Physicists Predict The Existence of Time Crystals: In particular, Wilczrek considers spontaneous symmetry breaking in a closed quantum mechanical system. This is where the mathematics become a little strange. Quantum mechanics forces physicists to think about imaginary values of time or iTime, as Wilczek calls it.
He shows that the same periodicities ought to arise in iTime and that this should manifest itself as periodic behaviour of various kinds of thermodynamic properties.
That has a number of important consequences. First up is the possibility that this process provides a mechanism for measuring time, since the periodic behaviour is like a pendulum. “The spontaneous formation of a time crystal represents the spontaneous emergence of a clock,” says Wilczek.