Relativistic Hydrodynamic Interpretation of de Broglie Matter Waves

We present a classical hydrodynamic analog of free relativistic quantum particles inspired by de Broglie’s pilot wave theory and recent developments in hydrodynamic quantum analogs. The proposed model couples a periodically forced Klein–Gordon equation with a nonrelativistic particle dynamics equati...

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Bibliographic Details
Published in:Foundations of physics 2023-02, Vol.53 (1), Article 20
Main Author: Dagan, Yuval
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Classical Mechanics
History and Philosophical Foundations of Physics
Klein-Gordon equation
Matter waves
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativistic effects
Relativistic particles
Relativity Theory
Statistical Physics and Dynamical Systems
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Summary:We present a classical hydrodynamic analog of free relativistic quantum particles inspired by de Broglie’s pilot wave theory and recent developments in hydrodynamic quantum analogs. The proposed model couples a periodically forced Klein–Gordon equation with a nonrelativistic particle dynamics equation. The coupled equations may represent both quantum particles and classical particles driven by the gradients of locally excited Faraday waves. Exact stationary solutions of the coupled system reveal a highly nonlinear mechanism responsible for the self-propulsion of free particles, leading to the onset of unsteady motion. Although the model is essentially nonrelativistic, a stabilizing mechanism for any particle traveling close to the wave signaling speed emerges through the coupling with the wavefield. Consequently, inline particle oscillations comparable to de Broglie’s wavelength are realized through this fully-classical model, suggesting a new classical interpretation for the motion of relativistic quantum particles.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-022-00657-8