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What can bouncing oil droplets tell us about quantum mechanics?

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A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be distinctly quantum. To explain this correspondence it has been suggested that the fluid mechanical system provides a single-particle classical model of de Broglie’s idiosyncratic ‘double solution’ pilot wave theory of quantum mechanics. In this paper we assess the epistemic function of the bouncing oil droplet experiments in relation to quantum mechanics. We find that the bouncing oil droplets are best conceived as an analogue illustration of quantum phenomena, rather than an analogue simulation, and, furthermore, that their epistemic value should be understood in terms of how-possibly explanation, rather than confirmation. Analogue illustration, unlike analogue simulation, is not a form of ‘material surrogacy’, in which source empirical phenomena in a system of one kind can be understood as ‘standing in for’ target phenomena in a system of another kind. Rather, analogue illustration leverages a correspondence between certain empirical phenomena displayed by a source system and aspects of the ontology of a target system. On the one hand, this limits the potential inferential power of analogue illustrations, but, on the other, it widens their potential inferential scope. In particular, through analogue illustration we can learn, in the sense of gaining how-possibly understanding, about the putative ontology of a target system via an experiment. As such, the potential scientific value of these extraordinary experiments is undoubtedly a significant one.

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  1. 1.

    Although recent experiments contest the single and double slit diffraction and interference results: at best these phenomena are difficult to reproduce (Pucci et al. 2018), and at worst cannot be reproduced at all (Andersen et al. 2015; Batelaan et al. 2016; Bohr et al. 2016).

  2. 2.

    For a detailed exploration of the connection between this aspect of de Broglie’s work and Schrödinger’s derivation of the equation that bears his name see Joas and Lehner (2009).

  3. 3.

    De Broglie (1924, p. 8) does presciently note, however, that one could recover the Newtonian picture by imagining a force to be active in such a process. Of course, this force is a function of the ‘quantum potential’ which Bohm was later to emphasise.

  4. 4.

    The phenomenon of Faraday instability is closely related to the more familiar phenomenon of grains of sand on the surface of a beaten drum forming geometrical patterns (Faraday 1831).

  5. 5.

    “These waves are… the travelling equivalent of the standing Faraday waves usually observed” (Protière et al. 2006, p. 91).

  6. 6.

    This point is also made by Bush (2015).

  7. 7.

    An excellent recent discussion specifically relating to representation via material models is Frigg and Nguyen (2018). Further accounts, all of which we take to be compatible with our use of ‘representation’ below, are Hughes (1997), Giere (1999), Suárez (2004), Contessa (2007), Bailer-Jones (2009), and Weisberg (2012). A good overview of various connected issues is provided in Gelfert (2016, Section 2).

  8. 8.

    We will not here consider the connection to the wide range of types of ‘analogue experiments’ found in the context of the life sciences. Whilst there are, for example, broad conceptual connections between our analysis below and the analysis of ‘surrogate models’ and ‘model organisms’, the differing degree of formalisation of the two sciences render the details of physical and biological analogue experiments importantly different. See, for example, Bolker (2009), Levy and Currie (2014), and Baetu (2015). In interests of space, we will also neglect the subtle connection between analogue experiments and arguments by analogy. See Bartha (2019) for further discussion.

  9. 9.

    The modelling domain can be understood as a prescribed spatial, temporal, and numerical (i.e. number of atoms) scale, together with a tolerance or error margin. The isomorphism is partial in the sense that it connects only a sub-set of terms. This distinguishes analogue simulation from a duality which would be a full isomorphism between empirical terms (Dardashti et al. 2019).

  10. 10.

    Note that, whereas Dardashti et al. (2015) focus on the syntactic isomorphism between effective laws, we are focusing upon a partial isomorphism between empirical terms. So far as analogue simulation goes this is not a significance difference, we choose a different formulation only to make the comparison with analogue illustration more clear.

  11. 11.

    This is unsurprising since core aspects of the Dardashti et al. (2015) conception of analogue simulation are drawn from earlier comparison of such practice with computer simulations due to Winsberg (2010) and Winsberg (2019).

  12. 12.

    The form of such inferences is explored in more detail in Evans and Thébault (2020).

  13. 13.

    It is worth noting that, in this case, the experimenters are not, as it happens, particularly interested in the second function of their experiment since their main focus is on simulating empirical phenomena, and in justifying their inferences based upon universality arguments. Most likely this is because the mathematical models of a black hole in terms of Schwarzschild geometry already has a variety of simple visual illustrations (e.g. topographic diagram or Penrose diagram).

