The phrases "perpetual-motion machine"—a concept derided by scientists since the mid-19th century—and "physics Nobel laureate Frank Wilczek" wouldn't seem to belong in the same sentence. But if Wilczek's latest ideas on symmetry and the nature of time are correct, they would suggest the existence of a bona fide perpetual-motion machine— albeit one from which energy could never be extracted. He proposes that matter could form a "time crystal," whose structure would repeat periodically, as with an ordinary crystal, but in time rather than in space. Such a crystal would represent a previously unknown state of matter and might have arisen as the very early universe cooled, losing its primordial symmetries.
"The papers themselves are perfectly respectable, undoubtedly correct, and interesting," says cosmologist Sean Carroll of the California Institute of Technology.
Known for his pioneering work in developing quantum chromodynamics, the theory that explains how the particles inside atomic nuclei stick together, Wilczek, a professor at the Massachusetts Institute of Technology, says he got his latest idea two years ago while teaching a course on group theory. That branch of mathematics, which uses matrices to describe the symmetries inherent in families of elementary particles, also describes and classifies the structure of crystals. Materials such as a liquid or a gas in equilibrium, made of uniformly distributed particles, exhibit perfect spatial symmetry—they look the same everywhere and in every direction.
But at very low or minimum energies, most materials can't retain that symmetry, and they crystallize. The regular geometric pattern of a crystal lacks complete spatial symmetry; the structure does not look the same everyplace. Because crystals have less symmetry than before, physicists say they exhibit spontaneous symmetry breaking. Equivalent processes occur in many domains of physics. A type of broken symmetry, which would be indicated by the presence of the Higgs boson now being hunted at the Large Hadron Collider, would explain why subatomic particles have mass.
Wilczek says he started wondering whether the concept of an ordinary three-dimensional crystal could be extended to four dimensions, with the extra dimension that of time. A time crystal would spontaneously break what Wilczek calls "the mother of all symmetries"—the symmetry of time translation, which holds physical laws remains the same regardless of what time it is. A time crystal would change with time but keep coming back to the same form it began with, like a clock whose moving hands periodically return to their original positions.
The difference from an ordinary clock or other periodic process is that a time crystal, as with a spatial crystal, would be a state of minimum possible energy. At first glance, that poses a contradiction. A time crystal by definition must change with time in order to break time translation symmetry. But a system with minimum energy ordinarily can't move. If it could, then additional energy could still be extracted, until the system achieved a true minimum energy, a motionless state.
"At first I thought this was easy, then that it was impossible," Wilczek noted in a recent lecture at Arizona State University at Tempe. "Now I think it's neither easy nor impossible."
He and Shapere showed that a material could have zero total energy yet still be in motion. They did so by mathematically reformulating the ordinary definition of kinetic energy (one-half mass times velocity squared) to a different but equally valid value that depends on a velocity in an alternative way (for instance, adding an additional term such as velocity to the fourth power and changing the sign of the usual kinetic energy).
"I'm just very surprised at this," says theoretical physicist Maulik Parikh of Arizona. "Frank found subtle exceptions that link motion and the state of being at minimum energy."
Carroll agrees: "It's amusing to find a system that features motion in its ground state, but it certainly doesn't violate any truly cherished beliefs of physics. I'm ready to believe that such a system could even be constructed in the real world."
The motion of the crystal "'spontaneously breaks' time translation symmetry, even if the theory itself does not contain any preferred time direction," says Cristian Armendáriz Picón of Syracuse University, who has studied the possibility of similar phenomena in cosmology.
Once set in motion, a time crystal could remain in motion forever, with no outside force needed to keep it going. This type of perpetual motion machine would not violate any known physical law because no energy could be extracted from the system without first adding energy. Such systems might even be arranged to convey information that would persist after everything else around them has died.
Carroll cautions, however, that a time crystal may not survive indefinitely. Even if the crystal has the minimum possible energy, it might not have the highest possible entropy, or disorder; a crystal blown up into individual particles and spread across space would have higher entropy. If so, the time crystal would eventually suffer such a fate, because the universe always evolves toward higher entropy. "I don't think it's realistic to expect such a thing to last literally forever—but much longer than anything else is quite conceivable," Carroll says.
The closest that modern technology has come to a time crystal, Wilczek says, is a current-carrying superconductor, a material that carries a moving, persistent current at low temperatures. In an ordinary superconducting cable, the current is constant, and if nothing actually changes with time, the superconductor does not qualify as a true crystal. But if engineers could construct a superconductor with a lumpy rather than uniform distribution of charged particles, then as the current flows, the lumps move, and the persistent current would change with time.
The concept of a time crystal, Armendáriz Picón says, may shed light on how natural phenomena that are asymmetric with time can be described in terms of symmetric theories. It could even apply to the origin and evolution of the universe. "One can think of these [time] crystals as a new form of matter, and this matter may be responsible for ill-understood phenomena such as the current stage of accelerated cosmic expansion," he says.
"It's early days" for the theory, Wilczek cautions. For physicists, time crystals are "like discovering a new continent," he said in a recent talk. But, he adds, whether that new continent is "a New World, or Antarctica, time will tell."