Maybe I can help give insight into this topic to those without a physics background. Our current best theory that describes reality at the small scale is quantum mechanics. In quantum mechanics, each "system" -- a collection of particles that you are interested in -- corresponds to one wavefunction (literally, a mathematical function). Glossing over some details, this is a function of spatial coordinates (a vector r) and time (t). For example, if your system is hydrogen, your wavefunction is a function of two coordinates -- the electron's position and the proton's position -- and time. You can perform some linear algebra on this function to predict what state the system will be in at any future time. And you can also predict what your measurements (position, momentum, spin, etc.) of this system will be. The Schrodinger equation is what governs the evolution of the wavefunction. I'll refer you to Wikipedia if you want to know the details of that equation.
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.
(1) How can the ground state not be an energy eigenstate? By definition, the lowest-energy state has a well-defined energy (that is, the lowest energy) and therefore ought to be in an energy eigenstate?
(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.
The problem is that they get a varying measurement after tagging an atom, so the system is not anymore in the ground state, because the tagged atom is exited and it will sooner or later decay to the ground state.
This article doesn't seem fair to physics. For instance, it says:
"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)
(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!
(7) Etc.
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?
I think you're confusing forever with a really long time.
(1) Asteroid's velocity is eventually overcome by external forces.
(2, 3) Structure decays.
(4) Bodies converge or diverge.
(5) Radioactive decay.
(6) You are observing a high energy system.
(7) Etc.
"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."
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.
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.
This article seems like it is abstracting away what would actually make this experiment more interesting than, say, spinning a dinner plate in a vacuum in zero-g.
A dinner plate spinning in the vacuum is not in a ground state -- it has substantial kinetic energy that is being converted into heat and electromagnetic radiation as it spins, and it will gradually slow down and stop. (Veeery gradually.)
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.
The experiment is interesting and I'll like to read the results. But I don't like a few details, probably most of them are errors in the press release.
* 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.
Time crystals and ion traps... I must have fallen asleep watching Doctor Who again.
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.
"Joking aside, this could be the E=mc^2 of our generation."
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.
My understanding as explained to me by CERN, You can build a Time Crystal but it is tough to observe it after. The object don't so much spin through infinity, as infinity spins through them. Building a Time Crystal changes how it moves through Space-Time. Since we are moving through Space-Time really quickly if you change for lack of a better word the inertia of matter by changing how it moves through Time it won't stand still for very long, (well not relative to you) this makes observation nearly impossible.
[+] [-] Xcelerate|13 years ago|reply
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.
[+] [-] tedsanders|13 years ago|reply
(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.
[+] [-] yog|13 years ago|reply
[+] [-] gus_massa|13 years ago|reply
[+] [-] tedsanders|13 years ago|reply
"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!
(7) Etc.
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
[+] [-] ivybridge|13 years ago|reply
[+] [-] bencollier49|13 years ago|reply
[+] [-] ISL|13 years ago|reply
Quantum Time Crystals (Wilczek) http://arxiv.org/abs/1202.2539
Classical Time Crystals (Shapere, Wilczek) http://arxiv.org/abs/1202.2537
Space-time Crystals of Trapped Ions ( Li, Gong, Yin, Quan, Yin, Zhang, Duan,Zhang ) http://arxiv.org/abs/1206.4772
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:
http://physics.aps.org/articles/v5/116
[+] [-] whatshisface|13 years ago|reply
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.)
[+] [-] ealloc|13 years ago|reply
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.
[+] [-] smosher|13 years ago|reply
[+] [-] dingfeng_quek|13 years ago|reply
http://www.scientificamerican.com/article.cfm?id=time-crysta...
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.
[+] [-] cpeterso|13 years ago|reply
[+] [-] royalsporks|13 years ago|reply
[deleted]
[+] [-] jlgreco|13 years ago|reply
[+] [-] gwillen|13 years ago|reply
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.
[+] [-] gus_massa|13 years ago|reply
* 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.
[+] [-] ryanthejuggler|13 years ago|reply
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.
[+] [-] jerf|13 years ago|reply
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.
[+] [-] unknown|13 years ago|reply
[deleted]
[+] [-] brandon_wirtz|13 years ago|reply
[+] [-] drudru11|13 years ago|reply
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.
[+] [-] riemannzeta|13 years ago|reply
[+] [-] losethos|13 years ago|reply
[deleted]
[+] [-] exabrial|13 years ago|reply