MIT News - Pilot-wave theory
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MIT news feed about: Pilot-wave theoryenFri, 12 Sep 2014 00:00:00 -0400Fluid mechanics suggests alternative to quantum orthodoxy
https://news.mit.edu/2014/fluid-systems-quantum-mechanics-0912
New math explains dynamics of fluid systems that mimic many peculiarities of quantum mechanics.Fri, 12 Sep 2014 00:00:00 -0400https://news.mit.edu/2014/fluid-systems-quantum-mechanics-0912Larry Hardesty | MIT News Office<p>The central mystery of quantum mechanics is that small chunks of matter sometimes seem to behave like particles, sometimes like waves. For most of the past century, the prevailing explanation of this conundrum has been what’s called the “Copenhagen interpretation” — which holds that, in some sense, a single particle really is a wave, smeared out across the universe, that collapses into a determinate location only when observed.</p><p>But some founders of quantum physics — notably Louis de Broglie — championed an alternative interpretation, known as “pilot-wave theory,” which posits that quantum particles are borne along on some type of wave. According to pilot-wave theory, the particles have definite trajectories, but because of the pilot wave’s influence, they still exhibit wavelike statistics.</p><p>John Bush, a professor of applied mathematics at MIT, believes that pilot-wave theory deserves a second look. That’s because Yves Couder, Emmanuel Fort, and colleagues at the University of Paris Diderot have recently discovered a macroscopic pilot-wave system whose statistical behavior, in certain circumstances, recalls that of quantum systems.</p><p>Couder and Fort’s system consists of a bath of fluid vibrating at a rate just below the threshold at which waves would start to form on its surface. A droplet of the same fluid is released above the bath; where it strikes the surface, it causes waves to radiate outward. The droplet then begins moving across the bath, propelled by the very waves it creates.</p><p>“This system is undoubtedly quantitatively different from quantum mechanics,” Bush says. “It’s also qualitatively different: There are some features of quantum mechanics that we can’t capture, some features of this system that we know aren’t present in quantum mechanics. But are they philosophically distinct?”</p><p><strong>Tracking trajectories</strong></p><p>Bush believes that the Copenhagen interpretation sidesteps the technical challenge of calculating particles’ trajectories by denying that they exist. “The key question is whether a real quantum dynamics, of the general form suggested by de Broglie and the walking drops, might underlie quantum statistics,” he says. “While undoubtedly complex, it would replace the philosophical vagaries of quantum mechanics with a concrete dynamical theory.”</p><p>Last year, Bush and one of his students — Jan Molacek, now at the Max Planck Institute for Dynamics and Self-Organization — did for their system what the quantum pioneers couldn’t do for theirs: They derived an equation relating the dynamics of the pilot waves to the particles’ trajectories.</p><p>In their work, Bush and Molacek had two advantages over the quantum pioneers, Bush says. First, in the fluidic system, both the bouncing droplet and its guiding wave are plainly visible. If the droplet passes through a slit in a barrier — as it does in the re-creation of a canonical quantum experiment — the researchers can accurately determine its location. The only way to perform a measurement on an atomic-scale particle is to strike it with another particle, which changes its velocity.</p><p>The second advantage is the relatively recent development of chaos theory. <a href="http://www.technologyreview.com/article/422809/when-the-butterfly-effect-took-flight/">Pioneered</a> by MIT’s Edward Lorenz in the 1960s, chaos theory holds that many macroscopic physical systems are so sensitive to initial conditions that, even though they can be described by a deterministic theory, they evolve in unpredictable ways. A weather-system model, for instance, might yield entirely different results if the wind speed at a particular location at a particular time is 10.01 mph or 10.02 mph.</p><p>The fluidic pilot-wave system is also chaotic. It’s impossible to measure a bouncing droplet’s position accurately enough to predict its trajectory very far into the future. But in a recent series of papers, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris applied their pilot-wave theory to show how chaotic pilot-wave dynamics leads to the quantumlike statistics observed in their experiments.</p><p><strong>What’s real?</strong></p><p>In a review article appearing in the <em>Annual Review of Fluid Mechanics</em>, Bush explores the connection between Couder’s fluidic system and the quantum pilot-wave theories proposed by de Broglie and others.</p><p>The Copenhagen interpretation is essentially the assertion that in the quantum realm, there is no description deeper than the statistical one. When a measurement is made on a quantum particle, and the wave form collapses, the determinate state that the particle assumes is totally random. According to the Copenhagen interpretation, the statistics don’t just describe the reality; they are the reality.</p><p>But despite the ascendancy of the Copenhagen interpretation, the intuition that physical objects, no matter how small, can be in only one location at a time has been difficult for physicists to shake. Albert Einstein, who famously doubted that God plays dice with the universe, worked for a time on what he called a “ghost wave” theory of quantum mechanics, thought to be an elaboration of de Broglie’s theory. In his 1976 Nobel Prize lecture, Murray Gell-Mann declared that Niels Bohr, the chief exponent of the Copenhagen interpretation, “brainwashed an entire generation of physicists into believing that the problem had been solved.” John Bell, the Irish physicist whose famous theorem is often mistakenly taken to repudiate all “hidden-variable” accounts of quantum mechanics, was, in fact, himself a proponent of pilot-wave theory. “It is a great mystery to me that it was so soundly ignored,” he said.</p><p>Then there’s David Griffiths, a physicist whose “Introduction to Quantum Mechanics” is standard in the field. In that book’s afterword, Griffiths says that the Copenhagen interpretation “has stood the test of time and emerged unscathed from every experimental challenge.” Nonetheless, he concludes, “It is entirely possible that future generations will look back, from the vantage point of a more sophisticated theory, and wonder how we could have been so gullible.”</p><p>“The work of Yves Couder and the related work of John Bush … provides the possibility of understanding previously incomprehensible quantum phenomena, involving 'wave-particle duality,' in purely classical terms,” says Keith Moffatt, a professor emeritus of mathematical physics at Cambridge University. “I think the work is brilliant, one of the most exciting developments in fluid mechanics of the current century.”</p>
Pilot-wave theoryQuantum mechanicsMathematicsSchool of ScienceWhen fluid dynamics mimic quantum mechanics
