Probing Quantum Behavior in a Large-Scale System
The amazing thing about this setup is that it closely mirrors the behaviors of electrons in quantum experiments. When confined to a circular pen, the droplet tends to hang out in certain concentric rings of the area, mimicking the quantized wave function of the electron. The double-slit experiment, which is commonly taken as evidence that even a single particle of matter behaves as a diffuse wave, also has a parallel—and one that doesn't require the droplet to be in two places at once. Instead, the droplet passes through one slit or the other, but the waves generated by its prior bounces pass through both. It's the interaction of these two wave sets that guide the droplet's motion and cause it to create interference-pattern-like behavior at the detector.
|The pattern produced by a double-slit experiment using single electrons. The alternating pattern of light and dark bands reveals the electrons' wavelike behavior.|
Image Credit: Dr. Akira Tonomura, CC BY-SA 3.0
The Copenhagen interpretation—the most popular interpretation of the results of quantum physics experiments—takes the stance that particles on their own don't have definite positions; they're probability distributions described by a wave function. But when the particle is observed—i.e. interacts with an electric field—the wave function "collapses" and the particle acquires a definite position, randomly assigned in accordance with the probability distribution. This is an intuitively confusing proposition, but it's one of the only consistent ways to explain the results of the double-slit experiment. Firing electrons at a pair of slits—even one particle at a time—produces the interference pattern characteristic of waves...unless you put a detector in front of the slits, to tell which slit the particle went through. If you do, the particles show up in two thin bands, corresponding to the silhouettes of the slits.
The takeaway is that even an individual particle displays wavelike behavior if unobserved, apparently passing through both slits and interfering with itself. But a competing interpretation, offered by Louis de Broglie—who first hypothesized matter's wavelike behavior way back in 1924—suggests that there's more to it than just the wave function.
De Broglie's theory of pilot waves suggested that particles of matter have definite positions, even when they're unobserved, but that each particle has an associated wave that guides its motion, allowing it to move in patterns other than a straight line—just like the droplets bouncing on a silicone bath. The electron passes through one slit or the other, but its pilot wave travels through both, and it's the interactions with the pilot wave that guide the electron's motion. This way of interpreting the experiment's results sits much better with a lot of people, partly because there's no need for randomness in a universe that appears to be deterministic at most other scales.
Now, the dynamics of this analog quantum system are getting further attention from an international collaboration of scientists. Representing a who's-who of big-name institutions, including MIT, UNC Chapel Hill, and the Max Planck Institute, the team published their work last week in the American Physical Society's newest journal, Physical Review Fluids.
The new work turns an eye to the interactions between multiple droplets, examining hours of experimental data and creating a mathematical model to describe their behavior in response to one another's pilot waves. While interacting droplets can exhibit multiple different types of behavior, such as attraction, repulsion, and a side-by-side "promenade", one of the most exciting results from the paper is the description of bound, orbiting pairs of walkers.
The dynamics of these droplets depend on the phase of their bounce, as well as the distance between them. Droplets are said to be perfectly "in phase" if they both reach the peak of their bounce at the same time, and perfectly "out of phase" if one reaches its highest point while the other is at its lowest. Since the surface waves created by the droplets take time to travel, the distance between them also plays an important role in determining their behavior.
If you've ever bounced on a trampoline with a friend, you've probably already got an intuitive understanding of the phenomenon at work here. A trampoline works by temporarily storing your kinetic energy in its springs, then giving it back—on top of the extra push you gave on the latest bounce. The fearsome "double bounce" happens when your friend comes down right before you and their energy gets transferred to you as well, catapulting you skyward.
When the droplets are just the right distance from one another, a similar effect can occur—the waves created by one droplet's bounce arrive under the other droplet just in time to "catch" it and guide it smoothly back up.
The upshot of this is that the pair forms a lower-energy state overall than the individual droplets, creating an attraction between the two. When their tangential velocity is just right to counter this attraction, they end up orbiting each other in a stable way.
|Two "walkers" orbit one another.|
Image Credit: Oza, et al. Physical Review Fluids.
It's not clear yet if there's an adequate quantum-mechanical analogy for this behavior. Perhaps the phase of the droplets' bounces could be related to the spin of electrons, which tend to form pairs and balance out, or perhaps the system could be used to explore a version of the Casimir effect. Whatever the case may be, this is another exciting development in a system that's already provided a surprising amount of insight into the realm of quantum physics.
Ooh, great question!
I imagine it's difficult to create the equivalent on a 2D surface, but I'm thinking the electric field used to detect the electrons at the slits might be roughly analogous to a region of water flowing parallel to the barrier that the slits are in. Disturbances in the laminar flow created by the bouncing droplet would be detectable, but the flow itself would wash out the pilot waves.
This is a wild guess, of course—if any of our other readers can think of a system that would wash out the pilot waves as the droplet travels through the slits, please post it!
Tuesday, May 16, 2017 at 1:41 PM
Maxwell's Demon said...
An interesting thought experiment, but what are the conditions that lead to the equivalent of the measured electron wave collapse observed in the double slit experiment?
Tuesday, May 16, 2017 at 12:59 PM