Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Today

Walking droplets, pilot waves, and word choices

John W. M. Bush

Published Mar 31, 2016• 0 citations
Publisher

Abstract

► Bush replies: I appreciate Jeffery Winkler’s opinion, but it has yet to be proven that dynamic nonlocality of the form exhibited by the walking droplets cannot give rise to a feature analogous to quantum nonlocality, that memory cannot account for entanglement. A proof, rather than an assertion, on this matter would be most welcome.I feel obliged to point out to Leslie Kerby that in my opening paragraph, I was appealing not to my male readership but rather to the careful reader. The cantankerous queen mother was a metaphor for the field of fluid mechanics, not women in science. She was, moreover, cast as the heroine.© 2016 American Institute of Physics.

DOI
10.1063/pt.3.3122

Related papers

Walking droplets, pilot waves, and word choices

Jeffery Winkler

After reading John Bush’s article “The new wave of pilot-wave theory” (Physics Today, August 2015, page 47), I want to remind readers of the limitations of the analogy. The oil-drop experiments provide a tangible partial analogue of the pilot-wave picture, but one that is restricted to single-particle phenomena. Such experiments cannot reproduce the types of phenomena that depend on entanglement; only in the case of a single particle does the wavefunction have the same mathematical form—a scalar function over space—as the waves in the oil.Once two particles are involved, the fact that the wavefunction is defined over the configuration space of the system rather than over physical space becomes crucial, and the partial analogy to the oil drops fails. In other words, the analogy does not extend to what most people consider the most interesting aspects of quantum mechanics.© 2016 American Institute of Physics.

Physics Today•Mar 31, 2016•1 citation

Spin lattices of walking droplets

Medina Machuca, Rodolfo Miguel

A millimeter-sized droplet may propel itself along the surface of a vibrating fluid through interaction with its own guiding or 'pilot' wave field. By virtue of the peculiarities of the resulting pilot-wave dynamics, this hydrodynamic system exhibits features which were previously thought to be exclusive to the microscopic, quantum realm. The plan of this work is to perform experiments and theory that will help to understand these hydrodynamic quantum analogs.

•Jun 25, 2018•0 citations

Introduction to focus issue on hydrodynamic quantum analogs

John W. M. Bush, Yves Couder, Tristan Gilet +2 more

Hydrodynamic quantum analogs is a nascent field initiated in 2005 by the discovery of a hydrodynamic pilot-wave system [Y. Couder, S. Protière, E. Fort, and A. Boudaoud, Nature 437, 208 (2005)]. The system consists of a millimetric droplet self-propeling along the surface of a vibrating bath through a resonant interaction with its own wave field [J. W. M. Bush, Annu. Rev. Fluid Mech. 47, 269–292 (2015)]. There are three critical ingredients for the quantum like-behavior. The first is “path memory” [A. Eddi, E. Sultan, J. Moukhtar, E. Fort, M. Rossi, and Y. Couder, J. Fluid Mech. 675, 433–463 (2011)], which renders the system non-Markovian: the instantaneous wave force acting on the droplet depends explicitly on its past. The second is the resonance condition between droplet and wave that ensures a highly structured monochromatic pilot wave field that imposes an effective potential on the walking droplet, resulting in preferred, quantized states. The third ingredient is chaos, which in several systems is characterized by unpredictable switching between unstable periodic orbits. This focus issue is devoted to recent studies of and relating to pilot-wave hydrodynamics, a field that attempts to answer the following simple but provocative question: Might deterministic chaotic pilot-wave dynamics underlie quantum statistics?

Chaos An Interdisciplinary Journal of Nonlinear Science•Sep 1, 2018•37 citations

Walking droplets, a form of wave-particle duality at macroscopic scale?

