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There's two things that can have symmetry here: The laws of physics themselves, and the system under investigation. The symmetries of the laws of physics don't

There's two things that can have symmetry here: The laws of physics themselves, and the system under investigation. The symmetries of the laws of physics don't get broken, but those of the system do. Compare a crystal to a gas: In a gas, the atoms are all bouncing around pretty randomly, so at any given point in space, there's roughly the same chance of finding an atom. Shift the gas to the left by distance x, and the local probability distribution of atom positions looks pretty much the same. In a crystal on the other hand, the atoms are still moving around and vibrating (so there's still some uncertainty in the positions of the atoms), but they tend to stay pretty close to their proper position in the crystal lattice. So the atoms are more likely to be in positions that line up with the rest of the crystal lattice than anywhere else. This breaks the symmetry. Shift by distance x and the peaks of that probability distribution no longer line up. The exception to this is if x is a multiple of the spacing of atoms in the crystal. Then you're shifting the peaks by exactly the right amount that they line up again when you're done. So a crystal doesn't completely break the symmetry of space, but it reduces it from a continuous symmetry (you can translate by any amount in any direction) to a much weaker discrete symmetry (only certain translations of space will preserve the symmetry). A time crystal is similar to an ordinary crystal except that instead of reducing symmetry of translations in space from a continuous symmetry to a discrete symmetry, it reduces symmetry of translations in time from a continuous symmetry to a discrete symmetry. EDIT: It's a little ironic that if you ask most people, they would say that a crystal is more symmetric that a gas, since a gas will look completely random and asymmetric if you take a snapshot of the positions of all the atoms at a single time. But since physicists care about the probability distribution of atom positions, they say that the gas is more symmetric than the crystal.

philipov 4y ago
What you've described is a repeating loop. What makes a time crystal more than that?
- raattgift 4y ago
  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.
  - skykooler 4y ago
    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.
    - raattgift 4y ago
      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.)
      - prox 4y ago
        Will it be possible to read the crystal without disturbing it, or is it a physical quantum limit that prevents it?
        raattgift 4y ago
        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.) Instead I'll direct you Sean Carroll's "Quantum Interrogation" blog posting as a starting point: <https://www.preposterousuniverse.com/blog/2006/02/27/quantum-interrogation/ https://www.preposterousuniverse.com/blog/2006/02/27/quantum...>. ("how you can detect something without actually looking at it") There is also the 2021 work by the Google & Stanford team (decent press release: <https://news.stanford.edu/2021/11/30/time-crystal-quantum-computer/ https://news.stanford.edu/2021/11/30/time-crystal-quantum-co...> open-access paper: <https://www.nature.com/articles/s41586-021-04257-w https://www.nature.com/articles/s41586-021-04257-w>, the PDF version of which (click in top right) is legible) which is at least suggestive that certain types of time crystals can be interrogated without breaking them.
parallel 4y ago
I feel like there must be more to it that this. Wouldn't any physical structure that's not homogeneous and isotropic also break symmetry in the same way. Does the room I'm in break symmetry as there's a different likelihood of hitting a wall depending on the direction I travel?
- peteradio 4y ago
  > Wouldn't any physical structure that's not homogeneous and isotropic also break symmetry in the same way. Does the room I'm in break symmetry as there's a different likelihood of hitting a wall depending on the direction I travel? Uhuh, but enough to be physically detectable?
- raattgift 4y ago
  The x in "distance x" (grandparent comment) is very small. "Very small" in this context is less than the lattice spacings, which for a typical crystal can be on the order of the wavelength of an X-ray (i.e., there's ~ 0.1-100 ångströms between the crystal's diffracting planes, so "distance x" must be a fraction of that length). A typical room is effectively a <https://en.wikipedia.org/wiki/Gas_in_a_box https://en.wikipedia.org/wiki/Gas_in_a_box>. If the walls of your box are good X-ray detectors then an isotropically-radiating X-ray source somewhere near the middle of the room will evidence an essentially uniform energy loss at the detectors, and and weak reflection from air molecules back towards the source. However, if you substituted the air in the room with a crystal lattice, the energy loss would be much stronger at detectors in some directions, and there would be strong reflections back towards the source along some directions. See <https://physicsopenlab.org/2018/01/18/bragg-diffraction/ https://physicsopenlab.org/2018/01/18/bragg-diffraction/> for some details.
- mr_toad 4y ago
  > Does the room I'm in break symmetry Symmetry breaking is very important to the study of condensed matter physics, including solid matter, and arguably it’s the reason your room exists at all. https://simple.wikipedia.org/wiki/Higgs_field https://simple.wikipedia.org/wiki/Higgs_field https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking
graycat 4y ago
> continuous symmetry (you can translate by any amount in any direction) Thanks for the definition. That is close to the math idea of automophic, that is, can map onto itself. So, what physics means is that translations are essentially automorphisms. Simple now that we have a clear definition!

