Macroscopic oil droplets mimicking quantum behavior: How far can we push an analogy?

We describe here a series of experimental analogies between fluid mechanics and quantum mechanics recently discovered by a team of physicists. These analogies arise in droplet systems guided by a surface (or pilot) wave. We argue that these experimental facts put ancient theoretical work by Madelung on the analogy between fluid and quantum mechanics into new light. After re-deriving Madelung’s result starting from two basic fluid-mechanical equations (the Navier-Stokes equation and the continuity equation), we discuss the relation with the de Broglie-Bohm theory. This allows to make a direct link with the droplet experiments. It is argued that the fluid-mechanical interpretation of quantum mechanics, if it can be extended to the general N-particle case, would have an advantage over the Bohm interpretation: it could rid Bohm’s theory of its strongly non-local character.