Mechanical analogy for the wave-particle: Helix on a vortex filament. (English) Zbl 1007.81004

Summary: The small amplitude-to-thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as de Broglie wave. The complex-valued algebra of quantum mechanics finds a simple mechanical interpretation in terms of differential geometry of the space curve. The wave function takes the meaning of the velocity, with which the helix rotates about the screw axis. The helices differ in type of the screw–right- or left-handed. Two kinds of the helical waves deflect in the inhomogeneous fluid vorticity field in the same way as spin particles in the Stern-Gerlach experiment.


81P05 General and philosophical questions in quantum theory
76B25 Solitary waves for incompressible inviscid fluids
35Q55 NLS equations (nonlinear Schrödinger equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy
76B47 Vortex flows for incompressible inviscid fluids
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