Rendering the Navier–Stokes Equations for a Compressible Fluid into the Schrödinger Equation for Quantum Mechanics

Abstract: The mass and momentum transfer phenomena in a compressible fluid represented by the Navier–Stokes equations are shown to convert into the Schrödinger equation for quantum mechanics. The complete Navier–Stokes equations render into an extended generalized version of Schrödinger equation. These results complement the Madelung’s (Zeitschrift für Physik 40 (3–4), pp. 322–326, 1926–1927) derivations that show how Schrödinger’s equation in quantum mechanics can be converted into the Euler equations for irrotational compressible flow. The theoretical results presented here join the classical Madelung paper to suggest the possibility that quantum effects at sub-atomic levels deal with a compressible fluid susceptible to wave propagation, rather than a particle. The link between such a fluid and the “quantum particle” is under current investigation.