Louis de Broglie's double solution theory confirms the wave-particle duality principle

Abstract: Louis de Broglie in the beginning 20th century voices his theory of a double solution, according to which a pilot wave accompanies a particle, simulated as a point singularity, along the most optimal path from its creation on a source up to the detection. The pilot wave is a real hidden wave, which is similar to the wave function resulting from the solution of the Schrödinger equation. This theory is in agreement with de Broglie's postulate about the matter waves. In this article we mention the Helmholtz decomposition theorem according to which any velocity may be represented as a sum of two velocities -- irrotational and solenoidal ones. The first velocity stems from the gradient of the scalar field. The second occurs from a pseudo-vector field. We proclaim that the gradients of the scalar field define guiding paths of the pilot wave. While the pseudo-vector field defines a particle solenoidal filling. We give mathematical models of the irrotational and solenoidal flows simulating the position of a particle in a guiding wave. Modified Navier-Stokes equation in pair with the continuity equation resulting in the Schrödinger equation gives such solutions consisting of superposition of the irrotational and solenoidal flow

mathematical physicsgeneral physicsquantum physics

Audience: researchers in the topic

( paper | slides )

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QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

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