Mechanical Analogy for the Wave-Particle: Helix on a Vortex Filament
| Scientific Paper | |
|---|---|
| Title | Mechanical Analogy for the Wave-Particle: Helix on a Vortex Filament |
| Read in full | Link to paper |
| Author(s) | Valery P Dmitriyev |
| Keywords | quantum physics, ideal fluid, line vortex, soliton. |
| Published | 2001 |
| Journal | Apeiron |
| Volume | 8 |
| Number | 2 |
| No. of pages | 31 |
| Pages | 1-31 |
Read the full paper here
Abstract
The small amplitude-to-thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as a 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. The helix represents the low curvature asymptotics of a loop-shaped soliton, the latter being governed by the nonlinear Schroedinger equation. The length of the redundant segment, needed in order to form a curvilinear configuration on the originally straight vortex filament, measures the mass of a particle. The unique size of the loop on the vortex filament can be determined by the balance between the energy of the redundant segment and the energy due to the curvature of the loop. The translational velocity of the soliton has the maximum at a value, which is inversely proportional to the length of the redundant segment. Insofar as the maximal velocity of a soliton is restricted from the above by the speed of the perturbation wave in the turbulent medium (i.e. the speed of light in vacuum), there must be a minimal redundant segment. Its length correlates with the Planck?s constant. In the stochastic environs a loop-shaped soliton disintegrates into the collection of the elementary asymptotic helices. An asymptotic helix obeys the linear Schroedinger equation with no dependence on mass. The mass of the particle appears explicitly when we describe the motion of the whole ensemble of the elementary splinters.
