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Physicists have filmed the oscillation of a time crystal (sciencealert.com)
288 points by IFR 40 days ago | hide | past | favorite | 99 comments

Since the article doesn't do a good job of explaining what a time crystal is, here's my attempt at summarizing the Wikipedia article [0].

Normally, a system which is driven by an external frequency oscillates at the same, or a multiple of the driving frequency. This is because the external conditions are symmetric under a time translation (i.e. a delay) by the period duration. This symmetry is normally preserved by the system.

A time crystal, however, will oscillate with a fraction (or rational multiple) of the driving frequency. This breaks the original time translation symmetry.

The analogy with normal 'spatial' crystals is through this symmetry breaking: Empty space is symmetric under all translations, but a crystal spontaneously breaks the symmetry group down to the smaller set of 'translations by a multiple of the lattice constant'.

The continuous symmetry of time translations cannot be spontaneously broken, due to thermodynamic arguments. Instead, we explicitly break down the time translation symmetry to 'delays by a multiple of the period duration'. A time crystal then spontaneously breaks the symmetry down even further, by multiplying the period duration / dividing the frequency.

[0]: https://en.wikipedia.org/wiki/Time_crystal

Every time the discussion of time crystal comes up, a simple analogy can explain what it is.

Regular crystal has repeatable structure in space, i.e. its lattice is the same shape over and over again across in space.

Time crystal is the kind of material that has repeatable structure across time, at the lowest energy state. It just means it changes its shape periodically over time.

An example of that is quartz crystal vibration where its structure bends and unbends over time. Quartz bending and unbending (vibration) is due to the piezoelectric effect when an external electric force is applied. The external force requirement disqualifies it as a time crystal.

The "at the lowest energy state" requirement means time crystal can "vibrate" by itself without external force applied. "Vibrate" is used loosely here. It could be the nuclear-spin flipped periodically, or some other structural changes that need no outside influence.

What you have described is an ideal time crystal. Unfortunately the time crystals we can create in the lab do need an external force, but this force can have a higher frequency than the oscillation of the crystal.

A powerful and mysterious device, whos mystery is only exceeded by its power.

Would it be accurate to say that the "Vibration" or nuclear-spin flipping doesn't emit energy or is neutral in the thermodynamic sense?

Spin waves are similar to vibrations (phonons) in a lot of respects, you still need energy to change a spin.

That said, some aspects of thermodynamics are counter-intuitive (well, actually most of it is). Vibrations are present even at 0 K because of the uncertainty principle, and that’s true for spin waves as well as actual vibrations. It does not mean that any energy is created. The difference with time crystals is that usually these vibrations don’t involve any symmetry breaking.

Time crystals are consistent with standard thermodynamics.

> Vibrations are present even at 0 K because of the uncertainty principle

Are you sure that's true? I can't remember the exact details but recall that being a common misinterpretation of the uncertainty principle

Yes it’s true. Kinetic energy is never exactly zero, that’s called zero-point energy. Perfect stillness does not exist at the atomic scale. It would involve knowing perfectly both positions and velocities (in case of atoms, the equivalent is true for spins).


If you could coax work out of it in a ground state, that would be a perpetual motion machine, so no, it had better not emit energy. But you could detect the spin flips to make a clock

I guess if it’s emitting energy then it’s not at the lowest energy state. The emitted energy draws the energy state down further.

For anyone struggling to make sense of this: I have a physics PhD, I have spent most of my career in fundamental research, I have read the Wikipedia article and other references multiple times, and attended several talks, and I still don't understand what qualifies as a time crystal. All I know that it seems to have something to do with subharmonic response.

The more deeper you get in a particular field, the more you realize how no one else has a clue. It's time we put credentials aside, I found this amusing: https://en.wikipedia.org/wiki/Michael_Crichton#GellMannAmnes...

The irony is that this applies to hacker news.

I don't really know what those people in physics do, but as a mathematician my definition of a time-crystal would be a 4-dimensional discrete structure. You have some 4-dimensional symmetries.

Just rotating in 3D is a bit boring. Interesting symmetries would be where you get the time-axis involved.

