**MIT scientists uncover quantum behavior in fluid dynamics, offering a new perspective on wave-particle duality.**

In the early days of quantum physics, in an attempt to explain the wavelike behavior of quantum particles, the French physicist Louis de Broglie proposed what he called a “pilot wave” theory. According to de Broglie, moving particles — such as electrons, or the photons in a beam of light — are borne along on waves of some type, like driftwood on a tide.

Physicists’ inability to detect de Broglie’s posited waves led them, for the most part, to abandon pilot-wave theory. Recently, however, a real pilot-wave system has been discovered, in which a drop of fluid bounces across a vibrating fluid bath, propelled by waves produced by its own collisions.

In 2006, Yves Couder and Emmanuel Fort, physicists at Université Paris Diderot, used this system to reproduce one of the most famous experiments in quantum physics: the so-called “double-slit” experiment, in which particles are fired at a screen through a barrier with two holes in it.

In the latest issue of the journal *Physical Review E (PRE)*, a team of MIT researchers, in collaboration with Couder and his colleagues, report that they have produced the fluidic analogue of another classic quantum experiment, in which electrons are confined to a circular “corral” by a ring of ions. In the new experiments, bouncing drops of fluid mimicked the electrons’ statistical behavior with remarkable accuracy.

“This hydrodynamic system is subtle, and extraordinarily rich in terms of mathematical modeling,” says John Bush, a professor of applied mathematics at MIT and corresponding author on the new paper. “It’s the first pilot-wave system discovered and gives insight into how rational quantum dynamics might work, were such a thing to exist.”

Joining Bush on the PRE paper are lead author Daniel Harris, a graduate student in mathematics at MIT; Couder and Fort; and Julien Moukhtar, also of Université Paris Diderot. In a separate pair of papers, appearing this month in the Journal of Fluid Mechanics, Bush and Jan Molacek, another MIT graduate student in mathematics, explain the fluid mechanics that underlie the system’s behavior.

#### Interference inference

The double-slit experiment is seminal because it offers the clearest demonstration of wave-particle duality: As the theoretical physicist Richard Feynman once put it, “Any other situation in quantum mechanics, it turns out, can always be explained by saying, ‘You remember the case of the experiment with the two holes? It’s the same thing.’”

If a wave traveling on the surface of water strikes a barrier with two slits in it, two waves will emerge on the other side. Where the crests of those waves intersect, they form a larger wave; where a crest intersects with a trough, the fluid is still. A bank of pressure sensors struck by the waves would register an “interference pattern” — a series of alternating light and dark bands indicating where the waves reinforced or canceled each other.

Photons fired through a screen with two holes in it produce a similar interference pattern — even when they’re fired one at a time. That’s wave-particle duality: the mathematics of wave mechanics explains the statistical behavior of moving particles.

In the experiments reported in PRE, the researchers mounted a shallow tray with a circular depression in it on a vibrating stand. They filled the tray with silicone oil and began vibrating it at a rate just below that required to produce surface waves.

They then dropped a single droplet of the same oil into the bath. The droplet bounced up and down, producing waves that pushed it along the surface.

The waves generated by the bouncing droplet reflected off the corral walls, confining the droplet within the circle and interfering with each other to create complicated patterns. As the droplet bounced off the waves, its motion appeared to be entirely random, but over time, it proved to favor certain regions of the bath over others. It was found most frequently near the center of the circle, then, with slowly diminishing frequency, in concentric rings whose distance from each other was determined by the wavelength of the pilot wave.

The statistical description of the droplet’s location is analogous to that of an electron confined to a circular quantum corral and has a similar, wavelike form.

“It’s a great result,” says Paul Milewski, a math professor at the University of Bath, in England, who specializes in fluid mechanics. “Given the number of quantum-mechanical analogs of this mechanical system already shown, it’s not an enormous surprise that the corral experiment also behaves like quantum mechanics. But they’ve done an amazingly careful job, because it takes very accurate measurements over a very long time of this droplet bouncing to get this probability distribution.”

“If you have a system that is deterministic and is what we call in the business ‘chaotic,’ or sensitive to initial conditions, sensitive to perturbations, then it can behave probabilistically,” Milewski continues. “Experiments like this weren’t available to the giants of quantum mechanics. They also didn’t know anything about chaos. Suppose these guys — who were puzzled by why the world behaves in this strange probabilistic way — actually had access to experiments like this and had the knowledge of chaos, would they have come up with an equivalent, deterministic theory of quantum mechanics, which is not the current one? That’s what I find exciting from the quantum perspective.”

