Fluid dynamics as a way to study quantum mechanics?

Recently, Yves Couder, a physicist at Université Paris Diderot, has conducted a series of experiments in which millimeter-scale fluid droplets, bouncing up and down on a vibrated fluid bath, are guided by the waves that they themselves produce. In many respects, the droplets behave like quantum particles, and in a recent commentary in the Proceedings of the National Academy of Sciences, John Bush, an applied mathematician at MIT who specializes in fluid dynamics, suggests that experiments like Couder’s may ultimately shed light on some of the peculiarities of quantum mechanics.
In Couder’s system — which Bush plans to explore further at MIT — a fluid-filled tray is placed on a vibrating surface. The intensity of the vibrations is held just below the threshold at which it would cause waves — so-called Faraday waves — on the surface of the fluid. When a droplet of the same fluid is placed on the surface, a cushion of air between the drop and the bath prevents the drop from coalescing. The droplet can thus bounce on the surface. The bouncing causes waves, and those waves, in turn, propel the droplet along the surface. Couder and his co-authors call these moving droplets “walkers.”

“One of their first experiments involved sending walkers towards a slit,” Bush says. “As they pass through the slit, they appear to be randomly deflected, but if you do it many times, diffraction patterns emerge.” That is, the droplets strike the far wall of the tray in patterns that reproduce the interference patterns of waves. “Their system is a macroscopic version of the classic single-photon diffraction experiments,” Bush says.

Wave-borne fluid droplets mimic other quantum phenomena as well, Bush says. One of these is quantum tunneling, subatomic particles’ apparent ability to pass through barriers. A walking droplet approaching a barrier across the tray will usually bounce off it, like a hockey puck off the wall. But occasionally, the droplet will take enough energy from the wave that it hops right over the barrier.

In a paper published in the same issue of PNAS, which is the subject of Bush’s commentary, Couder’s group reports its most startling discovery. If the vibrating fluid bath is also rotating, a walking droplet will lock into an orbit determined by the troughs of its wave. The notion that a subatomic particle has only a few allowed orbital states is called “quantization,” the very phenomenon that gives quantum mechanics its name.

Vibrating a tray of silicone oil causes so-called Faraday waves to form in the oil’s surface. Recent experiments in which fluid droplets reproduce the behavior of subatomic particles require holding the intensity of the vibrations just below the Faraday-wave threshold.
Credit: John Bush

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One Response to Fluid dynamics as a way to study quantum mechanics?

  1. Pingback: Fluid dynamics « Eikonal Blog

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