Riding the Rogue Quantum Waves

In February 1933 the U.S. Navy oiler USS Ramapo was making good time on its run across the South Pacific when an officer spied a monster directly astern on the horizon. A huge rogue wave—a solitary sea swell that is much larger and more powerful than the surrounding waves—rapidly overtook the ship. Later, the Ramapo’s crew, having somehow survived the freak encounter, triangulated the wave’s height at an astounding 34 meters (112 feet)—the tallest rogue wave ever recorded.

Now, a trio of physicists is taking inspiration from such rogue waves—and the model commonly used to describe how they grow to such immense heights—to see if they can help solve one of the biggest mysteries in physics. Supported by a research grant of over $50,000 from FQXi, Thomas Durt of the École Centrale de Marseille, in France, Ralph Willox at the University of Tokyo, in Japan, and Samuel Colin of the Brazilian Center for Physics Research, in Rio de Janeiro, are investigating an alternative to quantum theory which can explain how the definite everyday world we see around us emerges from the uncertain microscopic realm, where objects can be in multiple places at the same time.

In the decade before the Ramapo’s momentous meeting in the South Pacific, leading European theorists had begun laying the foundations of quantum theory. They were grappling with the notion that on small scales, particles can behave as waves, and waves as particles, depending on how they are measured. Stranger still was that a quantum particle-cum-wave has no location until it is observed; only when it is measured does it settle in one spot. In 1926, Austrian physicist Erwin Schrödinger encapsulated this uncertainty by describing quantum objects mathematically as "wavefunctions." Schrödinger’s equation enables physicists to predict the probability of finding the quantum object in a particular place, or indeed with other fixed properties, when they carry out their experiment to measure the object’s features.

According to standard quantum theory, the observer carrying out the experiment in some way causes the collapse of the quantum wave-function, forcing the quantum object to take on definite properties. But nobody can explain how or why that should happen. So Durt, Willox and Colin have turned to rogue ocean waves—which scientists today actually describe using a more complicated version of the Schrödinger equation—for an answer.

Soaking Energy

Although rogue waves have many causes, scientists believe they sometimes develop spontaneously from natural processes that occur amid a random background of smaller waves. Researchers hypothesize that an unusual wave type can form that somehow ’sucks’ energy from surrounding waves to grow to enormous heights. The version of the Schrödinger equation that is used to describe rogue wave formation is described as a "non-linear" equation because—unlike the linear Schrödinger equation that is commonly used in quantum theory—it allows for the possibility that the waves in the system interact with themselves, amplifying effects. One of the simplest models says that through such non-linear processes, a normal ocean wave ’soaks’ energy from the adjacent waves, reducing them to mere ripples as it rises in turn.

Could a similar effect be happening in quantum systems, enabling one type of quantum wave—corresponding to the quantum system being in one place, rather than spread over multiple locations, say—to grow at the expense of others? If so, this could explain how the quantum wavefunction collapses, as this single wave dominates over the others. "We aim to explain this spontaneous localization of the wave based on a process similar to the formation of rogue waves, whose birth is best described by a non-linear wave equation that describes extreme event amplification arising from small perturbations," Durt explains (see Classical and Quantum Gravity 31 (2014)).

Some years back, the mainstream view would have been that this approach is stretching an analogy too far, because subatomic systems and ocean waves are simply too different in character to be treated with the same math. But that’s changing: "Three or four years ago, I would have told you ’no, you will not find rogue wave-like phenomena in quantum mechanics’," notes Majid Taki, a physicist at the Lille University of Science and Technology, in France, who is an expert on non-linear waves in macroscopic environments.

"That’s because at the time we believed that rogue waves come only from highly non-linear conditions," Taki continues. Now, however, new research on rogue waves shows that they can be built in nearly linear systems that have only a small degree of non-linearity, a situation that is much closer to the quantum case. "I think now is the moment to try to find such effects in near-linear systems," says Taki, who is so convinced by the similarities that he advised Durt to pursue this approach.

Durt, Willox and Colin hope to develop new ways to test their model by carrying out experiments in an optical trap—a focused laser beam that generates small forces that physically hold tiny objects in empty space like ’optical tweezers.’ The plan is to drop a quantum object, such as a nano-sized sphere, in a gravity-free environment. Ideally, this test would be performed in space because, far from Earth’s gravity, it will be possible to see whether gravitational effects induced between the components of the nanosphere itself (the self-interaction required by the model) causes the object’s wavefunction to collapse (Physical Review A 93, 062102 (2016)).

"This is an ambitious proposal," says FQXi member Catalina Curceanu, a quantum physicist and expert on collapse models at the National Institute of Nuclear Physics in Frascati, Italy. "Such experiments are very difficult because of the extreme precision that’s required." Curceanu says. "It means pushing existing technology to extremes, which is a good thing."