4D is most likely a bit boring - having more dimensions and more time-dimensions helps greatly to get more symmetries to work with...

When I hear "time crystal", I think "the wielder of this object can travel through time, or at least do something far out, like see past events", not "a crystal that when vibrated breaks symmetry".

And whenever I hear time crystal, I think of bad sci-fantasy 80s movies.

“Mondor, you must grab the time crystal before the second moon equinox, or the Flarborg will be released from their electronic pen and ravage us like they’ve never ravaged before!”

“Oh. Well, we wouldn’t want that would we?”

I think of quartz crystals, used to measure time.

I believe the most recent iteration of star trek is particularly guilty of stealing "time crystals" from the science news headlines and applying it to this sci-fi trope.

Oh, but you can see past events while wielding (or not wielding) a time crystal.

Vision is far out: https://www.youtube.com/watch?v=FjHJ7FmV0M4

Maybe they can. Who knows what strange realms of physics this research leads us to.

I would say that gravitational waves break the idea that empty space is symmetrical

I mean, you're technically correct (the best kind of correct). But in the lab, we're pretty safe with neglecting the effects of general relativity.

I don't know... atomic clocks are approaching precision that can measure the effects of time dilation due to gravity on the order of inches. They have to take into account daily tectonic tides.

> The precision of current optical clocks is astounding. You may have heard that time goes more slowly when gravity is strong due to general relativity. Optical clocks are so sensitive they can measure the different flows of time 2cm apart in height. If I lay a book on the table, the bottom of the book is slightly closer to the center of the Earth than the top, so experiences slightly stronger gravity. This difference is measurable with an optical clock. Optical clocks are so sensitive we can no longer average the time of multiple clocks together—the ground you or a clock are sitting on typically rises and falls by ~5cm a day due to land tides. The seismic motion of the ground currently limits our ability to measure time. https://arstechnica.com/science/2021/01/a-curious-observers-...

Certainly for atomic clocks (nearly the very definition of precision), but the vast majority of lab work isn't anywhere near that level of precision. So yes, you may need to factor in GR if your goal is to measure the smallest possible thing, but for general work with macroscopic items, it's such a small difference it is completely unnecessary.

Gravitational waves have momentum, energy and even mass, so I wouldn't call a box full of them empty.

Not a physicist by a long shot. But that's makes no sense. Gravity waves maybe can behave like an object with mass. But them having mass makes no sense.

Energy and momentum, sure. But not mass. Same as light.

You're right, and your parent is not, for two reasons.

Firstly, gravitational radiation is observed to obey the classical massless wave function, just as in the large-number-of-photons-limit light obeys the classical massless wave function.

The second quantization [1] of each such massless wave function leads to a massless gauge boson of spin-2 and spin-1/2 respectively: the graviton and the photon. There is excellent experimental and observational support for this approach as an effective field theory -- as one takes the energies of the particles in either field (in isolation) higher, one runs into theoretical questions that have not been resolved.

However, this second-quantization approach conflicts with the approach taken in the Standard Model, which defines a massless gauge boson (also called a photon) and is silent about the quantum content of gravitation [2]. The photon is massless because it moves at "c", and vice-versa. For a Standard Model graviton to be defined, it must also be massless, or light must not always move at "c", leading to photons of different energies moving at different speeds (in vacuum) relative to an observer of those energies. This conflicts with experiment.

The "bigravity" [3] family of gravitational theories probes this variable-speed-of-light problem, and are amenable to study under the Parameterized Post-Newtonian Formalism with results that conflict with evidence [4]. In General Relativity, distant emitters of electromagnetic radiation and distant emitters of gravitational radiation must line up in the sky barring intervening matter that interacts with light. This is in fact what we observe in the Ligo/Virgo era, and since the Mercury MESSENGER experiments. In this case it's because our universe is Lorentzian, having 3 dimensions of space and 1 of time. In Lorentzian universes in General Relativity there is one type of geodesic ("lightlike" [5]) along which massless objects may move, and that geodesic is forbidden to massive objects.

