It's about being periodic in a lowest-energy configuration.
A spatial crystal freezes into a spatially-periodic configuration at its lowest energy: you don't need to add energy to keep a crystalline solid's microscopic components arranged in lattice-like form.
A time crystal freezes into a periodic configuration at its lowest energy: you don't need to add energy to keep a time crystal arranged in its temporally periodic arrangement. If at t_0 we have one spatial configuration, at t_1 another spatial configuration, ... at t_n-1 we have yet another spatial configuration, and at t_n we have the same spatial configuration as at t_0, and we have no net flow of energy into the spatial configuration at any t_x, we have a time crystal. The spatial configurations at any t_x need not be crystalline, they just have to differ at different points in their cycle.
An analogue clock is not a time crystal because even though the configuration of the hands at 12:00->12:01->...->11:59->12:00 is temporally periodic, you have to wind a clock (or power it in some other way) or it gets stuck at some arbitrary configuration -- it stops cycling unless "disturbed" with added energy. The clock's lowest-energy configuration has its hands always pointing to one hh:mm time, and no different time is shown over the course of a day.
A time crystal, being in its lowest-energy state, cycles through all its configurations endlessly until energy is added.
Does this mean you could use a time crystal to efficiently measure time accurately, by counting the number of cycles? I know we do that with quartz oscillators but those need energy input to keep oscillating.
Good question. I was about to edit this into my comment, but now it works better as a reply.
The act of "reading" the configuration of a time crystal disturbs the time crystal. So you either a set of maximally-similar time crystals that you read at various times during a day, or you need to re-freeze your single disturbed time-crystal each time you read it.
There are ordinary crystals which literally melt out of their crystalline state when handled / measured-by-bright-light. The organized pattern is broken with the additional energy. Time crystals are patterened over time, and that pattern breaks when they are handled / measured-by-bright-light.
You could think of it as having to shine a flashlight (or laser) through the time crystal to figure out which way it twists the light at a given time t_x. If you know the temporally-periodic structure, you can predict the different twisting when you turn on the light at t_x versus t_x+1 or t_x-1. But lighting up the crystal breaks the lowest-energy condition of the time crystal -- it's melted by the light it twists -- so you have to re-freeze it back into its predictable periodic structure, otherwise you might get the same twisting (or none) at t_{measured}+1, t_{measured}+2, ..., t_{measured}+n.
(It is fairly literally re-freezing: you have to do laser cooling or the like. And it takes energy to run the cooler, which removes energy from the not-lowest-energy-state broken time crystal, so thermodynamics isn't violated.)
That's a very good question. I started but abandoned a fairly deep answer, mostly because this is an area far from my expertise and in which it is easy to be howlingly wrong. (To be fair to me, subject matter experts have been arguing about this in the literature for some twenty years.)
I don't get why it's surprising. Any regular structure has resonance modes: struck a bridge or a violin and it will keep vibrating in a time-periodic fashion. Most structures are leaky and lose that initial energy quickly. Crystals are super-regular, nearly perfect macroscopic structures, so they lose energy slowly, and if the periodic motion only involves electrons in the crystal, the motion will conserve energy almost perfectly and may keep going for billions of years.
Practically speaking, this means we couldn't use the cyclic process to do work, because that would require it to have excess energy it could transfer. If a time crystal's periodic behavior were to spin, you couldn't use the rotation to push something. Right?
Right. Lowest-energy means that you can't pull energy out of a time crystal; there's no excess. Anything you try to attach to a time crystal will transfer energy into the crystal.
Practically all we can do with a time crystal is to measure it with the lightest possible touch and hope it doesn't break the periodicity. (So far, afaik, the periodicity has always been broken by the measurement process's energy input).
I don't know what we could do with large numbers of time crystals, though. One can't pick up a snowflake in one's bare hands and use it like a buzz saw to cut a sheet of paper (the snowflake melts on contact), but an avalanche of snowflakes can snap trees. Maybe for time crystals that rotate light a predictable amount at a given time t_x, we could create some sort of interesting lens from a large cloud of such time crystals arranged at different distances from a bright light source -- a sort of "anti-fog".
If the periodicity is broken by any measurement we have been able to make so far then how do we know the periodicity is there in the first place? Just theory? If it’s not too much of a burden could you outline the proof of the existence of time crystals?
> how do we know the periodicity is there ... Just theory?
Theory guides us, but experimentally you can for example make a whole bunch of time crystals (especially straightfoward for driven time crystals, which have a period that's an integer multiple of the driver, the driving force being laser light or microwaves) with an expected set of states it cycles through, and you can test those states once per time crystal. If you reliably get the states theory predicts, that's good evidence.
