Waves from a vibrating bowl
When a Tibetan singing bowl is filled with water and its rim is rubbed or struck, the bowl's walls vibrate, transferring energy to the liquid inside. This causes the rim to rapidly change shape between two slightly oval configurations. As the vibrational energy increases, the flat surface of the water becomes unstable and erupts into a field of standing waves. This phenomenon is named after Michael Faraday, who first described it in 1831. These "Faraday waves" form distinct geometric patterns, such as stripes or hexagons, and oscillate at half the frequency of the container's vibration, a characteristic of parametric resonance.
Vigorous excitation of the bowl creates complex wave patterns and cause droplets to eject from the fluid surface. High-speed imaging reveals that once ejected, these droplets do not immediately coalesce back into the bath. Instead, a thin layer of air trapped between the droplet and the vibrating surface allows them to levitate, bouncing or skidding across the water. Researchers at institutions including MIT have conducted controlled studies, acoustically exciting the bowl’s natural vibrational modes to analyze how the surface waves evolve with increasing amplitude.
A quantum mechanical analog
The behavior of these bouncing droplets is a physical system. It is a macroscopic physical system that displays behaviors once thought to be exclusive to quantum mechanics. The phenomenon was first identified as a "hydrodynamic quantum analog" in 2005 by Yves Couder and his colleagues. A droplet bouncing on the vibrating fluid bath is self-propelled by its own wave field. This "walker" system is a realization of the pilot-wave theory proposed by Louis de Broglie in 1927.
De Broglie’s theory suggested that particles are borne on a guiding "pilot wave," a concept largely superseded by the Copenhagen interpretation of quantum mechanics. In the lab, the droplet and its wave field provide a visible, classical system that mimics quantum phenomena. For example, two "walking" droplets can become bound and orbit each other at fixed, discrete distances, analogous to quantized energy levels in an atom. These systems have been used to replicate effects like quantum tunneling, the Zeeman effect, and single-particle diffraction patterns. The study of these hydrodynamic systems provides a tangible way to visualize the concepts of quantum field theory.