Yves Couder, Arezki Boudaoud, Suzie Protière +1 more

A FoRM

Europhysics news•Jan 1, 2010•43 citations

Single-particle Fraunhofer diffraction in a classical pilot-wave model

David Darrow, John W. M. Bush

Walking oil droplets offer a qualitative, classical analog of single-particle diffraction. Making this analog quantitative has proven challenging, leading recent authors to conjecture that no classical pilot-wave model could exhibit Fraunhofer diffraction. We revisit the problem with the recent, Lagrangian pilot-wave model of Darrow and Bush [], and find agreement with both single- and double-slit Fraunhofer patterns. We identify two distinct dynamical features that enable our model to capture Fraunhofer diffraction and distinguish it from previous classical pilot-wave models.

arXiv:2509.25574•Physical Review Research•Sep 10, 2025•2 citations

Hydrodynamic quantum analogues: droplets walking on the impossible pilot wave

John W. M. Bush

Bulletin of the American Physical Society•Nov 19, 2012•0 citations
► Bush replies: I appreciate Jeffery Winkler’s opinion, but it has yet to be proven that dynamic nonlocality of the form exhibited by the walking droplets cannot give rise to a feature analogous to quantum nonlocality, that memory cannot account for entanglement. A proof, rather than an assertion, on this matter would be most welcome.I feel obliged to point out to Leslie Kerby that in my opening paragraph, I was appealing not to my male readership but rather to the careful reader. The cantankerous queen mother was a metaphor for the field of fluid mechanics, not women in science. She was, moreover, cast as the heroine.© 2016 American Institute of Physics.
After reading John Bush’s article “The new wave of pilot-wave theory” (Physics Today, August 2015, page 47), I want to remind readers of the limitations of the analogy. The oil-drop experiments provide a tangible partial analogue of the pilot-wave picture, but one that is restricted to single-particle phenomena. Such experiments cannot reproduce the types of phenomena that depend on entanglement; only in the case of a single particle does the wavefunction have the same mathematical form—a scalar function over space—as the waves in the oil.Once two particles are involved, the fact that the wavefunction is defined over the configuration space of the system rather than over physical space becomes crucial, and the partial analogy to the oil drops fails. In other words, the analogy does not extend to what most people consider the most interesting aspects of quantum mechanics.© 2016 American Institute of Physics.
Hydrodynamic quantum analogs is a nascent field initiated in 2005 by the discovery of a hydrodynamic pilot-wave system [Y. Couder, S. Protière, E. Fort, and A. Boudaoud, Nature 437, 208 (2005)]. The system consists of a millimetric droplet self-propeling along the surface of a vibrating bath through a resonant interaction with its own wave field [J. W. M. Bush, Annu. Rev. Fluid Mech. 47, 269–292 (2015)]. There are three critical ingredients for the quantum like-behavior. The first is “path memory” [A. Eddi, E. Sultan, J. Moukhtar, E. Fort, M. Rossi, and Y. Couder, J. Fluid Mech. 675, 433–463 (2011)], which renders the system non-Markovian: the instantaneous wave force acting on the droplet depends explicitly on its past. The second is the resonance condition between droplet and wave that ensures a highly structured monochromatic pilot wave field that imposes an effective potential on the walking droplet, resulting in preferred, quantized states. The third ingredient is chaos, which in several systems is characterized by unpredictable switching between unstable periodic orbits. This focus issue is devoted to recent studies of and relating to pilot-wave hydrodynamics, a field that attempts to answer the following simple but provocative question: Might deterministic chaotic pilot-wave dynamics underlie quantum statistics?
Walking oil droplets offer a qualitative, classical analog of single-particle diffraction. Making this analog quantitative has proven challenging, leading recent authors to conjecture that no classical pilot-wave model could exhibit Fraunhofer diffraction. We revisit the problem with the recent, Lagrangian pilot-wave model of Darrow and Bush [], and find agreement with both single- and double-slit Fraunhofer patterns. We identify two distinct dynamical features that enable our model to capture Fraunhofer diffraction and distinguish it from previous classical pilot-wave models.