A research team led by Yves Couder at the Université Paris Diderot recently discovered that it's possible to make a tiny fluid droplet levitate on the surface of a vibrating bath, walking or bouncing across, propelled by its own wave field. Surprisingly, these walking droplets exhibit certain features previously thought to be exclusive to the microscopic quantum realm.

This finding of quantum-like behavior inspired another team of researchers, at the Massachusetts Institute of Technology (MIT), to examine the dynamics of these walking droplets. They describe their findings in the journal *Physics of Fluids*.

"This walking droplet system represents the first realization of a pilot-wave system. Its great charm is that it can be achieved with a tabletop experiment and that the walking droplets are plainly visible," explained John Bush, professor of applied mathematics in the Department of Mathematics at MIT. "In addition to being a rich, subtle dynamical system worthy of interest in its own right, it gives us the first opportunity to view pilot-wave dynamics in action."

The dynamics of the walking droplets are reminiscent of the pilot-wave dynamics proposed by Louis de Broglie in 1926 to describe the motion of quantum particles, in which microscopic particles such as electrons move in resonance with an accompanying guiding wave. Pilot-wave theory wasn't widely accepted and was superseded by the Copenhagen Interpretation of quantum mechanics, in which the macroscopic and microscopic worlds are philosophically distinct.

"Of course, if we ever hope to establish a link with quantum dynamics, it's important to first understand the subtleties of this fluid system," said Bush. "Our recent article is the culmination of work spearheaded by my graduate student, Jan Molacek, who developed a theoretical model to describe the dynamics of bouncing and walking droplets by answering questions such as: Which droplets can bounce? Which can walk? In what manner do they walk and bounce? When they walk, how fast do they go?"In the team's article, Molacek's theoretical developments were compared to the results of a careful series of experiments performed by Øistein Wind-Willassen, a graduate student visiting from the Danish Technical University, on an experimental rig designed by Bush's graduate student, Dan Harris.

"Molacek's work also led to a trajectory equation for walking droplets, which is currently being explored by my graduate student Anand Oza," Bush said. "Our next step is to use this equation to better understand the emergence of quantization and wave-like statistics, both hallmarks of quantum mechanics, in this hydrodynamic pilot-wave system."

The researchers will now seek and explore new quantum analogs, with the ultimate goal of understanding the potential and limitations of this walking-droplet system as a quantum analog system.

**Explore further:**
When fluid dynamics mimic quantum mechanics

**More information:**
The paper, "Exotic states of bouncing and walking droplets," authored by Øistein Wind-Willassen, Jan Molacek, Daniel M. Harris, and John W. Bush, appears in the journal *Physics of Fluids*. dx.doi.org/10.1063/1.4817612

## shavera

## connor_salisbury

However it was rare that I would observe this, and I was uncertain as to the route of reliably reproducing the behavior randomly observed sometimes as a non-scientist (though a science enthusiast).

Very interesting; I hope the pure science leads to something practical and beneficial someday. :-)

## casualjoe

The intelligence of this debate just dropped10 points, sorry.

## Infinum

## vacuum-mechanics

Maybe this simple understandable of 'water beetle wave' is much more reminiscent of the pilot-wave dynamics, and we could also explain and derive the quantum wave create by the motion of quantum particles such as of electron wave ….

http://www.vacuum...19〈=en

## Moebius

## MaxwellsDemon

I think the fact that there *is* a classical pilot-wave analogue is a compelling argument in support of the de Broglie-Bohm model. I don't understand why so many physicists defend the Copenhagen interpretation like it's their daughter's virtue.

