and not carefully enough, IMHO.

Yes, a (perfect, inorganic) crystal is a regular stacking of atoms. But it's more than that. There are mathematical properties of crystals (point groups in 3 dimensions, space groups (there are 230 of them)) that describe and constrain how the "regular stacking" (or unit cell) repeats. Basically, those rules describe how you can translate from one place in the crystal to another, how you can rotate the crystal, how you can form mirror planes (or not), etc., etc., and still end up with the same arrangement of atoms at that new position (

So, she's right but incomplete (and needlessly vague, IMHO) when talking about crystals in 3D space.

A "time crystal" is a kind-of unfortunate name, but it has similar mathematical ideas behind it. Instead of things repeating in a mathematically well-defined arrangement in 3D space, things repeat in time. Symmetry and how that symmetry is "broken" is important in both cases. And time crystals are studied in the quantum regime because of the difficulty in getting macroscopic (huge numbers of atoms) into a well defined state simultaneously.

Or, as a story at Phys.org says:

HTH a little.

Cheers,

Scott.

Yes, a (perfect, inorganic) crystal is a regular stacking of atoms. But it's more than that. There are mathematical properties of crystals (point groups in 3 dimensions, space groups (there are 230 of them)) that describe and constrain how the "regular stacking" (or unit cell) repeats. Basically, those rules describe how you can translate from one place in the crystal to another, how you can rotate the crystal, how you can form mirror planes (or not), etc., etc., and still end up with the same arrangement of atoms at that new position (

**and be able to fill all of space with it (no holes)**). It may seem academic, but the math is powerful because different surfaces of crystals can have different electrical, chemical, etc., properties and you can often have an inkling of that in advance from understanding the space group that a material is in. Space group P63mc (#186), e.g. gallium nitride (an important hexagonal polar semiconductor), has very different properties than P63/mmc (#184) titanium (e.g. hexagonal non-polar metal) because of that extra "m" (mirror) symmetry operator...So, she's right but incomplete (and needlessly vague, IMHO) when talking about crystals in 3D space.

A "time crystal" is a kind-of unfortunate name, but it has similar mathematical ideas behind it. Instead of things repeating in a mathematically well-defined arrangement in 3D space, things repeat in time. Symmetry and how that symmetry is "broken" is important in both cases. And time crystals are studied in the quantum regime because of the difficulty in getting macroscopic (huge numbers of atoms) into a well defined state simultaneously.

Or, as a story at Phys.org says:

A time crystal is a unique and exotic phase of matter first predicted by the American physicist Frank Wilczek in 2012. Time crystals are temporal analogs of more conventional space crystals, as both are based on structures characterized by repeating patterns.

Instead of forming repetitive patterns across three-dimensional (3D) space, as space crystals do, time crystals are characterized by changes over time that occur in a set pattern. While some research teams have been able to realize these exotic phases of matter, so far, these realizations have only been achieved using closed systems. This raised the question of whether time crystals could also be realized in open systems, in the presence of dissipation and decoherence.

Researchers at the Institute of Laser Physics at the University of Hamburg have recently realized a time crystal in an open quantum system for the first time. Their paper, published in Physical Review Letters, could have important implications for the study of exotic phases of matter in quantum systems.

[...]

HTH a little.

Cheers,

Scott.