  14. 14.

    For more discussion on how-possibly explanation see Forber (2010), Bokulich (2014), and Cuffaro (2015). Hangleiter et al. (2017) argue that how-possibly understanding can be understood as a supplementary function of certain forms of analogue simulation.

  15. 15.

    Since it is a virtue of any modelling framework to have as large a domain of validity as possible, the relativistic covariance of a model of the walker system is inherently desirable.

  16. 16.

    ϕ denotes a transverse displacement and not a phase.

  17. 17.

    It should be noted that \(\hbar _{\exp }\) here is not Planck’s constant, but is rather a “proportional coefficient between wave characteristics and particle characteristics” of the concretion model (Borghesi 2017, p.945). It appears that this specific notation was chosen to emphasise the isomorphism with the Planck-Einstein, and other quantum, relations.

  18. 18.

    One could argue that the energy, momentum, and position of each quantum in a pilot wave theory also count as extra-empirical terms, at least in the regime where evolution is unitary. This is because, according to pilot wave theory, the precise energy, momenta, and position of the quanta comprise ‘hidden’ variables. (This is, of course, not to mention the constraints on precise values of momentum and position supplied by the uncertainty principle.)

  19. 19.

    One only need search YouTube for an array of examples of the pedagogical value of the walker experiments.


  1. Allen, J.M.A., Barrett, J., Horsman, D.C., Lee, C.M., & Spekkens, R.W. (2017). Quantum common causes and quantum causal models. Physical Review X, 7, 031021.

    Article  Google Scholar 

  2. Andersen, A., Madsen, J., Reichelt, C., Rosenlund Ahl, S., Lautrup, B., Ellegaard, C., Levinsen, M.T., & Bohr, T. (2015). Double-slit experiment with single wave-driven particles and its relation to quantum mechanics. Physical Review E, 92, 013006.

    Article  Google Scholar 

  3. Bacciagaluppi, G., & Valentini, A. (2009). Quantum theory at the crossroads: reconsidering the 1927 solvay conference. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  4. Baetu, T.M. (2015). The ‘Big picture’: the problem of extrapolation in basic research. The British Journal for the Philosophy of Science, 67(4), 941–964.

    Article  Google Scholar 

  5. Bailer-Jones, D.M. (2009). Scientific Models in Philosophy of Science. University of Pittsburgh Press.

  6. Barceló, C., Liberati, S., & Visser, M. (2011). Analogue gravity. Living Reviews in Relativity, 14(1), 3.

    Article  Google Scholar 

  7. Bartha, P. (2019). Analogy and analogical reasoning. In Zalta, E.N. (Ed.) The Stanford Encyclopedia of Philosophy, Spring 2019 edn, Stanford University.

  8. Batelaan, H., Jones, E., Huang, W.C.W., & Bach, R. (2016). Momentum exchange in the electron double-slit experiment. Journal of Physics, 701, 012007.

    Article  Google Scholar 

  9. Boge, F.J. (2018). Why computer simulations are not inferences, and in what sense they are experiments. European Journal for Philosophy of Science, 9, 13.

    Article  Google Scholar 

  10. Bogen, J., & Woodward, J. (1988). Saving the phenomena. The Philosophical Review, 97(3), 303–352.

    Article  Google Scholar 

  11. Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of “Hidden” variables. I. Phys Rev, 85(2), 166–179.

    Article  Google Scholar 

  12. Bohr, T., Andersen, A., & Lautrup, B. (2016). Bouncing droplets, pilot-waves, and quantum mechanics. In Klapp, J., Sigalotti, L.D.G., Medina, A., López, A., & Ruiz-Chavarría, G. (Eds.) Recent advances in fluid dynamics with environmental applications. (pp. 335–349). Cham: Springer International Publishing.

  13. Bokulich, A. (2014). How the tiger bush got its stripes: ‘how possibly’ vs. ‘how actually’ model explanations. The Monist, 97(3), 321–338.

    Article  Google Scholar 

  14. Bolker, J.A. (2009). Exemplary and surrogate models: two modes of representation in biology. Perspectives in Biology and Medicine, 52(4), 485–499.

    Article  Google Scholar 

  15. Borghesi, C. (2017). Equivalent quantum equations in a system inspired by bouncing droplets experiments. Foundations of Physics, 47(7), 933–958.

