Pilot-Wave Hydrodynamics

Abstract

Yves Couder, Emmanuel Fort and coworkers have recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. We review experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. We then review theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantum-like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, while multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. We attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics, more closely related to de Broglie's original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through workers in stochastic electrodynamics.

Thermal delay of drop coalescence

“…Once the first drop has coalesced, following the thermal mixing process elucidated here, the temperature of its daughter droplets should be comparable to that of the bath. Finally, we note that thermally delayed drop coalescence may prove useful in levitating drops on vibrating baths (Bush 2015).…”

Simulations of pilot-wave dynamics in a simple harmonic potential

“…While claims of single-particle diffraction and interference [6] have been contested [7], tunneling [8,9], orbital quantization in both a rotating frame [10][11][12] and harmonic potential [13,14], and wavelike statistics in confined geometries [15][16][17][18] are all robust quantumlike phenomena. This hydrodynamic pilot-wave system and its relation to realist quantum theories, specifically, de Broglie's double-solution pilot-wave theory [19] and its modern extensions [20], were recently reviewed by Bush [21,22].…”

The wave-induced added mass of walking droplets

“…By virtue of their spatial delocalization, the walkers exhibit several features previously thought to be peculiar to the microscopic realm, including single-particle diffraction and interference (Couder & Fort 2006), tunnelling (Eddi et al 2009), quantized orbits (Fort et al 2010;Oza et al 2014;Perrard et al 2014a,b) and orbital level splitting in a rotating frame (Eddi et al 2012;Oza et al 2014), and wave-like statistics in confined geometries . The relationship between this hydrodynamic system and various realist models of quantum dynamics is discussed by Bush (2015). † Email address for correspondence: bush@math.mit.edu c Cambridge University Press 2014 Einstein (Bohm & Hiley 1982) and de Broglie (de Broglie 1926(de Broglie , 1987) both sought to reconcile quantum mechanics and relativity through consideration of the wave nature of matter (Chebotarev 2000).…”