Spin and Madelung fluid

TL;DR

This paper derives the quantum potential of the Madelung fluid from the Pauli current, revealing that quantum behavior is intrinsically linked to particle spin and internal Zitterbewegung motion.

Contribution

It provides a novel derivation of the quantum potential directly from the Pauli current, emphasizing the role of spin and internal motion in quantum mechanics.

Findings

Quantum potential arises from spin and Zitterbewegung

Velocity decomposition separates classical and quantum parts

Quantum behavior linked to internal spin motion

Abstract

Starting from the Pauli current we obtain the decomposition of the non-relativistic local velocity in two parts: one parallel and the other orthogonal to the momentum. The former is recognized to be the ``classical'' part, that is the velocity of the center-of-mass, and the latter the ``quantum'' one, that is the velocity of the motion in the center-of-mass frame (namely, the internal ``spin motion'' or {\em Zitterbewegung}). Inserting the complete expression of the velocity into the kinetic energy term of the classical non-relativistic (i.e., Newtonian) Lagrangian, we straightforwardly derive the so-called ``quantum potential'' associated to the Madelung fluid. In such a way, the quantum mechanical behaviour of particles appears to be strictly correlated to the existence of spin and Zitterbewegung.