https://news.mit.edu/2013/when-fluid-dynamics-mimic-quantum-mechanics-0729
MIT researchers expand the range of quantum behaviors that can be replicated in fluidic systems, offering a new perspective on wave-particle duality.Mon, 29 Jul 2013 04:00:00 -0400https://news.mit.edu/2013/when-fluid-dynamics-mimic-quantum-mechanics-0729Larry Hardesty, MIT News OfficeIn 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. <br /><br />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.<br /> <br />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.<br /><br />In the latest issue of the journal <i>Physical Review E</i> (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.<br /><br />“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.”<br /><br />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.<br /><br /><strong>Interference inference</strong><br /><br />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.’”<br /><br /><iframe frameborder="0" height="435" src="http://www.youtube.com/embed/nmC0ygr08tE?rel=0" width="580"></iframe> <br /><br /> 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.<br /><br />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.<br /><br />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 a silicone oil and began vibrating it at a rate just below that required to produce surface waves.<br /><br />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.<br /><br />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. <br /><br />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. <br /><br />“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 analogues 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.”<br /><br />“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.”<br />When the waves are confined to a circular corral, they reflect back on themselves, producing complex patterns (grey ripples) that steer the droplet in an apparently random trajectory (white line). But in fact, the droplet’s motion follows statistical patterns determined by the wavelength of the waves.Image: Dan HarrisFluid dynamicsMathematicsPilot-wave theoryResearchCan fluid dynamics offer insights into quantum mechanics?
https://news.mit.edu/2010/quantum-mechanics-1020
Experiments in which fluid droplets mimic the odd behavior of subatomic particles recall an abandoned interpretation of quantum mechanics.Wed, 20 Oct 2010 04:00:00 -0400https://news.mit.edu/2010/quantum-mechanics-1020Larry Hardesty, MIT News OfficeIn the first decades of the 20th century, physicists hotly debated how to make sense of the strange phenomena of quantum mechanics, such as the tendency of subatomic particles to behave like both particles and waves. One early theory, called pilot-wave theory, proposed that moving particles are borne along on some type of quantum wave, like driftwood on the tide. But this theory ultimately gave way to the so-called Copenhagen interpretation, which gets rid of the carrier wave, but with it the intuitive notion that a moving particle follows a definite path through space.<br /><br />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 <em>Proceedings of the National Academy of Sciences</em>, 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.<br /><br />The wave-particle duality is best illustrated by a canonical experiment in quantum mechanics that’s generally referred to as the two-slit, or two-hole, experiment. As the theoretical physicist Richard Feynman ’39 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.’”<br /><br />Suppose you have a tray of water, and across the middle of the tray is a barrier with two openings in it. At one end of the tray is a vibrating rod, and at the other is a pressure sensor. The rod’s vibration sends waves across the surface of the water, and when they pass through the openings in the barrier, two new waves form on the opposite side.<br /><br />On their way to the pressure sensor, these waves run into each other. Where a wave crest meets another crest, they combine to produce a bigger crest. But where a crest and a trough meet, they cancel each other out. The pressure sensor thus registers an “interference pattern” — stripes of various size that represent strong crests, with gaps between them where waves canceled each other out.<br /><br />So what happens when you shoot <em>light</em> at a detector, through a barrier with two holes in it? Again, you get an interference pattern: light appears to behave like a wave. But light also comes in particles, or photons, which can be fired at the detector one at a time. What happens then?<br /><br />As the first few photons strike the detector, they leave a seemingly random scattering of dots, like the bullet holes left in a target by a mediocre marksman. But over time, the dots form a pattern — the same interference pattern produced by a beam of light. How is that possible, given that the photons were fired one at a time?<br /><br /><strong>Different stories</strong><br /><br />Pilot-wave theory proposes that the photons ride on the back of some type of mystery waves, which interact with each other no matter the number of photons that pass through the holes. That interaction is what guides the photons to the detector. When the Austrian physicist Erwin Schrödinger proposed his famous wave equation, which remains the fundamental equation of quantum physics, he was actually describing the guiding wave.<br /><br />Since the Copenhagen interpretation dispenses with the guiding wave, however, it interprets Schrödinger’s equation as instead describing the probability that the photon will be found at a given location. Moreover, until the photon strikes the detector, it’s in a sort of metaphysical limbo, with no definite location. As it passes through the holes, it can thus interfere <em>with itself</em>, which explains the interference pattern at the detector.<br /><br />In formulating his wave equation, Schrödinger was inspired by the theories of Louis de Broglie, who originated pilot-wave theory and whose work on wave-particle duality earned him the 1929 Nobel Prize in Physics. Pilot-wave theory was revived in the 1950s by the physicist David Bohm and still has some proponents, but for the most part, it has faded from view.<br /><br /><strong>Scaling up</strong><br /><br />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.”<br /><br />“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.<br /><br />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. <br /><br />In a paper published in the same issue of <em>PNAS</em>, 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.<br /><br />In the early 1800s, the English scientist Thomas Young conducted experiments with ripple tanks to convince the scientific community that light was a wave. “With Couder’s system, one can now explore aspects of wave-particle duality in a fluid system,” Bush says. “How might the development of quantum mechanics have differed had Couder’s system been known to its founding fathers?”<br /><br />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 BushInnovation and Entrepreneurship (I&E)MathematicsPilot-wave theoryQuantum computing