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Could bouncing droplets help us sort out the nature of reality?

Oct. 2, 2013
Courtesy of the
American Institute of Physics,
Larry Hardesty/MIT News Office
and World Science staff

The strange, beau­ti­ful be­hav­ior of ti­ny liq­uid drop­lets may be re­lat­ed to the seem­ingly non­sen­si­cal laws gov­ern­ing na­ture at the small­est scales, phys­i­cists say.

A pa­per pub­lished on­line Aug. 13 in the jour­nal Phys­ics of Flu­ids pre­s­ents equa­t­ions for how liq­uid drop­lets can bounce and “walk” over pools of the same fluid with­out fall­ing in. Phys­i­cists say the drop­lets are guid­ed by waves they them­selves make in the pool—a situa­t­ion rem­i­nis­cent of a the­o­ry devised long a­go to ex­plain the baf­fling be­hav­iors of sub­a­tom­ic par­t­i­cles.

A pair of drop­lets locked into a dance. This is seen in the last of three "boun­cing-dro­plet" vid­eos view­able here: (1, 2, 3), pro­vided by MIT's Dan Har­ris and John Bush.


Known as pilot-wave the­o­ry, it fell out of fa­vor, but nev­er went away.

“This walk­ing drop­let sys­tem repre­s­ents the first real­iz­a­tion of a pilot-wave sys­tem,” said John Bush, a math­e­ma­ti­cian at the Mas­sa­chu­setts In­sti­tute of Tech­nol­o­gy. But un­like the case with the tiny realms that pi­lot-wave theory was de­vised to ex­plain, the drop­lets are “plainly vis­i­ble,” he added.

“It gives us the first op­por­tun­ity to view pilot-wave dy­nam­ics in ac­tion.”

The new work is an out­growth of re­search a few years ago by Yves Couder, a phys­i­cist at Uni­ver­sité Par­is Di­de­rot, who first re­ported the be­hav­ior of the roughly millimeter-sized drop­lets. 

Coud­er’s find­ings fed in­to an old de­bate.

In the early 1900s, phys­i­cists con­tested how to ex­plain sub­a­tom­ic par­t­i­cles’ strange be­hav­ior, such as their ten­den­cy to be­have both as par­t­i­cles and waves. This is per­plex­ing be­cause waves are not trad­i­tion­ally con­sid­ered phys­ical objects—they’re os­cil­la­tions. And par­t­i­cles act­ing like waves de­fies com­mon sense. For in­stance, waves in­ter­fere with each oth­er: if you drop two stones in a pond, their outward-mov­ing waves will al­ter each oth­er’s ap­pear­ance as they meet. In­di­vid­ual ob­jects can’t “in­ter­fere” with each oth­er like that, one would think. But sub­a­tom­ic par­t­i­cles, such as pho­tons, or par­t­i­cles of light, do—and they don’t even have to be mov­ing at the same time. Their mu­tu­al “in­ter­ference” can be seen in the pat­terns they form when they strike a sur­face and the land­ing loca­t­ions are marked.

Pilot-wave the­o­ry, proposed by Lou­is de Brog­lie in the 1920s, rec­on­ciled these prob­lems by pro­pos­ing that mov­ing par­t­i­cles are borne along on some sort of wave, like drift­wood on the tide. 

But no one ev­er quite ex­plained what that wave was. The the­o­ry ul­ti­mately gave way to the so-called Co­pen­ha­gen in­ter­preta­t­ion on quan­tum me­chan­ics, which pre­vails to­day. It gets rid of the car­ri­er wave—but with it the com­mon-sense no­tion that a par­t­i­cle trav­els a def­i­nite path. It holds that ti­ny par­t­i­cles have no def­i­nite loca­t­ion or tra­jec­to­ry un­til a meas­ure­ment take place, an idea that, if not ter­ribly sat­is­fy­ing, at least solves the prob­lems at hand math­e­mat­ic­ally.

En­ter Coud­er’s re­search.

He placed an oil-filled tray on a sur­face that was vi­brat­ing not quite strongly enough to pro­duce waves. When a drop­let of the same flu­id was placed on the sur­face, a cush­ion of air be­tween the drop and the bath pre­vented the drop from merg­ing. The drop­let then bounced on the sur­face. The bounc­ing caused waves, which in turn pro­pelled the drop­let along.

