A time crystal would be perpetual motion, so it cannot exist

What actually happened

A time crystal is the temporal cousin of an ordinary crystal. A salt crystal breaks symmetry in space: its atoms sit in a pattern that repeats at fixed intervals across a room. A time crystal breaks symmetry in time: its state repeats at fixed intervals into the future, settling into a rhythm that is not the one it was driven at. The idea was proposed by Frank Wilczek in 2012 and was initially argued to be impossible in equilibrium.

The resolution is that a time crystal is not equilibrium and not perpetual motion. It never does useful work, so you cannot extract energy from it, and its entropy stays flat rather than decreasing; the second law is untouched. What it does is maintain order in time the way a magnet maintains order in space, as a stable collective phase rather than a trick.

In 2021 a collaboration including Google, Stanford, Oxford and the Max Planck Institute demonstrated one on the Sycamore chip, and a separate group reported a version using nitrogen defects in diamond. It is now catalogued alongside superfluids, superconductors and Bose-Einstein condensates as a real, if exotic, state of matter, one no classroom periodic-of-phases chart contained.