Why bouncing droplets are a pretty good model of quantum mechanics

Abstract

In 2005, Couder, Protière, Fort and Badouad showed that oil droplets bouncing on a vibrating tray of oil can display nonlocal interactions reminiscent of the particle-wave associations in quantum mechanics; in particular they can move, attract, repel and orbit each other. Subsequent experimental work by Couder, Fort, Protière, Eddi, Sultan, Moukhtar, Rossi, Moláček, Bush and Sbitnev has established that bouncing drops exhibit single-slit and double-slit diffraction, tunnelling, quantised energy levels, Anderson localisation and the creation/annihilation of droplet/bubble pairs.In this paper we explain why. We show first that the surface waves guiding the droplets are Lorentz covariant with the characteristic speed c of the surface waves; second, that pairs of bouncing droplets experience an inverse-square force of attraction or repulsion according to their relative phase, and an analogue of the magnetic force; third, that bouncing droplets are governed by an analogue of Schrödinger's equation where Planck's constant is replaced by an appropriate constant of the motion; and fourth, that orbiting droplet pairs exhibit spin-half symmetry and align antisymmetrically as in the Pauli exclusion principle. Our analysis explains the similarities between bouncing-droplet experiments and the behaviour of quantum-mechanical particles. It also enables us to highlight some differences, and to predict some surprising phenomena that can be tested in feasible experiments.

No-Go Theorems Face Background-Based Theories for Quantum Mechanics

“…At any rate, such 'non-factorizing' correlations do exist in nature, as the reader will easily infer from the examples given in the Appendix. findings of this work and ours corroborate each other (see [16][17] for other recent work inspired by the droplet experiments [1][2][3][4]). Finally, and needless to say, we believe it is now highly desirable to revisit, and investigate the precise link with, the pilot-wave theory of de Broglie and Bohm (in particular in its hydrodynamic formulation); and also sub-quantum theories à la Nelson, which invoke a Brownian background medium [23][24]26].…”

“…It is easy to see that for each of the 4 couples of angles (x,y) intervening in XBI (cf. (4)) M(x,y) can be written as in (17) with two new degrees of freedom (1(x,y), 2(x,y)) for each couple (x,y). For instance, if we choose for (a,b'): P(2|b') = 1 = P(1|a) (the latter probability already being fixed above) and P(2|1,2) = 1, we find as in (15) that:…”

Current-based Simulation Models of Quantum Motion

“…If those macroscopic experiments are able to reproduce -to a certain extent -quantum mechanical experiments like diffraction of a single object or double-slit interference, then at least it should be worth to investigate this mechanism peculiarly with regard to quantum mechanical similarities. This has also been suggested by other authors, for example by Brady and Anderson [BA14] or Richardson et al [Ric14]. In other words, consider the bouncing mass to be an elementary particle like an electron or a neutron whose intrinsic oscillation generates and affects the wave-like landscape around itself.…”

A subquantum arrow of time

“…Interestingly, quantum-like behaviour is found in the motion of oil drops, which, when tapped, collide with surface waves created earlier. [28,29] This proves the possibility that true quantum behaviour originates from classical stochastic forces. On another track, De Raedt and Michielsen have designed learning algorithms for event-by-event simulation, which reproduce the quantum predictions for many photon and neutron experiments without any quantum input.…”