    Article  Google Scholar 

  16. de Broglie, L. (1924). Recherches sur la théorie des quanta. PhD thesis, University of Paris.

  17. de Broglie, L. (1927a). La méchanique ondulatoire et la structure atomique de la matière et du rayonnement. Le Journal de Physique et le Radium, 8, 225–241.

    Article  Google Scholar 

  18. de Broglie, L. (1927b). La nouvelle dynamique des quanta. In The proceedings of the 1927 Solvay conference, translated and published in Bacciagaluppi and Valentini (2009), pp. 373–406.

  19. de Broglie, L. (1959). L’interprétation de la mécanique ondulatoire. Le Journal de Physique et le Radium, 20(12), 963–979.

    Article  Google Scholar 

  20. de Broglie, L. (1971). L’interpretation de la mécanique Ondulatoire par la théorie de la Double Solutioń. In d’Espagnat, B. (Ed.) Foundations of quantum mechanics (pp. 345–367). New York: Academic Press.

  21. Bush, J.W.M. (2015). Pilot-Wave Hydrodynamics. Annual Review of Fluid Mechanics, 47 (1), 269–292.

    Article  Google Scholar 

  22. Cavalcanti, E.G., & Lal, R. (2014). On modifications of Reichenbach’s principle of common cause in light of Bell’s theorem. Journal of Physics A: Mathematical and Theoretical, 47(42), 424018.

    Article  Google Scholar 

  23. Cirac, J.I., & Zoller, P. (2012). Goals and opportunities in quantum simulation. Nature Physics, 8(4), 264–266.

    Article  Google Scholar 

  24. Contessa, G. (2007). Scientific representation, interpretation, and surrogative reasoning. Philosophy of Science, 74(1), 48–68.

    Article  Google Scholar 

  25. Costa, F., & Shrapnel, S. (2016). Quantum causal modelling. New Journal of Physics, 18(6), 063032.

    Article  Google Scholar 

  26. Couder, Y., & Fort, E. (2006). Single-particle diffraction and interference at a macroscopic scale. Physical Review Letters, 97, 154101.

    Article  Google Scholar 

  27. Couder, Y., & Fort, E. (2012). Probabilities and trajectories in a classical wave-particle duality. Journal of Physics: Conference Series, 361(1), 012001.

    Article  Google Scholar 

  28. Crowther, K., Linnemann, N.S., & Wüthrich, C. (2019). What we cannot learn from analogue experiments. Synthese, pp 1–26.

  29. Cuffaro, M.E. (2015). How-Possibly Explanations in (quantum) computer science. Philosophy of Science, 82(5), 737–748.

    Article  Google Scholar 

  30. Dardashti, R., Thébault, K.P.Y., & Winsberg, E. (2015). Confirmation via analogue simulation: what dumb holes could tell us about gravity. The British Journal for the Philosophy of Science, 68(1), 55–89.

    Article  Google Scholar 

  31. Dardashti, R., Hartmann, S., Thébault, K.P.Y., & Winsberg, E. (2019). Hawking radiation and analogue experiments: a bayesian analysis. Studies In History and Philosophy of Modern Physics, 67, 1–11.

    Article  Google Scholar 

  32. Dawid, R., & Hartmann, S. (2018). The no miracles argument without the base rate fallacy. Synthese, 195 (9), 4063–4079.

    Article  Google Scholar 

  33. Dray, W.H. (1957). Laws and explanation in history. Oxford: Oxford University Press.

    Google Scholar 

  34. Eddi, A., Fort, E., Moisy, F., & Couder, Y. (2009). Unpredictable tunneling of a classical Wave-Particle association. Physical Review Letters, 102, 240401.

    Article  Google Scholar 

  35. Eddi, A., Sultan, E., Moukhtar, J., Fort, E., Rossi, M., & Couder, Y. (2011). Information stored in faraday waves: the origin of a path memory. Journal of Fluid Mechanics, 674, 433–463.

    Article  Google Scholar 

  36. Eddi, A., Moukhtar, J., Perrard, S., Fort, E., & Couder, Y. (2012). Level splitting at macroscopic scale. Physical Review Letters, 108, 264503.

    Article  Google Scholar 

  37. Einstein, A. (1905). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik, 322(6), 132–148.

    Article  Google Scholar 

  38. Evans, P.W., & Thébault, K.P.Y. (2020). On the limits of experimental knowledge. Philosophical Transactions of the Royal Society A, 378, 20190235.

