From the Newton's laws to motions of the fluid and superfluid vacuum: vortex tubes, rings, and others

摘要

Owing to three conditions (namely: (a) the velocity is represented by sum ofirrotational and solenoidal components; (b) the fluid is barotropic; (c) a bathwith the fluid undergoes vertical vibrations) the Navier-Stokes equation admitsreduction to the modified Hamilton-Jacobi equation. The modification term isthe Bohmian(quantum) potential. This reduction opens possibility to define acomplex-valued function, named the wave function, which is a solution of theSchr\"{o}dinger equation. The solenoidal component being added to the momentumoperator poses itself as a vector potential by analogy with the magnetic vectorpotential. The vector potential is represented by the solenoidal velocitymultiplied by mass of the fluid element. Vortex tubes, rings, and balls alongwith the wave function guiding these objects are solutions of this equation.Motion of the vortex balls along the Bohmian trajectories gives a model ofdroplets moving on the fluid surface. A peculiar fluid is the superfluidphysical vacuum. It contains Bose particle-antiparticle pairs. Vortex linespresented by electron-positron pairs are main torque objects. Bundles of thevortex lines can transmit a torque from one rotating disk to other unmoveddisk.