In­i­tial ex­pe­ri­ments sug­gested that the drop­lets acted like waves in some cir­cum­stances—much as sub­a­tom­ic par­t­i­cles do.

The more re­cent pa­per looked at the drop­let tra­jec­to­ries in fur­ther de­tail.

“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?”

The pa­per com­pared Mo­lacek’s de­vel­op­ments to the re­sults 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”—be­ha­vior at the small­est scales.

In­ter­est­ing­ly, pilot-wave the­o­ry is si­m­i­lar to a view pro­posed by great phys­i­cist Isaac New­ton three cen­turies ago. He main­tained that par­t­i­cles of light gen­er­ate waves as skip­ping stones do, and that these waves in turn af­fect the mo­tion of the par­t­i­cles. In this pic­ture, the sub­stance form­ing the ac­tu­al waves was “the ae­ther”—a hy­po­thet­ical flu­id-like sub­stance then be­lieved to fill space. Phys­i­cists con­clud­ed much lat­er that there is no ae­ther.


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The strange, beautiful behavior of tiny liquid droplets may be related to the seemingly nonsensical laws that govern the even smaller objects of the subatomic world, physicists say. A paper published online Aug. 13 in the journal Physics of Fluids presents equations for how liquid droplets can bounce and walk over pools of the same liquid without actually merging into them. Physicists say these droplets are guided by waves that they themselves make in the pool—a situation reminiscent of a long-ago theory to explain the baffling behavior of subatomic particles. That theory, called pilot-wave theory, fell out of favor but never quite went away. “This walking droplet system represents the first realization of a pilot-wave system”—though it involves objects that are big enough to be “plainly visible,” said John Bush, a mathematician at the Massachusetts Institute of Technology. “It gives us the first opportunity to view pilot-wave dynamics in action.” The new work is an outgrowth of research a few years ago by Yves Couder, a physicist at Université Paris Diderot, who first reported the behavior of the roughly millimeter-sized droplets. Already then, Couder’s findings fed into an old debate. In the early 1900s, physicists contested how to explain subatomic particles’ strange behavior, such as their tendency to behave both as particles and waves. This is difficult because particles acting like waves defies common sense. For instance, waves interfere with each other: if you drop two stones in a pond, their outward-moving waves will alter each other’s appearance as they meet. Individual objects can’t “interfere” with each other like that, one would think. But subatomic particles, such as photons, or particles of light, do—and they don’t even have to be moving at the same time. Their mutual “interference” can be seen in the patterns they form when they strike a surface and the landing locations are marked. Pilot-wave theory, originated by the physicist Louis de Broglie, reconciled these problems by proposing that moving particles are borne along on some sort of wave, like driftwood on the tide. But no one ever quite explained what that wave was. The theory ultimately gave way to the so-called Copenhagen interpretation on quantum mechanics, which prevails today. It gets rid of the carrier wave—but with it the common-sense notion that a particle travels a definite path. It holds that tiny particles have no definite location or trajectory until a measurement take place, an idea that, if not terribly satisfying, at least solves the problems at hand mathematically. Enter Couder’s research. He placed an oil-filled tray on a surface that was vibrating not quite strongly enough to produce waves. When a droplet of the same fluid was placed on the surface, a cushion of air between the drop and the bath prevented the drop from merging. The droplet then bounced on the surface. The bouncing caused waves, which in turn propelled the droplet along. Initial experiments suggested that the droplets, which are clearly particles, nonetheless acted like waves in some circumstances—much as subatomic particles do. The more recent paper looked at the droplet trajectories in further detail. “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?” The paper compared Molacek’s developments to the results 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.” Interestingly, pilot-wave theory is similar to a view proposed by great physicist Isaac Newton three centuries ago. He maintained that particles of light generate waves as skipping stones do, and that these waves in turn affect the motion of the particles. In this picture, the substance forming the actual waves was the “aether”—a hypothetical fluid-like substance then believed to fill all of space. Physicists concluded much later that there is no aether.