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

TL;DR

This paper explores how fluid dynamics, vortex structures, and quantum-like equations relate, proposing a model where vortex objects and superfluid vacuum phenomena can be described through modified Hamilton-Jacobi and Schrödinger equations.

Contribution

It introduces a novel approach linking fluid mechanics with quantum equations, modeling vortex structures and superfluid vacuum phenomena using modified Hamilton-Jacobi and Schrödinger equations.

Findings

Vortex tubes, rings, and balls are solutions to the modified Schrödinger equation.

Vortex objects can be guided by wave functions similar to quantum particles.

Superfluid vacuum contains vortex lines that transmit torque via electron-positron pairs.

Abstract

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