In chemistry you have what are called stationary states. These are solutions to the time-independent Schrodinger equation Hψ(r) = Eψ(r) [H is an operator; E is a scalar]. Now, when you plug ψ(r) into the time-dependent Schrodinger equation, you get Ψ(r, t) = exp(-iEt/hbar)ψ(r), where i is the imaginary unit, E is the energy, t is time, and hbar is the reduced Planck's constant. So you can see there is clearly a time dependence.
However, when you measure some property of a system, you aren't measuring the wavefunction but rather the results of some linear operator acting on the wavefunction (each operator corresponds to a probability distribution of what measurement you will get). So despite the fact that the wavefunction has a time dependence, your measurement probability distribution functions do not!
Now the other thing you need to know is that so far these stationary states all correspond to ground states. What is a ground state? It is the lowest energy level that a system can obtain. You might think that the different orbitals an atom can have in chemistry are all stationary states, but they're not. They can spontaneously decay to a lower-energy state. You need quantum field theory to prove that, and I don't even know how to do that, so I won't.
The deal with these time crystals is that Dr. Wilczek has proposed a lowest-energy system that corresponds to cyclical time-varying measurement probability distribution functions. So despite being a stationary state, your measurements depend on when in the cycle you take them! This has not ever been done experimentally, so it looks as though the Zhang and Li group are going to attempt to do so.
(2) You said: "Our current best theory that describes reality at the small scale is quantum mechanics." I don't disagree, but I'd like to emphasize that "at the small scale" might not have been necessary. I think it's a shame when people think that quantum mechanics only applies to small things.
(3) The way that I understand time crystals is that they are analogous to real crystals. And just as the translational symmetry of a crystal creates a corresponding quasi-momentum for the momentum, so does the time-translational symmetry introduce a quasi-energy similar to energy. Is that correct? Perhaps it helps answer my first question.
2) I certainly agree that QM is the basis to everything. However, with the quantum gravity issue, I didn't want to imply it was a grand unified theory to someone who wasn't familiar with QM.
3) I haven't taken a solid state physics course, so I'm afraid I don't know enough to answer that.
> Then we can use a global probe laser which is only scattered by the mark ion (state dependent ﬂuorescence) to measure its angular displacement after a time separation Δt. [...] After the measurement, we can cool the ions back to the ground state and repeat the experiment again.
Whether the distinguishability of one ion over the others changes the quantum statistics is an important and subtle problem.
You're right to be skeptical. When the time comes to interpret the results of this experiment, you'll find yourself in good company. Doubly so if the experiment resolves T violation.
"How can something move, and keep moving forever, without expending energy? It seemed an absurd idea — a major break from the accepted laws of physics."
I don't think that something moving forever is a major break from the laws of physics. Consider the following:
(1) An asteroid flies through space forever (doesn't violate laws of physics)
(2) A current persists in a superconductor forever (again, no violation)
(3) Heck, currents can ever persist in non-superconductors (http://en.wikipedia.org/wiki/Persistent_current)
(4) The motion of the Earth around the sun (the two-body problem doesn't violate physics)
(5) Even the motion of an electron around a nucleus is perpetual motion in a sense
(6) The fact that things have temperature means that their molecules are always moving!
Anyway, there are many examples of perpetual motion in physics. The key point is that you cannot extract infinite energy from them, just like you can't extract infinite energy from a time crystal. So why does the article act like time crystals are a big deal in this respect?
-A grumpy physicist
(Aside: nothing exists forever - even time crystals - because eventually the universe will be a bunch of infinitely far apart black holes or something. So I'm not sure how that assumption is relevant.)
The examples you gave above are forever; I just started assuming things like eternity and I can go on to assume no external forces/stuff in the way. (So not disagreeing with your initial statement, just adding.)
For example, even ignoring the fact that the sun is going to explode before the universe does, the earth's rotation around the sun is gradually getting slower and slower. If the sun, and the universe, did last forever then the earth would eventually come to a halt.
In the case of these crystals, my impression is that even in that hypothetical never-ending universe, the movement in these crystals would never slow down.
In addition to that, the tidal forces will compress and decompress the mass of both objects, which effectively converts potential energy (the distance between the two objectds) into heat. Even though the moon is on a trajectory to eventually leave earth orbit, every tide that comes in and leaves lowers the rotation speed of the moon. While the moon has no liquids on it's surface, which makes the effect nearly invisible, it does have tides (slight variations in the angle and magnitude of gravity at it's surface) which move objects around and the energy for that does indeed come from orbital decay. Similarly, the earth loses orbital energy to the sun.
Quantum Time Crystals (Wilczek)
Classical Time Crystals (Shapere, Wilczek)
Space-time Crystals of Trapped Ions ( Li, Gong, Yin, Quan, Yin, Zhang, Duan,Zhang )
All three papers appeared in a single issue of Physical Review Letters (The fancy Physics journal).
PRL also issued this Physics Viewpoint, a popular science article:
An object in motion will remain in motion, until acted on by an external force.
The real interesting thing here is that something can move, but have no energy - potential or otherwise. Unlike things we are used to, if a time crystal train hit you you wouldn't feel a thing. (Well, not exactly, but it gets the point across.)
