Journal of Applied Mathematics
Volume 2 (2002), Issue 5, Pages 241-263

Mechanical analogy for the wave-particle: helix on a vortex filament

Valery P. Dmitriyev

Lomonosov University, P.O. Box 160, Moscow 117574, Russia

Received 22 October 2001; Revised 13 February 2002

Copyright © 2002 Valery P. Dmitriyev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.