In February 2012, the Nobel Prize-winning physicist Frank Wilczek decided to go public with a strange and, he worried, somewhat embarrassing idea. Impossible as it seemed, Wilczek had developed an apparent proof of “time crystals” — physical structures that move in a repeating pattern, like minute hands rounding clocks, without expending energy or ever winding down. Unlike clocks or any other known objects, time crystals derive their movement not from stored energy but from a break in the symmetry of time, enabling a special form of perpetual motion.

“Most research in physics is continuations of things that have gone before,” said Wilczek, a professor at the Massachusetts Institute of Technology. This, he said, was “kind of outside the box.”