    Article  Google Scholar 

  39. Faccio, D., Belgiorno, F., Cacciatori, S., Gorini, V., Liberati, S., & Moschella, U. (2013). Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons, from Theory to Experiment. Springer,

  40. Faraday, M. (1831). On a peculiar class of Acoustical Figures; and on certain Forms assumed by groups of particles upon vibrating elastic Surfaces. Philosophical Transactions of the Royal Society of London, 121, 299–340.

    Article  Google Scholar 

  41. Feldbacher-Escamilla, C.J., & Gebharter, A. (2020). Confirmation based on analogical inference: Bayes Meets Jeffrey. Canadian Journal of Philosophy, 50(2), 174–194.

    Article  Google Scholar 

  42. Forber, P. (2010). Confirmation and explaining how possible. Studies in History and Philosophy of Biological and Biomedical Sciences, 41(1), 32–40.

    Article  Google Scholar 

  43. Fort, E., Eddi, A., Boudaoud, A., Moukhtar, J., & Couder, Y. (2010). Path-memory induced quantization of classical orbits. Proceedings of the National Academy of Sciences, 107(41), 17515–17520.

    Article  Google Scholar 

  44. Franklin, A., & Perovic, S. (2016). Experiment in physics. In Zalta, E.N. (Ed.) The Stanford Encyclopedia of Philosophy, Winter 2016 edn, Stanford University.

  45. Frigg, R., & Nguyen, J. (2018). The turn of the valve: representing with material models. European Journal for Philosophy of Science, 8(2), 205–224.

    Article  Google Scholar 

  46. Gelfert, A. (2016). How to do science with models: a philosophical primer. Switzerland: Springer.

    Book  Google Scholar 

  47. Georgescu, I.M., Ashhab, S., & Nori, F. (2014). Quantum simulation. Reviews of Modern Physics, 86, 153–185.

    Article  Google Scholar 

  48. Giere, R.N. (1999). Using models to represent reality. In Magnani, L., Nersessian, N.J., & Thagard, P. (Eds.) Model-based reasoning in scientific discovery (pp. 41–57). Boston: Springer.

  49. Hangleiter, D., Carolan, J., & Thébault, K. (2017). Analogue quantum simulation: A philosophical prospectus. arXiv:1712.05809 [quant-ph].

  50. Harris, D.M., Moukhtar, J., Fort, E., Couder, Y., & Bush, J.W.M. (2013). Wavelike statistics from pilot-wave dynamics in a circular corral. Physical Review E, 88, 011001.

    Article  Google Scholar 

  51. Holland, P. (2005). Quantum back-reaction and the particle law of motion. Journal of Physics A: Mathematical and General, 39(3), 559–564.

    Article  Google Scholar 

  52. Hughes, R.I.G. (1997). Models and representation. Philosophy of Science, 64, S325–S336.

    Article  Google Scholar 

  53. Joas, C., & Lehner, C. (2009). The classical roots of wave mechanics: schrodinger’s̈ transformations of the optical-mechanical analogy. Studies in History and Philosophy of Modern Physics, 40(4), 338–351.

    Article  Google Scholar 

  54. Laudan, L. (1981). A confutation of convergent realism. Philosophy of Science, 48(1), 19–49.

    Article  Google Scholar 

  55. Leifer, M.S., & Spekkens, R.W. (2013). Towards a formulation of quantum theory as a causally neutral theory of bayesian inference. Physical Review A, 88(5), 052130.

    Article  Google Scholar 

  56. Levy, A., & Currie, A. (2014). Model organisms are not (theoretical) models. The British Journal for the Philosophy of Science, 66(2), 327–348.

    Article  Google Scholar 

  57. Lyons, T.D. (2002). Scientific realism and the pessimistic meta-modus tollens. In Clarke, S., & Lyons, T.D. (Eds.) Recent Themes in the Philosophy of Science: Scientific Realism and Commonsense (pp. 63–90). Dordrecht: Springer.

  58. Lyons, T.D. (2003). Explaining the success of a scientific theory. Philosophy of Science, 70(5), 891–901.

    Article  Google Scholar 

  59. Massimi, M. (2007). Saving unobservable phenomena. The British Journal for the Philosophy of Science, 58(2), 235–262.

