2011 Laufer Lecture
Professor of Applied Mathematics
Massachusetts Institute of Technology
Title: “Hydrodynamic Quantum Analogues: Droplets Walking on the Impossible Pilot Wave”
Yves Couder and coworkers have recently reported the results of a startling series of experiments in which droplets walking on a vibrating fluid surface exhibit several dynamical features previously thought to be peculiar to the microscopic realm, including single-particle diffraction and interference, tunneling and quantized orbits. In an attempt to develop a connection between the fluid and quantum systems, we explore the Madelung transformation, whereby Schrödinger’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. A surprising correspondence between the walking droplets and de Broglie’s pilot wave theory of quantum mechanics is developed. New experiments are presented, and indicate the potential value of this hydrodynamic approach to both visualizing and understanding quantum mechanics.
John Bush is a Professor of Applied Mathematics at MIT. Having completed his BSc in Physics at University of Toronto, he went on to Harvard for his PhD in Geophysics, then the University of Cambridge for postdoctoral research. In 1998, he joined the faculty of MIT, where he is now the Director of the Applied Mathematics Laboratory. Bush’s research began in geophysics, but then shifted towards the effects of surface tension. In the past five years, he has been working primarily in biological fluid mechanics and biomimicry, with a view to rationalizing and exploiting Nature’s designs. Most recently, he has been exploring hydrodynamic analogues of quantum systems.