The Schrödinger Equation in the Context of Fluid Mechanics
We derive a mapping between the Schrödinger equation and the Navier-Stokes equation, which generalizes the one proposed by Madelung in 1926 with the Euler equation. Since fluid mechanics is the paradigm of an emergent theory, these maps support the interpretation of quantum mechanics as an effective theory, emerging from a more fundamental one. In the new mapping, moreover, the quantum potential is identified with the viscous term, in line with recent studies that claim that quantumness has a dissipative origin.
This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license.