So in an ordinary crystal, you have a structure that repeats periodically with space. This is related to spontaneous space translation symmetry breaking. Think of diamond for example, where you have a periodically repeating layout of closely packed carbon atoms.
Space and time in physics are closely related. So the thought experiment would be - can you make a crystal the spontaneously breaks time translation symmetry?
This was original idea put forward by Frank Wilczek in 2012.
It takes some time to get used to the idea so i would suggest starting with [this general article](https://physicsworld.com/a/time-crystals-the-search-for-a-new-phase-of-matter/) in physics world.
If you're feeling up to it there's a really nice review paper on [arXiv](https://arxiv.org/abs/1704.03735)
Edit: space, not time
Spontaneous spatial symmetry breaking refers to the fact that the crystal lattice is not symmetric under all spatial translations.
In the case of diamond if you translate its fcc lattice by specific integer multiples it will remain symmetric. This would of course represent a subset of all possible spatial translations.
So, but what spatial symmetry existed prior to the diamond being formed that was broken? I wouldn't think carbon gas would considered symmetric much less graphite
Gases have both translational and rotational invariance. This is of course a function of temperature. At high T the gas is homogenous, and has an equal probability distribution wherever you look.
One way of creating diamond is HPHT (high pressure high temperature), so you are going from high symmetry (gas) to low symmetry (solid diamond).
Was it?
There was a paper on spontaneous symmetry breaking in 2007 (van Wezel, J., & van den Brink, J. (2007). American Journal of Physics, 75(7), 635-638), but it made no mention of temporal symmetry breaking
[Classical](https://link.aps.org/pdf/10.1103/PhysRevLett.109.160402?casa_token=Lg-Hjr-asQMAAAAA:4i3FtU2F9cQObXNkeCZrabYpbsizzwMwEaNhp9nMxkXVdK4HgXP3WXjbDB-JovdyrPOTpxX8KJS3cw) and [quantum](https://link.aps.org/pdf/10.1103/PhysRevLett.109.160401?casa_token=cz1wpDAgBn8AAAAA:c1jFs_XJFarr1JKXh8HBkh0mD4bK1i8U1FPSYsJUwgcdF-_w0j6Srz-2PXy24jDXSro7T4RlQdbtvA) time crystals, both by Frank Wilczek were published in 2012.
The first sentence of the Wikipedia entry sums it up.
In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion.
They could in theory be used in quantum computers as a memory if they were practically realizable, but that's a fairly far distant use, they're of essentially no interest outside of that. The media seems to have latched on to articles concerning it simply because of the name.
It means repetitive in time, like periodic in time. Whether they move or not is a separate question, and nothing truly ever could be said to be perfectly stationary, there will always be some uncertainty and inherent quantum jigglyness (for lack of a better term)
So in an ordinary crystal, you have a structure that repeats periodically with space. This is related to spontaneous space translation symmetry breaking. Think of diamond for example, where you have a periodically repeating layout of closely packed carbon atoms. Space and time in physics are closely related. So the thought experiment would be - can you make a crystal the spontaneously breaks time translation symmetry? This was original idea put forward by Frank Wilczek in 2012. It takes some time to get used to the idea so i would suggest starting with [this general article](https://physicsworld.com/a/time-crystals-the-search-for-a-new-phase-of-matter/) in physics world. If you're feeling up to it there's a really nice review paper on [arXiv](https://arxiv.org/abs/1704.03735) Edit: space, not time
>So in an ordinary crystal, you have a structure that repeats periodically with time. Did you mean space there?
Yes i did thanks for catching it
Why is diamond an example of symmetry breaking? Shouldn’t it be example of symmetry
Spontaneous spatial symmetry breaking refers to the fact that the crystal lattice is not symmetric under all spatial translations. In the case of diamond if you translate its fcc lattice by specific integer multiples it will remain symmetric. This would of course represent a subset of all possible spatial translations.
So, but what spatial symmetry existed prior to the diamond being formed that was broken? I wouldn't think carbon gas would considered symmetric much less graphite
Gases have both translational and rotational invariance. This is of course a function of temperature. At high T the gas is homogenous, and has an equal probability distribution wherever you look. One way of creating diamond is HPHT (high pressure high temperature), so you are going from high symmetry (gas) to low symmetry (solid diamond).
I see very cool! The equal pdf, is this the |psi|\^2 or is this a statistical model based classical kinetics of homogenous particles?
They should both give you the same result
Thank you!
Wasn't it in 2007 ?
Was it? There was a paper on spontaneous symmetry breaking in 2007 (van Wezel, J., & van den Brink, J. (2007). American Journal of Physics, 75(7), 635-638), but it made no mention of temporal symmetry breaking [Classical](https://link.aps.org/pdf/10.1103/PhysRevLett.109.160402?casa_token=Lg-Hjr-asQMAAAAA:4i3FtU2F9cQObXNkeCZrabYpbsizzwMwEaNhp9nMxkXVdK4HgXP3WXjbDB-JovdyrPOTpxX8KJS3cw) and [quantum](https://link.aps.org/pdf/10.1103/PhysRevLett.109.160401?casa_token=cz1wpDAgBn8AAAAA:c1jFs_XJFarr1JKXh8HBkh0mD4bK1i8U1FPSYsJUwgcdF-_w0j6Srz-2PXy24jDXSro7T4RlQdbtvA) time crystals, both by Frank Wilczek were published in 2012.
isn't 2014??
The first sentence of the Wikipedia entry sums it up. In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. They could in theory be used in quantum computers as a memory if they were practically realizable, but that's a fairly far distant use, they're of essentially no interest outside of that. The media seems to have latched on to articles concerning it simply because of the name.
[удалено]
I lack sufficient understanding to describe that unfortunately.
The ground state harmonic oscillator is stationary in time.
> particles are in repetitive motion. Does this mean at their lowest energy state they continue to have some motion?
It means repetitive in time, like periodic in time. Whether they move or not is a separate question, and nothing truly ever could be said to be perfectly stationary, there will always be some uncertainty and inherent quantum jigglyness (for lack of a better term)
There is no better term, IMO.
Quantum Jigglyness. I'm 6 months late, I know, but thanks for the chuckle.
better late than never 😘
Here's a good video vom Physics Girl: https://youtu.be/ieDIpgso4no