    Article  Google Scholar 

  60. Moláček, J., & Bush, J.W.M. (2013). Drops walking on a vibrating bath: towards a hydrodynamic pilot-wave theory. Journal of Fluid Mechanics, 727, 612–647.

    Article  Google Scholar 

  61. Pearl, J. (2009). Causality: models, reasoning and inference, 2nd edn. New York: Cambridge University Press.

    Book  Google Scholar 

  62. Persson, J. (2012). Three conceptions of explaining how possibly—and one reductive account. In de Regt, H.W., Hartmann, S., & Okasha, S. (Eds.) EPSA Philosophy of Science: Amsterdam 2009 (pp. 275–286). Netherlands: Springer.

  63. Protière, S., Couder, Y., Fort, E., & Boudaoud, A. (2005). The self-organization of capillary wave sources. Journal of Physics: Condensed Matter, 17(45), S3529.

    Article  Google Scholar 

  64. Protière, S., Boudaoud, A., & Couder, Y. (2006). Particle–wave association on a fluid interface. Journal of Fluid Mechanics, 554, 85–108.

    Article  Google Scholar 

  65. Pucci, G., Harris, D.M., Faria, L.M., & Bush, J.W.M. (2018). Walking droplets interacting with single and double slits. Journal of Fluid Mechanics, 835, 1136–1156.

    Article  Google Scholar 

  66. Reutlinger, A., Hartmann, S., & Hangleiter, D. (2017). Understanding (with) Toy Models. The British Journal for the Philosophy of Science, 69(4), 1069–1099.

    Article  Google Scholar 

  67. Spirtes, P., Glymour, C.N., & Scheines, R. (2000). Causation, prediction and search, 2nd edn. New York: MIT Press.

    Google Scholar 

  68. Suárez, M. (2004). An inferential conception of scientific representation. Philosophy of Science, 71(5), 767–779.

    Article  Google Scholar 

  69. Thèbault, K.P.Y. (2019). What can we learn from analogue experiments?. In Dardashti, R., Dawid, R., & Thèbault, K.P.Y. (Eds.) Why trust a theory?: epistemology of fundamental physics (pp. 184–201). Cambridge: Cambridge University Press.

  70. Unruh, W.G. (1981). Experimental black-hole evaporation? Physical Review Letters, 46(21), 1351–53.

    Article  Google Scholar 

  71. Van Fraassen, B.C. (1980). The Scientific Image. Oxford University Press.

  72. Vervoort, L. (2016). No-Go Theorems face Background-Based theories for quantum mechanics. Foundations of Physics, 46(4), 458–472.

    Article  Google Scholar 

  73. Vickers, P. (2013). A confrontation of convergent realism. Philosophy of Science, 80(2), 189–211.

    Article  Google Scholar 

  74. Weisberg, M. (2012). Simulation and similarity: Using models to understand the world. Oxford University Press.

  75. Winsberg, E. (2010). Science in the age of computer simulation. Chicago: University of Chicago Press.

    Book  Google Scholar 

  76. Winsberg, E. (2019). Computer simulations in science. In Zalta, E.N. (Ed.) The Stanford Encyclopedia of Philosophy, Spring 2019 edn, Stanford University.

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This work grew out of a Research Group Fellowship in 2015 at the Munich Center for Mathematical Philosophy, with fellow group members Radin Dardashti, Matt Farr, and Alex Reutlinger. We are grateful to the hospitality of Ludwig-Maximilians-Universität and Stephan Hartmann for hosting us during the early stages of this research. For valuable discussion, comments, and feedback we are greatly appreciative to Guido Bacciagaluppi, Christian Borghesi, Paul Teller, Eric Winsberg, two anonomous referees, and to audiences in Brisbane and Canberra.

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PWE’s work on this paper was supported by the Templeton World Charity Foundation (TWCF 0064/AB38), the University of Queensland, and the Australian Government through the Australian Research Council (DE170100808). KT’s work on this paper was supported by the Arts and Humanities Research Council, UK (AH/P004415/1). Both authors contriubted equally to the manuscipt.

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Evans, P.W., Thébault, K.P.Y. What can bouncing oil droplets tell us about quantum mechanics?. Euro Jnl Phil Sci 10, 39 (2020).

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  • Quantum mechanics
  • Pilot wave theory
  • Walker experiments
  • Analogue experimentation
  • Analogue illustration
  • How-possibly explanation