The idea of "massive" gravitational radiation is a theoretical curiosity that is undermined by new evidence gathered practically daily (e.g. in the results of sky searches for supernova and binary eclipses (and other multibody eclipses) by e.g. ASAS-SN : http://www.astronomy.ohio-state.edu/asassn/index.shtml ).

Secondly, gravitational radiation can be included in exact vacuum solutions to the Einstein Field Equation of General Relativity, and this is grad student textbook and lecture note material. The notable feature of vacuum solutions is that the stress-energy tensor T_{\mu\nu} is defined to be zero everywhere in the spacetime. That one introduces "test probes" into the spacetime to see how they move under the influence of gravitation does not change this crucial feature.

For the most part, one should take "energy" and "momentum" as referring to coordinate-system-dependent components of the stress-energy tensor. If we write down the stress-energy tensor as a 4x4 matrix, labelling 0..3 on the rows and columns, with a different matrix at every point, then we can think about the matrix at one point pretty straightforwardly as showing the flux of momentum into the point from each dimension of space or time, and the flux of momentum out of the point along each dimension of space or time. One conventionally takes energy or mass-energy as the time-time component: momentum that comes to this spacetime point from the past and leaves this spacetime point for the future, the spatial coordinates being constant. (We'd write this as T_{00} != 0. Compare the totally inelastic absorbtion of a photon from "the left" (spacetime direction 1) that we'd write as T_{10} != 0 because the momentum stays at the same spatial coordinates going into the future.) But in a vacuum, T is everywhere zero, so there is no energy, stress-energy, energy-momentum, or however you want to label the nonzeros (generally this depends on how one slices up the tensor into components).

In a vacuum solution, it is difficult (and usually meaningless) to talk about the "energy" of gravitational radiation because there is no matter to feel it, and it usually has to be defined on some surface at infinity; this is because the only nonzeros are in the Einstein tensor.

Alternatively, one can impose a notional "box", to try to tease out the wording of your parent comment. In a Lorentzian universe, this can be done with pseudotensors, but these are fragile to changes of systems of coordinates (which is a "bad code smell" in relativity). Essentially one draws a boundary around a region of spacetime and counts the contents of the pseudotensor and the stress-energy tensor on either side of the region's boundary. This is perfectly reasonable in practical astrophysical applications of General Relativity, but is not a good foundation on which to build an argument that "a box of full of [gravitational waves and nothing else]" is non-empty. It is more in line with General Relativity to study a box of electrically neutral gas immersed in an otherwise-vacuum spacetime that contains gravitational waves, and study the evolution of the stress-energy of that gas. Yes, the gas's equation of motion depends on the gravitational waves, and could in principle be heated or cooled by the interaction with the gravitational waves, but when you step back what you are seeing is the behaviour of the sources (the stress-energy, the gas in the box) telling an otherwise vacuum spacetime how to curve. The objection to thinking of gravitational waves as having some peculiar energy-momentum is mostly that it distracts one from that fundamental point, and the follow-on that when "curvature tells matter how to move" the moving matter backreacts on the curvature. One gets lost very quickly in realistic general-relativistic spacetimes when one loses sight of matter as the background-independent sources of curvature.)

So, in summary, using conventional notions of mass, you are right that massive gravitational waves are unphysical (except maaaaaaaaaybe in the extremely early universe, but that's speculation that hasn't (yet) been (wholly) eliminated by evidence). Additionally, gravitational waves are insubstantial -- they can be represented in a vacuum, which is by definition devoid of any substance -- so it is perfectly fine (and usual practice, in my experience) to call a region full of gravitational waves "empty space".

- --

[1] https://en.wikipedia.org/wiki/Second_quantization

[2] The Standard Model fields are all Lorentz-covariant and so work everywhere that the radius of curvature is much larger than the particle wavelength. That is pretty much everywhere in the universe except near very small black holes (as yet unobserved), deep inside bigger black holes (possibly unobservable in principle), and very near the hottest densest phase of or universe (not yet directly observed, but plenty of indirect evidence). The coupling of the Standard Model to gravitation is more than good enough to do accurate and precise high-energy astrophysics (the spectra of supernovae and blazars; the equation of state for neutron stars) for the time being.

