This project is an experimental and theoretical investigation of the "walking droplet" system, in which a millimeter-size droplet bounces across a vibrating fluid bath, propelled by a resonant interaction with the waves created when it strikes the fluid surface. The walking droplet exhibits several features previously thought unique to the microscopic quantum realm. The outcome of this project will be a critical assessment of the potential and limitations of the walking droplet system as an analog for microscopic behavior. Although the walking droplet system was discovered only a decade ago, a similar conception for the motion of microscopic quantum particles was formulated in the 1920s by pioneering physicist Louis de Broglie. De Broglie envisioned microscopic particles moving in resonance with what he called a "pilot wave." Working from this conception, de Broglie deduced a number of equations that became the cornerstones of modern quantum theory, and correctly predicted the phenomenon of electron diffraction, for which he received the Nobel Prize. Despite this early success, the pilot wave concept was overshadowed by the viewpoint that the statistical predictions of quantum mechanics stand alone as a complete description of physical reality on the microscopic scale, with no role for any additional physical structure. This project revisits these competing models, and asks whether chaotic pilot-wave dynamics, of the form conceived by de Broglie and now realized in the walking droplet system might plausibly underlie quantum statistics. If the answer is yes, then the prevailing view of the microscopic realm will require drastic revision, with deep implications for the philosophy of science. The PIs have designed a walking droplet apparatus, controlled by a free smartphone app, which can be built for less than $60. The PIs have used the walking droplet experiment for a variety of science outreach activities.
This project will both question and inform the philosophical foundations of modern physics. The bouncing drop system, characterized by a resonant interaction between a particle and its guiding wave, is a rich new dynamical system that extends the range of classical systems to include features previously thought to be exclusive to the microscopic realm. It is, moreover, the first macroscopic realization of a pilot-wave dynamics of the form that was postured in the 1920s by Louis de Broglie, who, in his double-solution theory, envisaged microscopic quantum particles moving in resonance with a guiding wave. This study builds upon prior work that has yielded both the most refined bouncing-drop experimental system in operation and the most sophisticated theoretical models. Together the theory and experiments provide predictive power for the dynamics and stability of this hydrodynamic pilot-wave system. This project will apply these refined experimental and theoretical tools to revisit key hydrodynamic quantum analog systems involving boundary interactions, including motion in confined geometries and single-particle diffraction and interference. The project will also examine several new analog systems, including refraction of walkers across discrete steps, where a modified Snell's Law is obeyed, and scattering from circular obstacles, where a property akin to electromagnetic self-induction arises. Hydrodynamic analogs of the quantum mirage, Kapitza-Dirac effect, and Bragg scattering will also be explored. This class of problems will lead to a better understanding of pilot-wave hydrodynamics, and add to the growing list of hydrodynamic quantum analogs. In providing the opportunity to observe and understand pilot-wave dynamics on a macroscopic scale, the bouncing droplet system invites a critical revisitation of de Broglie's pilot-wave mechanics, and an examination of its viability as the basis for a realist quantum dynamics.