Here are some earlier articles on this work:

Single-particle interference observed for macroscopic objects, 9/28/2006

http://phys.org/n...511.html

Can fluid dynamics offer insights into quantum mechanics? 10/20/2010

http://phys.org/n...ics.html

Quantum physics first: Researchers observe single photons in two-slit interferometer experiment, 6/2/2011

http://phys.org/n...ter.html

When fluid dynamics mimic quantum mechanics, 7/29/1013

http://phys.org/n...ics.html

## Macrocompassion

## shavera

Fluids have waves. Quantum Mechanics has wavelike solutions to equations (due to the d'Alembertian appearence within Quantum Mechanics). It's no surprise fluid dynamics and quantum mechanics share similarities, but the fact that they share equations of the form d^2 / dt^2 = d^2 /dx^2 doesn't mean that quantum mechanics *is* fluid mechanics.

## MaxwellsDemon

See what I mean? You can't even imply that the Copenhagen interpretation is less than sacrosanct without getting voted down. Anyway, thanks for the reply but you seem to think that I'm advocating some kind of kooky aether wave theory or whatever…nope.

I was saying that the way this experiment illustrates a classical model of wave-particle behavior, provides a nice intuitive analogue to the pilot wave theory (where the particle and the wave are coupled, as they are in this experiment, but *without* a fluid). And PWT also offers an intuitive way of interpreting the classic double-slit experiment (and everything else for that matter):

http://phys.org/n...ter.html

So I don't understand why comprehensibility is some kind of taboo in QM, and why the de Broglie-Bohm model gets a bad rap. The two interpretations make the same successful predictions, so why not go with the one that can be readily visualized..and simultaneously do away with all that observer/wavefunction collapse business, eh?

## Ducku

The Quantum mysticism meme is very strong and will take a very long time to break down. I have no doubt that these experiments prove that de Broglie-Bohm was right.

"Science advances one funeral at a time." -Max Planck

## KBK

## MrVibrating

lol

## MrVibrating

It's a long-standing convention that we only describe behaviours, ignoring questions of what constitutes the corporeal as unuseful distractions - eg. Newton, Einstein and Feynman (shut up and calculate) all stressed this point.

The above point, together with Bell's elimination of local determinants results in a deep-seated resignation to the inevitability of a causality breakdown - that reason becomes futile and further enquiry pointless.

Anyone objecting to this prevailing cynicism is already on the fringe; their questions invalidated.

Personally, given determinism's dominance in every other sphere, i'm in no rush to abandon it. I cannot separate it from causality itself, hence knowing very little else, there must be a non-local hidden variable, or fundamental substrate, and it must reside in vacuum properties. The alternative is unthinkable.

## MaxwellsDemon

It seems that you're right about the prevailing attachment to the rather mystical Copenhagen interpretation meme, but perhaps it's going too far to call these experiments "proof" of pilot wave theory. But then, I do tend to take skepticism to a somewhat pathological extreme – I don't consider any model "proven," because they all break down in one extreme or another, and at least until we have a working grand unified theory, all of our models of reality are subject to change sooner or later.

I actually wish there were –more- skepticism of prevailing models, because if there were, nice competing theories like PWT would get more of the attention they deserve.

@MrVibrating

Oh I don't see Newton, Einstein or Feynman in that camp at all – all of those guys were deeply concerned with the fundamental nature of reality. Newton defines classical physics, and both of Einstein's relativity theories are sublimely sensible in my opinion, classically comprehensible, albeit intuitively unexpected. And Feynman didn't say that, David Mermin did, and he's not proud of it:

http://fisica.cie...cula.pdf

But I agree with your general philosophical stance – theoretical progress is fueled by sensible conceptual modeling, and the de Broglie Bohm model offers just that. Perhaps what seems to be imponderable is just a deterministic system with a certain level of "noise," as you seem to suggest. At the very least, the fact that the two interpretations yield the correct predictions, should give pause, and all due proper consideration to both competing models. Because successful math is great, but until we have a universal theory of all forces, a deeper comprehension is called for.

## Ducku

"Proof" is maybe a strong word, but I'm convinced that if Yves Couders experiments where known in 1927 the Copenhagen interpretation would have been only a footnote in history. Now on the other hand the establishment is too deeply invested in the current paradigm, and the ship is not easily turned. What is needed to turn tings around I don't know. Too many funerals.

## jch

Nov 06, 2013