Hydrodynamic quantum analogues

Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139-4307
USA

Yves Couder, Emmanuel Fort and coworkers have recently reported the results of a startling series of experiments in which droplets bouncing on a vibrating fluid surface exhibit several dynamical features previously thought to be peculiar to the microscopic realm. In an attempt to develop a connection between the fluid and quantum systems, we explore the Madelung transformation, whereby Schrodinger's equation is recast in a hydrodynamic form. Doing so allows us to demonstrate that the capillary pressure associated with the fluid's interfacial tension plays the role of the quantum pressure, and that the capillary Faraday waves play the role of de Broglie's matter waves. New experiments are presented, and indicate the potential value of this hydrodynamic approach to both visualizing and understanding quantum mechanics.