While this isn't quite what a "time crystal" is, imagine a two-dimensional universe that contains just one arrow in it. Now spin the arrow. Now plot the full state of the system, using the third dimension as time. You get a sort of spiral thing going along the dimension you used for time. This periodic structure is sort of like what they mean by "time crystal"; it's a periodic structure in the time dimension.

Now, there's more to it than that. I'm not proposing this as a full explanation of what it means, just trying to get the B-class sci-fi ideas out of the way to sketch out the complicated bit of what they mean. As a crystal is a periodic atomic structure in space, a time crystal is a periodic atomic structure in time. There's more to both, of course, but that should help get the woo-woo out of the way.

How is a "time crystal" different from a plain old [EDIT: quantum] harmonic oscillator?

Energy. A time crystal is at its lowest energy state.

A harmonic oscillator has energy in it - if you took away the energy it would stop moving.

i.e. to stop a time crystal add energy. To stop a harmonic oscillator take away energy.

The other responses have not addressed the possibility that you are referring to a quantum harmonic oscillator. If you are, that is a very good question. I believe the resolution here is that while the phase of a quantum harmonic oscillator in the ground state changes with time, the results of bracketing any hermitian operator (i.e. measuring a physical quantity) does not change throughout time. Therefore in the ground state of the quantum harmonic oscillator, the system is time translation invariant. So a quantum harmonic oscillator does not form a time crystal.

Well, yeah, I thought it was a given that we're in quantum-land here. In classical physics the lowest energy state of a system is necessarily static.

I believe that the idea is the time crystal remains in its ground state the entire time (especially given the work of the author on anyons).

Thank you for dispelling the woo-woo.

thanks for the worthy attempt at explanation, but the b-class sci-fi feel of this remains so strong, i cannot help but associate this having to do with Sleestaks and Time Pylons

To quote scott alexander, "Mysterious “time crystals” may hold the secret to outlasting entropy. No word yet on whether you have to get all seven, or whether they are hidden in temples themed around the seven elements."

> Since this construct is in the lowest energy state it could in principle survive the heat death of the universe and continue forever.[5]

whaaaaat? We could leave messages for inter dimensional travelers at the end of time?

> inter dimensional travelers

I hate this name guts. Where those travelers came from? From the width or from the length?

Who said there are only 3+1 dimensions?

Yeah, but time cube isn't hard to understand. It's perfectly clear. It is the answer to everything. It is the grand unified theory. It is a box containing a consistent system of axioms capable of proving all truths about the arithmetic of the natural numbers. It is love. It is life. It is Time Cube.