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European Journal of Physics

Bouncing droplets: a classroom experiment to visualize wave-particle duality on the macroscopic level

Pascal Sleutel, Erik Dietrich, Jan T. van der Veen, Wouter van Joolingen

Published Jul 27, 2016• 3 citations
Publisher

Abstract

Abstract This study brings a recently discovered macroscopic phenomenon with wave-particle characteristics into the classroom. The system consists of a liquid droplet levitating over a vertically shaken liquid pool. The droplets allow visualization of a wave–particle system in a directly observable way. We show how to interpret this macroscopic phenomenon and how to set up and carry out this experiment. A class of students performed single slit diffraction experiments with droplets. By scoring individual droplet trajectories students find a diffraction pattern. This pilot application in the classroom shows that students can study and discuss the wave–particle nature of the bouncing droplet experiment. The experiment therefore provides a useful opportunity to show wave–particle behavior on the macroscopic level.

DOI
10.1088/0143-0807/37/5/055706

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Abstract This study brings a recently discovered macroscopic phenomenon with wave-particle characteristics into the classroom. The system consists of a liquid droplet levitating over a vertically shaken liquid pool. The droplets allow visualization of a wave–particle system in a directly observable way. We show how to interpret this macroscopic phenomenon and how to set up and carry out this experiment. A class of students performed single slit diffraction experiments with droplets. By scoring individual droplet trajectories students find a diffraction pattern. This pilot application in the classroom shows that students can study and discuss the wave–particle nature of the bouncing droplet experiment. The experiment therefore provides a useful opportunity to show wave–particle behavior on the macroscopic level.
We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through numerical means we obtain single-slit diffraction and double-slit interference patterns that strongly resemble those reported in experiment and that reflect a striking resemblance to quantum diffraction and interference on a phenomenological level. We, however, identify evident differences from quantum mechanics which arise from the governing equations at the fundamental level.
Different schools have different explanations for the wave-particle duality of microscopic particles. Hidden variable interpretation, pilot wave interpretation, stochastic processes interpretation and so on all think that the generation of wave-particle duality has deeper reasons. According to these interpretations, macroscopic objects can also exhibit significant wave-particle duality. The authors performed a round-hole diffraction experiment of powder particles: some powder particles of the same mass and shape are freely dropped to a plane one by one through a circular hole. At first, the powder particles are distributed disorderly on the plate in the box. With the increase of the number of falling powder particles, a diffraction pattern composed of several concentric rings is gradually presented. This implies that wave-particle duality is not unique to microscopic particles, and it is also exhibited by macroscopic objects. The experimental results help to reveal the nature of wave-particle duality.
Abstract Quantum mechanics, the cornerstone of modern physics, is often perceived as abstract and complex, particularly by beginners, with regard to the wave-particle duality of microscopic particles. Traditional teaching methods often fail to foster an intuitive understanding of these concepts among students. Consequently, the search for more effective, interactive teaching tools has become a priority for educators. Our objective is to demystify complex quantum mechanical concepts, spark students’ interest in learning, and deepen their understanding, ultimately improving teaching effectiveness. In our research, we used LabVIEW software to develop a visual display and interactive simulation for double-slit interference and circular aperture diffraction experiments of electrons. This module allows students to simulate these experiments and adjust parameters, providing an intuitive observation of quantum behavior under various conditions. The results indicate that using the LabVIEW multimedia module significantly enhances students’ comprehension and interest in quantum mechanics, particularly with respect to wave-particle duality. We also employed the Feynman path integral idea to explain some of the simulation phenomena. This LabVIEW-based simulation not only renders abstract concepts more tangible and visual but also fosters active learning and experimental investigation. We posit that this study introduces a novel and valuable tool for teaching quantum mechanics and provides insights for the future of quantum mechanics education.
A droplet bouncing on a vertically vibrated bath can become coupled to the surface wave it generates. It thus becomes a "walker" moving at constant velocity on the interface. Here the motion of these walkers is investigated when they pass through one or two slits limiting the transverse extent of their wave. In both cases a given single walker seems randomly scattered. However, diffraction or interference patterns are recovered in the histogram of the deviations of many successive walkers. The similarities and differences of these results with those obtained with single particles at the quantum scale are discussed.
In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.