[3] https://en.wikipedia.org/wiki/Bimetric_gravity

[4] https://en.wikipedia.org/wiki/Alternatives_to_general_relati... in the table "Bimetric" for three examples (Rosen, Rastall, Lightman-Lee). The nonzeros in the \alpha_1 parameter are fatal to these theories as that parameter is very highly constrained by direct experiment involving human artifacts and around other bodies in the solar system; the \alpha_2 parameter is highly constrained to zero by observations of millisecond pulsars, which casts serious doubt on the non-zeroes in that column. \gamma is also constrained by experiment within the solar system. One has to "wash out" the effect of bigravity by making the decoupling or vanishing of the second metric happen very very near the big bang (so that light behaves entirely masslessly at all energies when the distortions in the cosmic microwave background develop). A "washing out" can still have effects early in cosmic inflation, so these theories are not dead, just that they predict smaller and smaller differences from standard single-metric General Relativity.

[5] https://en.wikipedia.org/wiki/Causal_structure#Tangent_vecto...

[6] http://aether.lbl.gov/www/classes/p139/homework/hw12.pdf

Could you elaborate on that?

How does this compare to the behavior of nonlinear optical crystals like lithium triborate? They are also pumped at a lower frequency (e.g. 1064nm photons) but lase at twice that (532nm).

In some way, it's the inverse: a nonlinear optical system can multiply frequencies, while a time crystal divides a frequency. That's not as easy as multiplying, due to the symmetry concerns I mentioned.

It's basically a frequency divider, but as a system of cold atoms instead of an electronic circuit, and in a different frequency regime.

What are potential applications?

Do the allow some kind of special optical devices?

>"Now, if crystals can interact not only in space but also in time, we add another dimension of possible applications. The potential for communication, radar or imaging technology is huge."

Could anyone expand on this in an accessible way? What kinds of changes could we see in imaging or communication technology?

just a random guess and hypothesis with absolutely no basis besides this article. I think they may be able to 'sync' up transmitters which are then used to encode and decode based on time and space. Like time-sensitive antennas which adds another means of encoding....???

I do not look forward to seeing how the US defense industry eventually utilizes this technology.

Far out! Here is the 13 second video from the Max Planck Society in all its glory: https://youtu.be/kUY3TglEUCU

Honestly, the video just looks like someone re-inverted an image several times over using a fade. What am I missing?

> Time crystals should be stable and coherent over long time periods, because they - theoretically - oscillate at their lowest possible energy state. The team's research shows that driven magnonic time crystals can be easily manipulated, opening a new way to reconfigure time crystals. This could open up the state of matter for a range of practical applications.

> "Classical crystals have a very broad field of applications," said physicist Joachim Gräfe of the Max Planck Institute for Intelligent Systems.

> "Now, if crystals can interact not only in space but also in time, we add another dimension of possible applications. The potential for communication, radar or imaging technology is huge."

That is cool!

I've never seen such a weird aspect ratio on YouTube either.

Is there any particular reason it's unlisted?

What are time crystals? Try this:

* Physicists Predict The Existence of Time Crystals https://www.technologyreview.com/s/426917/physicists-predict...

* How to Build A Space-Time Crystal https://www.technologyreview.com/2012/06/26/255685/how-to-bu...

(Reposted from an earlier submission in 2016: https://news.ycombinator.com/item?id=12655530)

How do Time Crystals differ from the quartz crystals used for time keeping in electronics? Is the only difference that Time Crystals oscillate without needing an electric field?

From my very limited knowledge of physics, time crystals can theoretically oscillate forever without any excitation at their ground state, though laws of theromodynamics are not broken and energy cannot be extracted from their oscillations. In a normal crystal oscillater, power is needed to keep the crystal oscillating.

While this may be that they can oscillate forever, measuring it is an act of removing energy from it.

Not necessarily. You can measure things in ways that add energy: e.g. radar waves contribute a tiny bit of energy to the things they bounce off. Yet they measure where objects are.

You can also measure some things in ways that add exactly 0 energy. If some quantum system absorbs exactly nothing of a certain wavelength, that tells you something about the system.

