Common crystals exhibit broken translation symmetry: they have repeated patterns in space and are not invariant under arbitrary translations or rotations. The laws of physics are unchanged by arbitrary translations and rotations. However, if we hold fixed the atoms of a crystal, the dynamics of an electron or other particle in the crystal depend on how it moves relative to the crystal, and particle momentum can change by interacting with the atoms of a crystal — for example in Umklapp processes. Quasimomentum, however, is conserved in a perfect crystal.
Time crystals show a broken symmetry analogous to a discrete space-translation symmetry breaking. For example, the molecules of a liquid freezing on the surface of a crystal can align with the molecules of the crystal, but with a pattern less symmetric than the crystal: it breaks the initial symmetry. This broken symmetry exhibits three important characteristics:
* the system has a lower symmetry than the underlying arrangement of the crystal,
* the system exhibits spatial and temporal long-range order (unlike a local and intermittent order in a liquid near the surface of a crystal),
* it is the result of interactions between the constituents of the system, which align themselves relative to each other.