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Bush JWM, Oza AU. Hydrodynamic quantum analogs. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 84:017001. [PMID: 33065567 DOI: 10.1088/1361-6633/abc22c] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Accepted: 10/16/2020] [Indexed: 06/11/2023]
Abstract
The walking droplet system discovered by Yves Couder and Emmanuel Fort presents an example of a vibrating particle self-propelling through a resonant interaction with its own wave field. It provides a means of visualizing a particle as an excitation of a field, a common notion in quantum field theory. Moreover, it represents the first macroscopic realization of a form of dynamics proposed for quantum particles by Louis de Broglie in the 1920s. The fact that this hydrodynamic pilot-wave system exhibits many features typically associated with the microscopic, quantum realm raises a number of intriguing questions. At a minimum, it extends the range of classical systems to include quantum-like statistics in a number of settings. A more optimistic stance is that it suggests the manner in which quantum mechanics might be completed through a theoretical description of particle trajectories. We here review the experimental studies of the walker system, and the hierarchy of theoretical models developed to rationalize its behavior. Particular attention is given to enumerating the dynamical mechanisms responsible for the emergence of robust, structured statistical behavior. Another focus is demonstrating how the temporal nonlocality of the droplet dynamics, as results from the persistence of its pilot wave field, may give rise to behavior that appears to be spatially nonlocal. Finally, we describe recent explorations of a generalized theoretical framework that provides a mathematical bridge between the hydrodynamic pilot-wave system and various realist models of quantum dynamics.
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Affiliation(s)
- John W M Bush
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States of America
| | - Anand U Oza
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, United States of America
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Grössing G, Fussy S, Mesa Pascasio J, Schwabl H. Vacuum Landscaping: Cause of Nonlocal Influences without Signaling. ENTROPY 2018; 20:e20060458. [PMID: 33265548 PMCID: PMC7512975 DOI: 10.3390/e20060458] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 06/08/2018] [Accepted: 06/11/2018] [Indexed: 01/09/2023]
Abstract
In the quest for an understanding of nonlocality with respect to an appropriate ontology, we propose a “cosmological solution”. We assume that from the beginning of the universe each point in space has been the location of a scalar field representing a zero-point vacuum energy that nonlocally vibrates at a vast range of different frequencies across the whole universe. A quantum, then, is a nonequilibrium steady state in the form of a “bouncer” coupled resonantly to one of those (particle type dependent) frequencies, in remote analogy to the bouncing oil drops on an oscillating oil bath as in Couder’s experiments. A major difference to the latter analogy is given by the nonlocal nature of the vacuum oscillations. We show with the examples of double- and n-slit interference that the assumed nonlocality of the distribution functions alone suffices to derive the de Broglie–Bohm guiding equation for N particles with otherwise purely classical means. In our model, no influences from configuration space are required, as everything can be described in 3-space. Importantly, the setting up of an experimental arrangement limits and shapes the forward and osmotic contributions and is described as vacuum landscaping.
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Andersen A, Madsen J, Reichelt C, Rosenlund Ahl S, Lautrup B, Ellegaard C, Levinsen MT, Bohr T. Double-slit experiment with single wave-driven particles and its relation to quantum mechanics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:013006. [PMID: 26274269 DOI: 10.1103/physreve.92.013006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2014] [Indexed: 06/04/2023]
Abstract
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.
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Affiliation(s)
- Anders Andersen
- Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Jacob Madsen
- Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Christian Reichelt
- Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Sonja Rosenlund Ahl
- Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Benny Lautrup
- Niels Bohr International Academy, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
| | - Clive Ellegaard
- The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
| | - Mogens T Levinsen
- The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
| | - Tomas Bohr
- Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
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Perrard S, Labousse M, Miskin M, Fort E, Couder Y. Self-organization into quantized eigenstates of a classical wave-driven particle. Nat Commun 2015; 5:3219. [PMID: 24476755 DOI: 10.1038/ncomms4219] [Citation(s) in RCA: 88] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2013] [Accepted: 01/07/2014] [Indexed: 11/09/2022] Open
Abstract
A growing number of dynamical situations involve the coupling of particles or singularities with physical waves. In principle these situations are very far from the wave particle duality at quantum scale where the wave is probabilistic by nature. Yet some dual characteristics were observed in a system where a macroscopic droplet is guided by a pilot wave it generates. Here we investigate the behaviour of these entities when confined in a two-dimensional harmonic potential well. A discrete set of stable orbits is observed, in the shape of successive generalized Cassinian-like curves (circles, ovals, lemniscates, trefoils and so on). Along these specific trajectories, the droplet motion is characterized by a double quantization of the orbit spatial extent and of the angular momentum. We show that these trajectories are intertwined with the dynamical build-up of central wave-field modes. These dual self-organized modes form a basis of eigenstates on which more complex motions are naturally decomposed.
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Affiliation(s)
- Stéphane Perrard
- Matières et Systèmes Complexes, Université Paris Diderot, CNRS UMR 7057, 10 rue Alice Domon et Léonie Duquet, 75205 Paris, France
| | - Matthieu Labousse
- Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 1 rue Jussieu, 75238 Paris, France
| | - Marc Miskin
- 1] Matières et Systèmes Complexes, Université Paris Diderot, CNRS UMR 7057, 10 rue Alice Domon et Léonie Duquet, 75205 Paris, France [2] Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 1 rue Jussieu, 75238 Paris, France [3]
| | - Emmanuel Fort
- Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 1 rue Jussieu, 75238 Paris, France
| | - Yves Couder
- Matières et Systèmes Complexes, Université Paris Diderot, CNRS UMR 7057, 10 rue Alice Domon et Léonie Duquet, 75205 Paris, France
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Labousse M, Perrard S. Non-Hamiltonian features of a classical pilot-wave dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022913. [PMID: 25215805 DOI: 10.1103/physreve.90.022913] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2013] [Indexed: 06/03/2023]
Abstract
A bouncing droplet on a vibrated bath can couple to the waves it generates, so that it becomes a propagative walker. Its propulsion at constant velocity means that a balance exists between the permanent input of energy provided by the vibration and the dissipation. Here we seek a simple theoretical description of the resulting non-Hamiltonian dynamics with a walker immersed in a harmonic potential well. We demonstrate that the interaction with the recently emitted waves can be modeled by a Rayleigh-type friction. The Rayleigh oscillator has well defined attractors. The convergence toward them and their stability is investigated through an energetic approach and a linear stability analysis. These theoretical results provide a description of the dynamics in excellent agreement with the experimental data. It is thus a basic framework for further investigations of wave-particle interactions when memory effects are included.
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Affiliation(s)
- M Labousse
- Institut Langevin, ESPCI ParisTech, CNRS - UMR 7587, 1 rue Jussieu, 75005 Paris Cedex 05, France, EU
| | - S Perrard
- Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, CNRS - UMR 7057, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France, EU
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Harris DM, Moukhtar J, Fort E, Couder Y, Bush JWM. Wavelike statistics from pilot-wave dynamics in a circular corral. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:011001. [PMID: 23944402 DOI: 10.1103/physreve.88.011001] [Citation(s) in RCA: 51] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2012] [Revised: 05/02/2013] [Indexed: 06/02/2023]
Abstract
Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.
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Affiliation(s)
- Daniel M Harris
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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