Crystals may be possible in time as well as space

Theory proposes objects in their lowest energy state can loop in the fourth dimension forever

What sounds like the title of a bad fantasy movie — time crystals — could be the next big thing in theoretical physics.

In two new papers, Nobel Prize–winning physicist Frank Wilczek lays out the mathematics of how an object moving in its lowest energy state could experience a sort of structure in time. Such a “time crystal” would be the temporal equivalent of an everyday crystal, in which atoms occupy positions that repeat periodically in space.

The work, done partly with physicist Alfred Shapere of the University of Kentucky, appeared February 12 on

“We don’t know whether such things do exist in nature, but the surprise is that they can exist,” says Maulik Parikh, a physicist at Arizona State University in Tempe.

Scientists don’t know how important time crystals may turn out to be, or whether they have any practical application at all. But Wilczek, of MIT, says the concept reminds him of the excitement he felt when he helped describe a new class of fundamental particles, called anyons, in the early 1980s. “I had very much the same kind of feeling as I’m having here,” he says, “that I had found a new logical possibility for how matter might behave that opened up a new world with many possible directions.”

Wilczek dreamed up time crystals after teaching a class about classifying crystals in three dimensions and wondering why that structure couldn’t extend to the fourth dimension — time.

To visualize a time crystal, think of Earth looping back to its same location in space every 365¼ days; the planet repeats itself periodically as it moves through time. But a true time crystal is made not of a planet but of an object in its lowest energy state, like an electron stripped of all possible energy.

This object could endlessly loop in time, just as electrons in a superconductor could theoretically flow through space for all eternity. “It’s doing what it wants to do, and what it wants to do is move,” says Wilczek.

In a sense the time crystal would be a perpetual motion machine: If scientists could build one in a lab, it would run forever. Yet it wouldn’t violate the second law of thermodynamics because the crystal would be in its lowest energy state; no useful energy could be extracted from it.

Wilczek is already dreaming of extending the time crystal concept into imaginary time, a theoretical concept of the fourth dimension that runs in a different direction than the one people experience.

“I don’t know if this will be of lasting value at all,” he says, “but I’m having fun.”

Editor’s Note: Frank Wilczek is a member of the board of Society for Science and the Public, which publishes Science News.

Alexandra Witze is a contributing correspondent for Science News. Based in Boulder, Colo., Witze specializes in earth, planetary and astronomical sciences.

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