Since the article doesn't do a good job of explaining what a time crystal
is, here's my attempt at summarizing the Wikipedia article [0].
Normally, a system which is driven by an external frequency oscillates at the same, or a multiple of the driving frequency. This is because the external conditions are symmetric under a time translation (i.e. a delay) by the period duration. This symmetry is normally preserved by the system.
A time crystal, however, will oscillate with a fraction (or rational multiple) of the driving frequency. This breaks the original time translation symmetry.
The analogy with normal 'spatial' crystals is through this symmetry breaking: Empty space is symmetric under all translations, but a crystal spontaneously breaks the symmetry group down to the smaller set of 'translations by a multiple of the lattice constant'.
The continuous symmetry of time translations cannot be spontaneously broken, due to thermodynamic arguments. Instead, we explicitly break down the time translation symmetry to 'delays by a multiple of the period duration'. A time crystal then spontaneously breaks the symmetry down even further, by multiplying the period duration / dividing the frequency.
[0]: https://en.wikipedia.org/wiki/Time_crystal
Normally, a system which is driven by an external frequency oscillates at the same, or a multiple of the driving frequency. This is because the external conditions are symmetric under a time translation (i.e. a delay) by the period duration. This symmetry is normally preserved by the system.
A time crystal, however, will oscillate with a fraction (or rational multiple) of the driving frequency. This breaks the original time translation symmetry.
The analogy with normal 'spatial' crystals is through this symmetry breaking: Empty space is symmetric under all translations, but a crystal spontaneously breaks the symmetry group down to the smaller set of 'translations by a multiple of the lattice constant'.
The continuous symmetry of time translations cannot be spontaneously broken, due to thermodynamic arguments. Instead, we explicitly break down the time translation symmetry to 'delays by a multiple of the period duration'. A time crystal then spontaneously breaks the symmetry down even further, by multiplying the period duration / dividing the frequency.
[0]: https://en.wikipedia.org/wiki/Time_crystal