Hydrodynamics of Superfluid Quantum Space: de Broglie interpretation of the quantum mechanics

TL;DR

This paper models quantum mechanics using a superfluid quantum space, deriving the Schrödinger and Bohmian equations from fluid dynamics, providing a physical interpretation of particles as vortices guided by a pilot wave.

Contribution

It introduces a hydrodynamic framework for quantum mechanics based on superfluid space, linking the de Broglie-Bohm interpretation with fluid equations.

Findings

Derivation of Schrödinger equation from superfluid flow equations

Identification of vortices as particles guided by a pilot wave

Connection between quantum trajectories and fluid dynamics

Abstract

The ubiquitous ether coming from the ancient times up to middle of the twenty century is replaced by a superfluid quantum space. It represents by itself a Bose-Einstein condensate consisting of enormous amount of virtual particle-antiparticle pairs emerging and disappearing in an infinitely ongoing dance. Flowing of this medium in the non-relativistic limit is described by the modified Navier-Stokes equation along with the continuity equation. The first equation admits the splitting on to two coupled equations. They are the quantum Hamilton-Jacobi equation and the equation for vorticity. The quantum Hamilton-Jacoby equation paired with the continuity equation can be reduced to the \Schrodinger equation. These two equations representing the kernel of the Bohmian mechanics give finding bundle of the Bohmian trajectories. Whereas the vorticity equation gives solutions for vortices moving along such trajectories. As the result we come to the de Broglie's interpretation of quantum mechanics according to which there is a pilot-wave guiding the particle (in our case it is a vortex clot) from a source up to its detection along an optimal path that is the Bohmian trajectory.