You don’t need to remove energy from an object to measure it.

If you shine a flashlight into a dark room, you are measuring the positions of objects inside, and those objects don’t lose their energy.

you are changing the momentum of the things you are mentioning. the considerations here are on a more quantum scale than furniture in a room.

So could it be said then that it's more efficient? Say, you'd need less energy to measure time with a time crystal than a quartz crystal?

I have no knowledge of them but the article says it oscillates at lower energy levels, almost nil, compared to a quartz crystals. Since it is still unexplored territory there are lots of possible applications.

I also wonder how a time crystal is different from a harmonic oscillator.

Harmonic oscillator can have a ground state where it doesn’t move (i.e. you can stop it if you remove the enegy).

Time crystals move at the ground state - you cannot stop them by removing the energy.

You actually can't remove all the energy from a quantum harmonic oscillator, 1/2 hbar omega will be in it even in the ground state.

Normally, a system (like a quartz) which is driven by an external frequency, oscillates at the same or a multiple of the driving frequency. This is because the external conditions are symmetric under a time translation (i.e. a delay) by the period duration. This symmetry is normally preserved by the system.

A time crystal, however, will oscillate with a fraction (or rational multiple) of the driving frequency. This breaks the original time translation symmetry.

When quantum mechanics are involved, I feel like someone from 400 years ago might feel today using a smartphone. And probably as a society we are now like starting to experiment with electricity. I wonder what will be the smartphones in that future.

Does anybody else agree the name "Time Crystal" could be better somehow?

TimeSplitters Future Perfect - Cortez, get the time crystals!

I always think of doctor who when I hear it - not that its a bad thing.

No. It's technically very accurate name. https://en.wikipedia.org/wiki/Time_crystal

(Not an expert) I read the first few paragraphs on that link. So, by analogy, we might call (normal) crystals with flaws "space crystals". Or maybe they should be "space-flawed crystals" and "time-flawed crystals" - a "flaw", in the usual sense, being a break in the regular crystalline structure. The adjective describes the (nature of the) breakdown in regular structure, not the regular structure. No? I wouldn't defend "space crystal" as a "technically very accurate name".

But then how would I think about Crash Bandicoot and Neo Cortex whenever there is news!

Frank Wilczek was hoping for a writers credit on the next Indiana Jones reboot.

I like how much it sounds like futuristic science fiction technology!

The more verbose 'time-translational-symmetry-breaking-structure' isn't much better. So crystal it is.

yes, it sounds too mystic for science

> So, where the structure of regular crystals repeats in space, in time crystals it repeats in space and time.

Does that mean anything that behaves like a wave is a form of time crystal? For example ocean currents moving in unison causes all atoms in that wave to follow a very specific pattern similar to what is described in the article.

I wonder how this links in to optical crystals? KTP, used in solid state lasers, will halve the frequency of a IR laser (1064nm) to produce green light (532nm).

I suppose this is equivalent to adding electrical energy to a crystal to make it oscillate.

532 nm corresponds to double the frequency of 1064 nm, not half. Any nonlinear response generates harmonics of a signal but not subharmonics. This is why in electronics a single diode can be used as a frequency doubler, but a digital flip-flop is required for frequency division.

In the experiment, the crystals were driven by RF excitation. Do time crystals generally require a constant energy source to oscillate? I would assume not, since they're called crystals...

Also, is the oscillation frequency temperature dependent?

Unfortunately, time crystals do require an external excitation. The key is that the excitation does not have the same frequency as the time crystal.

Exactly, thinking about a parametric oscillation might help

>filmed at up to 40 billion frames per second

that's quite a feat on anyone's watch

It probably was filmed on a camera not a watch.


how many frames per seconds are our eyes recording at?

Our vision is not frame-based at all. Each receptor cell can trigger inependently. Chopping up the signal into image frames is simply a technical trick that makes us perceive continuous motion due to the finite recovery time of the cells (persistence of vision).

I can't tell if you're joking, but in case anyone else is wondering: Most people can perceive between 30-60 frames per second. Some (mostly gamers) reportedly perceive up to 120 frames per second. Though whether this counts as recording is a matter for philosophers.