The actual interesting thing about this crystal is that the atoms will spontaneously start spinning as you remove energy from the system. Ie, in the ground state (the lowest energy state) the atoms are in motion. This is in contrast to all the physical systems we are familiar with where the ground state is motionless.
The reason it is called a 'time crystal' is that the ground state 'breaks symmetry' in time in the same way that a regular crystal 'breaks symmetry' in space - in the sense that if you translate the system in space, you do not usually get back its original state, unlike a gas. And, this symmetry breaking occurs as you cool the system. Crystals self-organize in a periodic grid as you cool them from the liquid state, just as this time crystal will set itself in periodic motion as you cool it.
One consequence of the symmetry breaking is that the atoms will have to move either clockwise, or counterclockwise, and will "randomly" choose one of the two.
I'm about half-way through this and it feels more and more like it was written by someone who would also ask why a permanent magnet can support a load against gravity without expending any energy - it's the same fundamental attribution error.
EDIT: In fact finishing it, I'm really confused as to what's new here. Giant external magnetic field, and stuff just coasting in a circle? Nothing about this feels implausible in a classical sense with a ring of charged ions.
Since 1) the Nobel-winning physicist, 2) the peer reviewed journal AND 3) the main critic of his theory agree that there is something new there, you probably ARE confused as to what they really meant.
I think an appeal to authority is appropriate here. Time and again I've seen simplistic comments in tech forums, putting down new scientific theories based on some misunderstanding of what new they claim, with the argument that "it's just like" some other older theory.
And all this criticism usually based on a 10000 miles high explanation of the idea in some popular science article. As if that is enough to capture all the nuances of the thing.
I may not be quite proficient in Physics to be able to say what's the case here (then again I doubt many if any at HN are at the level of the article's professor), but I've seen the same kind of responses many times in comments about other fields of study.
If general relativity is correct, that system will generate gravity waves which will take away energy and the orbit will decay. This is a small effect, however, so we generally don't have to worry about it. E.g., Earth's orbit is decaying by about the width of a hydrogen atom every few hundred years.
Here, the theory is that the system is already in its lowest-energy state, despite the fact that part of it is still in motion.
EDIT: A lot of comments appear confused about stuff in the article from Wired. That's due to the journalism. The Scientific American article addresses many of issues raised here.
The theory here is that you can have a system that is already in a ground state, where it can't decay further, and is still spinning (and will spin forever without gaining or losing energy.)
I don't have the expertise to properly understand the details, but it seems like it's along similar lines as something like an electron 'orbiting' a nucleus in ground state -- unlike the plate, the electron will never stop 'orbiting' because it has no energy to lose.
The electron, though, is delocalized -- it's in every place around the nucleus at once. So there's no periodic motion involved. By contrast, this experiment will tag one of the atoms in the ring so we can watch it move periodically.
* Perpetual mobile:
It's theoretically possible to build a system that moves forever. But it's impossible is to connect it to some kind of generator to extract energy for free, while the system continues moving at the same rate. And the real systems have some kind of friction that dissipates a part of the energy, so the real systems usually stop in a while.
The few cases where the movement can last forever is the movement in the superfluids and the current in the superconductors. They are not very ordered systems like this 100 Ca ring so they are not cristal-like. But the movement of the electrons in a superconductor is very similar to the moment of the Ca ring.
* Tagging a Ca:
The problem with quantum systems is that they act strangely. If the system is small enough the Ca lost their individuality and become indistinguishable bosons. (I'm almost sure Ca are bosons, nor fermions.) So to describe their state you must use Slater permanent (or determinants) and not look at each one individually. So any perturbation changes the whole system and is not useful to tag one Ca. (If the system is big enough, you can approximate it classically, but 100 Ca doesn't appear to be very big.)
* Quantum Gravity:
The Quantum Theory and Special Relativity are joined since 1928 by Dirac. The same ideas were later used in QED, QCD, and all the Standard Model. So all the calculations of the collisions in the LHC use a theory that includes Quantum Theory and Special Relativity. And the only way to use Special Relativity is to have a common structure for space and time.
Those theories are not related to the continuity or discontinuity or periodicity of the space or time. Nobody knows how to joint Quantum Theory and General Relativity, but in my opinion the problem is not related at all to the existence of space-crystals and the inexistence of time-crystals.
Joking aside, this could be the E=mc^2 of our generation. We take for granted that the speed of light is the universal speed limit and that DNA has a helical shape, but a century ago we knew neither of these things. The internet, in the scheme of things, is still in its adolescence (at best). The thing that fascinates and scares me more than anything is that in 50 years science will have already advanced beyond recognition.
No, it's way less interesting than it sounds. It's interesting, but the inevitable science fiction overtones make it sound way more interesting than it actually is. It's really "just" another "humdrum" implication of quantum mechanics. It's also another interesting way of exploring the mathematical relationship between the time and space dimensions, which itself, while very interesting, isn't as interesting as putting those words in a science fiction show would make them sound. It's the hard kind of interesting that involves years of mathematics study and the resulting profound realizations about the nature of the universe that raise two questions for every question answered, not the kind of interesting that produces aliens before the next commercial break. If you want the profound realizations, they're there for the taking, but it does take the work.
(Note that I'm not disagreeing with you, just pointing out an apparent paradox)
Something tells me that as soon as they build these, the cast from Time Bandits is going to bust through the wall and steal them.