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."