The systems considered here have periodic drives (in the article, "Floquet"). This means that time-translational symmetry is already partially broken. The system is only the same after waiting times that are multiples of the period T of the drive.
The time-translational symmetry breaking occurs because the state of the system is not periodic with period T as would normally happen but periodic with period 2T.
In terms of frequencies, if the drive frequency is f = 1/T, then this system responds at a frequency f/2, whereas normal systems can only respond at frequencies f, 2f, 3f, ... that correspond to harmonics.
Additionally, this time-translational symmetry breaking makes a stable phase of matter -- that is, you don't have to fine tune any parameters of the system to see the effect, and experimental noise won't destroy it. It also doesn't matter which initial state you prepare your experiment in. While not as exotic as a time-translational symmetry breaking without a drive to partially break the symmetry first, it is still pretty surprising that this type of phase exists at all. It is likely that spontaneous breaking of full time-translational symmetry can never be stable in the same sense.
You're absolutely correct. There are some nice papers by Potter, Vasseur et al. and Else and Nayak which illustrate your latter point in gory mathematical detail (they derive constraints from symmetry on symmetry protected topological phases and then use math to relate that to the sort of Floquet phases you can protect using symmetries). Of course, if you're actually Dominic Else, I defer to you...
e: Hah, I commented without reading the article, this is the PRL publication of the Else and Nayak paper, with an added co-author, I had read the preprint a few months ago. The other paper good to read to enlighten oneself in this context is https://arxiv.org/abs/1510.04282
> In terms of frequencies, if the drive frequency is f = 1/T, then this system responds at a frequency f/2, whereas normal systems can only respond at frequencies f, 2f, 3f, ... that correspond to harmonics.
Interesting. I heard it described once that a particle with spin of 1/2 is like a particle that you have to rotate twice (through two 360 degree rotations) before it's in the same configuration. Wikipedia actually has a visualization that seems to depict this reasonably: https://en.wikipedia.org/wiki/Spin-%C2%BD
Anyway, your description makes it sound like this system by responding at f/2 might have an analogous property with time. Is this at all a reasonable or correct analogy?
This is a great question. (I am the first author on the "Floquet time crystals" paper referred to btw). The analogy is not perfect because what actually happens to a spin-1/2 particle under a 360 degree rotation is it comes back to the same configuration, but its wavefunction picks up a quantum phase factor of (-1), which is not observable. On the other hand, a Floquet time crystal does actually does go to an observably different state under a time shift. The best analogy is really to, for example, a magnet, which does go to an observably different state if you rotate it (because the north and south poles rotate).
The appendix relates this +/1 (Z2) phase factor to the so called "cat states" of the spin system. There are deeper ways to understand its more general consequences through a type of math called cohomology theory but it's not possible to make general statements about time per se. Now, if you're interested in how information moves in spin systems with respect to time I urge you to explore the fascinating topic of Lieb-Robinson bounds, but I feel like this overview might boil down for you what the paper is trying to accomplish more idiomatically: http://www.condmatjournalclub.org/jccm-content/uploads/2016/...
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.
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.
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."
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.
I got redirected to the http //www.thesofttic.com/ZiWblMur/win-f/gi/?SiteID=4905&conversion=11ee233b-a3f6-4b44-8d5f-9c578b58eb29 from the link. Anyone who know why or what that is? Is phys.org really infected with malware?
Oh no. This is going to get picked up by one of those nutbag spiritual clickbait sites and tomorrow my girlfriend is going to tell me about an amazing discovery about crystals which can be used to power a time travel device.
Interesting, that Microsoft sponsors such a research that I can't see being used by the business for visible future. I am not a shareholder so can't make a view of this is good or not.
A lot of research done in Microsoft Research is blue skies research that has nothing to do with MSFT's goals. Hell, MSR for the past decade has set the example for open research in industry-controlled labs, so I would have been surprised if MSFT hadn't already started sponsoring theoretical research in STEM subjects.
(This doesn't justify a lot of the crap that MSFT and other tech corps have done to our industry over the years, but we should give credit where it's due)
Ex MSFT Researcher here. It's fun to work at MSR. Not everything done there is valuable, but it is very diverse and you are given pretty much Carte Blanche to fuck around with whatever you want. Just come up with some stuff now and again.
Certainly not a bunch of evil people that's for sure.
The connection with quantum information (the theme of research at Station Q) is through the many-body localization (MBL) aspect of this system. These are phases that store quantum information at finite temperature. Normal quantum systems thermalize and lose any information of their initial state. (Actually, the information spreads chaotically throughout the system and becomes hard to retrieve, so its effectively lost.) In MBL systems, the information does not spread, and the system does not thermalize. You can read the information of the initial state back out after waiting a long time.
The point is that they are still paying money. Calling it a "tax write-off" to the layman sounds like they're just doing it to reduce how much they pay in taxes. I.e. It sounds like tax-evasion/fraud.
His point specifically is that tax write-offs don't reduce how much you have to pay overall. They may even increase it. They just redirect some of it to other purposes such as research instead of paying taxes.
Station Q, where this research occurs, tries to do the basic research to build a topological quantum computer, which if it turns out to be physically possible (which is as far as I know neither proved nor disproved) is considered by many people as a much more scalable approach to build quantum computers than existing ones. The reason (according to https://en.wikipedia.org/w/index.php?title=Topological_quant...) is "The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. The smallest perturbations can cause a quantum particle to decohere and introduce errors in the computation, but such small perturbations do not change the braids' topological properties."
Microsoft hopes to be the starters of a similar revolution for quantum computers as there was for "binary" computers.
Though ianai's reason of tax writeoff is probably also a part of the story. :-)
Heat death === no remaining thermodynamic free energy. The universe is all one temperature, though theories vary widely on what this temperature might be.
At high temperatures crystals vaporize, absorbing heat. At low temperatures, gases sublimate onto the crystal, releasing heat. Either way, if you have crystals, the universe hasn't completed its heat death yet because you could use the crystal to do work.
By that definition, wouldn't the heat death never actually happen? Space is expanding, so there should be some particles that zip off and never collide with anything.
Also, couldn't a sublimating gas disrupt a time crystal?
The universe will not necessarily experience heat death, so whether "regular" crystals or time crystals cannot survive something that may not happen could be irrelevant.
> "I always thought that making physics more complicated made physics potentially more wrong."
There's no correlation between complexity and correctness. An explanation can be too simple as well as too complex. Nature is what it is, our understanding of it evolves over time.
The systems considered here have periodic drives (in the article, "Floquet"). This means that time-translational symmetry is already partially broken. The system is only the same after waiting times that are multiples of the period T of the drive.
The time-translational symmetry breaking occurs because the state of the system is not periodic with period T as would normally happen but periodic with period 2T.
In terms of frequencies, if the drive frequency is f = 1/T, then this system responds at a frequency f/2, whereas normal systems can only respond at frequencies f, 2f, 3f, ... that correspond to harmonics.
Additionally, this time-translational symmetry breaking makes a stable phase of matter -- that is, you don't have to fine tune any parameters of the system to see the effect, and experimental noise won't destroy it. It also doesn't matter which initial state you prepare your experiment in. While not as exotic as a time-translational symmetry breaking without a drive to partially break the symmetry first, it is still pretty surprising that this type of phase exists at all. It is likely that spontaneous breaking of full time-translational symmetry can never be stable in the same sense.