This is many orders of magnitude more than that.

Its wierd because I could differentiate between 120Hz and 240Hz but I think its because the computer generates still images without motion blur. So 120Hz with perfect motion blur would be indistinguishable from 240Hz I think

If only it were that simple! There's no-such-thing as 'perfect motion blur', it's all a matter of taste.

You can do things like open the virtual shutter to full-open (so that not a single virtual-photon reflected off the virtual-motion will be missed by the virtual-sensor), which makes the motion recorded during one frame continue directly (with no time 'gap') into the next frame. This can help make things seem 'smoother' for sure but it's still relying hugely on persistence-of-vision.

I'm super surprised (and a bit incredulous tbh!) to hear of a perceivable difference between 120 and 240fps! need to go double-blind on that stuff to be sure I reckon!

On a computer game you can spot the 240fps because of the intermediate frames when you have visual elements moving very quickly across the screen. It's not because of 'faster eyes' I don't think. Like when you move your mouse very quickly you'll see twice as many mouse cursors en route.

Afaik you can also detect images that are present for a millisecond (eg white screen with one black frame at 1000fps).

You can detect very small numbers of photons (sometimes a single photon), your eyes don't care about the frame rate. The question is, can you tell the difference between 120FPS and 240FPS

Still an excellent question! There's this (no proper references) that seems to suggest ppl lose the ability to make meaningful judgements about frame rate (or ~differentiate differences) after around 150fps:


This (150>120) seems to suggest that many people would be able to see (maybe it'd be better to call it "feel" the difference at this point) the difference between 120 and 240fps. but they most likely couldn't tell 150 from 240fps.

It sounds like these room-temperature time crystals must be driven by continually applying external energy via the driving frequency, or did I misread that?

Is it feasible to create my own time crystals? Or acquire one?

I would love to add a time crystal to my existing space crystal collection, even if it requires some sort of support to maintain the driving frequency.

I haven't read the paper yet, but it sounds like I could apply a particular frequency to a strip of nickel-iron alloy and practically achieve such an effect?

Do any physicists here know whether that would be feasible?

Yes, with microwave RF and a magnetic strip in a static field you can make one, but just keep in mind you'll need an X-ray synchrotron and a 40 billion fps camera to see it.

I wish someone would show that charge parity time (CPT) symmetry can be broken so we'd have to rewrite the entire laws of physics from scratch but this time would do it more efficiently.

In 2001 I worked on spectral analysis of a jet-type flow and realized a PIV software with matlab. Of course images that I used issued from a high speed camera, have nothing to do with the 40 billion frames per second we are talking about here ! It was just fascinating to see the particles moving in milliseconds.

We are talking here about 40 Cycles Per Nanosecond !! It's not just fascinating, it's Hilariously crazy !

This is a wonderful development! Learning about far-out advances in physics is amazing, but they sometimes feel like they are too removed from everyday reality beyond helping us understand some semantic piece of how the Universe works. Does anybody know if time crystals have any practical uses?

from the article at the end. suggest u read it hashman.

"Classical crystals have a very broad field of applications," said physicist Joachim Gräfe of the Max Planck Institute for Intelligent Systems.

"Now, if crystals can interact not only in space but also in time, we add another dimension of possible applications. The potential for communication, radar or imaging technology is huge."

Is a spinning t-handle exhibiting the tennis racket effect a time crystal?

ELI5 why we can't make a perpetual motion machine out of this?

These physicists have never properly acknowledged the prior work of Otis Eugene Ray on this subject. How typical!

how the f do you guys know so much about this?

why aren't electrons spinning round an atom called "time particles"? Technically by the time they run out of energy, the universe will have died so they are "super time particles".

I think they are not actually spinning, they are around the nucleus in a probability cloud. I dont think we could use that as a timing mechanism but Im not a physicist

Another scummy website that hijacks the back button. I wish there were a way to block domains from the results I see on HN.

haha I cant wait to hear about this from my local rock/crystal dealer ooommmmmmmm shiva Shankarrrr mahatmahariiii ganjaaaaaa

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