philipov 4y ago

What you've described is a repeating loop. What makes a time crystal more than that?

raattgift 4y ago
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.
- skykooler 4y ago
  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.
  - raattgift 4y ago
    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.)
    - prox 4y ago
      Will it be possible to read the crystal without disturbing it, or is it a physical quantum limit that prevents it?
      - raattgift 4y ago
        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.) Instead I'll direct you Sean Carroll's "Quantum Interrogation" blog posting as a starting point: <https://www.preposterousuniverse.com/blog/2006/02/27/quantum-interrogation/ https://www.preposterousuniverse.com/blog/2006/02/27/quantum...>. ("how you can detect something without actually looking at it") There is also the 2021 work by the Google & Stanford team (decent press release: <https://news.stanford.edu/2021/11/30/time-crystal-quantum-computer/ https://news.stanford.edu/2021/11/30/time-crystal-quantum-co...> open-access paper: <https://www.nature.com/articles/s41586-021-04257-w https://www.nature.com/articles/s41586-021-04257-w>, the PDF version of which (click in top right) is legible) which is at least suggestive that certain types of time crystals can be interrogated without breaking them.

parallel 4y ago

I feel like there must be more to it that this. Wouldn't any physical structure that's not homogeneous and isotropic also break symmetry in the same way. Does the room I'm in break symmetry as there's a different likelihood of hitting a wall depending on the direction I travel?

peteradio 4y ago
> Wouldn't any physical structure that's not homogeneous and isotropic also break symmetry in the same way. Does the room I'm in break symmetry as there's a different likelihood of hitting a wall depending on the direction I travel? Uhuh, but enough to be physically detectable?
raattgift 4y ago
The x in "distance x" (grandparent comment) is very small. "Very small" in this context is less than the lattice spacings, which for a typical crystal can be on the order of the wavelength of an X-ray (i.e., there's ~ 0.1-100 ångströms between the crystal's diffracting planes, so "distance x" must be a fraction of that length). A typical room is effectively a <https://en.wikipedia.org/wiki/Gas_in_a_box https://en.wikipedia.org/wiki/Gas_in_a_box>. If the walls of your box are good X-ray detectors then an isotropically-radiating X-ray source somewhere near the middle of the room will evidence an essentially uniform energy loss at the detectors, and and weak reflection from air molecules back towards the source. However, if you substituted the air in the room with a crystal lattice, the energy loss would be much stronger at detectors in some directions, and there would be strong reflections back towards the source along some directions. See <https://physicsopenlab.org/2018/01/18/bragg-diffraction/ https://physicsopenlab.org/2018/01/18/bragg-diffraction/> for some details.
mr_toad 4y ago
> Does the room I'm in break symmetry Symmetry breaking is very important to the study of condensed matter physics, including solid matter, and arguably it’s the reason your room exists at all. https://simple.wikipedia.org/wiki/Higgs_field https://simple.wikipedia.org/wiki/Higgs_field https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking

graycat 4y ago

> continuous symmetry (you can translate by any amount in any direction) Thanks for the definition. That is close to the math idea of automophic, that is, can map onto itself. So, what physics means is that translations are essentially automorphisms. Simple now that we have a clear definition!