretation of quantum mechanics.Charles E. Engelke - 1986 - Foundations of Physics 16 (9):917-921.
    In a two-channel interference experiment such as that considered in the preceding companion paper, a quantum may be localizable predominantly in one channel by a time-coincident experiment on a correlated quantum. The Copenhagen interpretation of quantum mechanics then requires a coincidence intensity prediction having the same reduced interference between channels as if the probability amplitude in the other channel had been attenuated by a filter. The quantum mechanical treatment of correlated systems originated by von Neumann does predict this reduced interference, (...)
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  • On the existence of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞ in nature.Waldyr A. Rodrigues & Jian-Yu Lu - 1997 - Foundations of Physics 27 (3):435-508.
    We present the theory, the experimental evidence and fundamental physical consequences concerning the existence of families of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞, which are solutions of the homogeneuous wave equation, the Maxwell equations, and Dirac, Weyl, and Klein-Gordon equations.
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  • Testing de Broglie’s Double Solution in the Mesoscopic Regime.T. Durt - 2022 - Foundations of Physics 53 (1):1-19.
    We present here solutions of a non-linear Schrödinger equation in presence of an arbitrary linear external potential. The non-linearity expresses a self-focusing interaction. These solutions are the product of the pilot wave with peaked solitons the velocity of which obeys the guidance equation derived by Louis de Broglie in 1926. The degree of validity of our approximations increases when the size of the soliton decreases and becomes negligible compared to the typical size over which the pilot wave varies. We discuss (...)
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