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What can bouncing oil droplets tell us about quantum mechanics?

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Abstract

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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Notes

  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.

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Acknowledgements

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). https://doi.org/10.1007/s13194-020-00301-0

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Keywords

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