Reference: “Wavelike statistics from pilot-wave dynamics in a circular corral” by Daniel M. Harris, Julien Moukhtar, Emmanuel Fort, Yves Couder and John W. M. Bush, 10 July 2013, *Physical Review E*.

DOI: 10.1103/PhysRevE.88.011001

Related Publications:

- “Drops bouncing on a vibrating bath” by Jan Molaceka1 and John W. M. Bush, 28 June 2013,
*Journal of Fluid Mechanics*.

DOI: 10.1017/jfm.2013.279 - “Drops walking on a vibrating bath: towards a hydrodynamic pilot-wave theory” by Jan Molaceka1 and John W. M. Bush, 28 June 2013,
*Journal of Fluid Mechanics*.

DOI:10.1017/jfm.2013.280

One thing “troubles” me with this experiment. . .I am not lying awake over it though. . .

There is an explicit “driving energy source” present in this Experiment. .The Shaker. . .although the shaking frequency is of low enough amplitude to prevent the development of measurable surface waves in the fluid surface there is nevertheless a low level systematic excitation frequency at play to keep the process in motion. This low amplitude excitation energy is likely the source of the preferential rings formed by the statistical position of the droplet. This can be explained in an analogous way as the statistical electron “positions” in “wave-like orbits and are defined by the Schrodinger Wave Equation Orbits. The electrons do not actually “move” in circular bur are more frequently found at instantaneous positions on those circles that between them. Location Probability Equation

There is obviously a “coupling” between the waves the bouncing droplets creates and the excitation energy frequency a sort resonance effect on a molecular level of the exited fluid. . .If the excitation frequency is shut down early in the experiment then certainly the probability rings will NOT develop noticeably and the bouncing droplet motion will cease and the droplet will merge with the fluid and the fluid motion will cease too.

Specific to the experiment is that different excitation frequencies will generally develop unique probability circles. . .indication that it is not really an “elementary particle” quantum effect but a low level Classical Mechanics Effect.. . very analogous to sand patterns that develop over time on vibrating membranes. Using membranes of arbitrary shapes creates unique forms for where the sand grains are preferentially found. It is to be noted that the sand grains are NOT exclusively present on the preferred areas but also keep bouncing on and through the non-preferential areas.

It would be interesting ti find out if this experiment were repeated with oval vessels, square rectangular, triangular and arbitrarily shaped vessels. I suspect that the preferred location regions will develop very similarly as sand patterns on vibrating membranes.

Of course. . .how exactly the physical shape of the Fluid Shaker will influence the preferential location of the droplets in no less interesting than how the frequency will influence it.

This “wave effect” many not be exactly identical to the “de Broglie Waves” exhibited by electrons, neutrons and essentially all fundamental “particles” but it could well be that that the interaction of electrons with for example in the (Double) Slit Experiments (1) ALWAYS also interact with the atomic and molecular frequencies of the materials in which the slits are made.. . .Shooting electrons through slits that are 10 cm wide and 1 m apart ALSO produces de Brogli Wave Interference Patterns. . .but these are not at all easily detectible. . It would require horribly expensive testing with sensors that will detect single electron impacts OR experiments that require horribly long testing periods . . .

The de Brogli wavelength of an electron is 0,12 nanometer if it has a speed of 6630 km/sec.

(1)From among other sources and casual discussions with people at the FOM Institute at Nieuwegein, The Netherlands.

Essentially when you shoot electrons at a target without using any hole at all a circular set of interference patterns results with the centre at the “target position” and there most electrons will appear to impact. According to the modern concept of what an electron is and how it behaves some electrons will end up at 180 degrees away from the target spot, this is behind the electron Gun, and there it will “impact” without having followed any specific paths through space. . .

An individual electron is defined in terms of a 3-Dimensional spatial electric field with 1/r^2 Charge Density and Charge “e”, as a Point Source, with mass “m” and a few more quantum numbers such a + or – 1/2 Spin and a + or – Magnetic Moment. . .If there is another Quantum Number to define it I have forgotten it.. . .It does not really deserve the name Particle and it might be better to call it Casper The Ghost.

The idea of the “empty” space in qm (outside the relativity limits) made the pilot-wave theory baseless.The turbulent interacting space can(as we see) explain the mystic features of the quantum particles and the lack of the tragectories.So this mystic has its structure and explanation!