In October 1927, some of the greatest minds in physics gathered for the Fifth Solvay International Conference to debate the troubling implications of the then-nascent theory of quantum mechanics. A particularly contentious topic was the perplexing “wave-particle duality,” in which objects we typically think of as particles—like photons and electrons—exhibit wave-like properties as well, and things we think of as waves, like light, sometimes behave like particles.
The French physicist Louis de Broglie proposed a means by which a photon or electron could behave like both a particle and a wave, complementary aspects of the same phenomenon. He reasoned that the particles could be carried along by what he dubbed “pilot waves”—fluid-like ripples in space and time—much like a buoys bobbing along with the tide.
De Broglie won the Nobel Prize in Physics just two years later, but it wasn’t for pilot waves. His contemporaries largely dismissed his explanation for the dual nature of subatomic particles. Now, more than 80 years later, a series of experiments on the behavior of oil droplets bouncing along a vibrating liquid surface have provided a macroscale analog of de Broglie’s pilot waves, replicating some of the stranger properties of quantum mechanics.
Quantum mechanics seeks to describe nature at the level of individual atoms and the particles that comprise them. But when physicists began delving into this strange new realm at the dawn of the 20th century, they discovered that the old, deterministic laws of classical physics no longer apply at that scale. Instead, uncertainty reigns supreme. It is a world governed by probabilities, and many physicists found this disquieting, to say the least. Hence Albert Einstein’s famous declaration at the Solvay conference that God does not play dice with the universe, prompting Niels Bohr to counter, “Einstein, stop telling God what to do.”
At the heart of the discomfort is the question of uncertainty. Flip a coin, and it will land either heads or tails; in principle, with complete information about the coin, the hand doing the flipping, and the movement of air molecules around the flip, it is possible to predict the outcome. In the quantum world, things hover in a fuzzy, nebulous cloud of probability called a wave function that encompasses all potential states, with no prospect of gaining further information. Flip a quantum coin, and it is both heads and tails until we look. Things become definite only when an observation forces them to settle on a specific outcome.
To Einstein, the notion of observation dictating the outcome of an experiment was ridiculous, since it denied the existence of a solid underlying reality. Even Schrödinger, inventor of the wave function, was deeply disturbed by the implications of what he’d helped create, memorably declaring, “I don’t like it, and I’m sorry I ever had anything to do with it.”
De Broglie’s alternative pilot wave theory was an attempt to restore that underlying solid reality. Instead of the wave function, de Broglie’s pilot wave theory employs two equations, one describing an actual wave and the other describing the path of an actual particle and how it interacts with, and is guided by, the wave equation. It is deterministic, like a classical coin flip. In principle, at least, we can glean sufficient information to plot a particle’s path, something that is not allowed in Bohr’s interpretation of quantum mechanics.
While the idea of pilot wave theory never really caught on, it stubbornly refused to die. A physicist named David Bohm proposed a modified version in the 1950s that also failed to gain much traction. But perhaps the pilot wave’s time has come at last.
The latest resurgence of interest began in Paris about ten years ago, when Yves Couder and Emmanuel Fort of Diderot University started experimenting with oil droplets bounced off a vat of vibrating liquid. The droplet’s impact causes waves to ripple outward, like tossing a pebble in a pond. If the liquid in the vat vibrates at just the right frequency, usually quite close to the droplet’s natural resonant frequency, the droplet interacts with the ripples it creates as it bounces along, which in turn can affect its path. That’s eerily similar to de Broglie’s notion of a pilot wave. Such a system turns out to be a fantastic means for simulating weird quantum effects like the dual nature of light and matter.
The 19th century physicist Thomas Young demonstrated this with his famous “double-slit” experiment. In the double slit experiment, a series of photons or electrons strike a screen with two slits in it before landing on a detector behind the screen. If you consider photons and electrons to be particles, you would expect the detector light up along the path through the slits and nowhere else. But that’s not what Young found. Instead, Young discovered an interference pattern of alternating light and dark bands, suggesting that the would-be particles were acting like water waves passing through a barrier wall with two openings. But if one places detectors near the slits to “see” which slit each particle went through, then the interference pattern disappears—the waves start acting like particles. It is the essence of quantum weirdness.
Couder and Fort replicated Young’s experiment by steering their bouncing droplets toward such a screen with a slit, helped along by the pilot waves created by the vibrating liquid. While they appear to scatter randomly as they pass through the slit, over time, wavy interference patterns emerge. “Guided” by the pilot waves, the droplets appear to be drawn to those regions where the wavefronts add together, and steer clear of those regions where the wavefronts cancel each other out. Disturbing the pilot wave destroys the interference pattern, much like measuring the path of particles as they hit the screen does.
Last year, pilot wave theory received another boost when MIT physicists Daniel Harris and John Bush used a similar fluid system to mimic a “quantum corral,” in which electrons are trapped within a ring of ions. Harris and Bush made a shallow tray with a circle-shaped trough in the center to serve as the walls of the “corral.” They filled the tray with silicon oil and mounted it on a vibrating stand tuned to a frequency just shy of that required to produce pilot waves spontaneously, without the droplet, according to Bush. Above that threshold, the roiling sea of waves will interfere with the droplet’s walk. Below it, the surface remains smooth except for the waves produced by the bouncing droplet. The closer one tunes the vibrations to that threshold, the more robust and long-lived the generated pilot waves will be.
When the bouncing droplet produced waves, those waves bounced off the walls and interfered with each other, producing pretty interference patterns. They also affected the trajectory of the droplet. At first it looked like it was bouncing along randomly, but over time (around 20 minutes), the droplet was far more likely to drift towards the center of the circle, and increasingly less likely to be found in the rippling rings spreading out from that center. That probability distribution for the single droplet proved very similar to that of an electron trapped in a quantum corral.
The droplet experiments provide an intriguing analogue or “toy model” for de Broglie’s pilot waves, but there is still no direct evidence of pilot waves at the quantum scale. “Time will tell whether the quantum-like behavior of the walking dropets is mere coincidence,” Bush told me via email. Also, the theory is currently limited to describing the simplest interactions between particles and electromagnetic fields. “It is not by itself capable of representing very much physics,” Oxford University physics philosopher David Wallace told Quanta earlier this year. “In my own view, this is the most severe problem for the theory, though, to be fair, it remains an active research area.”
Nobody is claiming that quantum mechanics is wrong; there is too much experimental evidence that the equations do make accurate predictions about how things work at the subatomic scale. But the implications of the standard interpretations remain troubling. The pioneers of quantum mechanics came up with the most plausible theory they could, given the resources they had, and they transformed modern physics in the process. Contemplating the possibility of pilot wave theory might lead to a fresh interpretation of quantum weirdness, one that prompts physicists to rethink their longstanding assumptions about the true nature of the quantum world. Another transformation could be lurking in the wings.
Author’s picks for further reading
Cocktail Party Physics, Scientific American: The Photon Has Two Faces
Jennifer Ouellette on quantum interference, the wave-particle duality, and that “cheeky over-achieving upstart” Thomas Young.
Quanta: Fluid Tests Hint at Concrete Quantum Reality
Natalie Wolchover on macroscale analogs for pilot wave physics.