Physicist proves impossibility of quantum time crystals

Aug 22, 2013 by Lisa Zyga feature
Physicist proves impossibility of quantum time crystals
Image by Sam Rohn,

( —Is it possible that a moving object could have zero energy? The common sense answer is no, since motion itself is kinetic energy, but this answer has been challenged recently by the concept of quantum time crystals. First proposed in 2012 by the Nobel Laureate Frank Wilczek at MIT, quantum time crystals are theoretical systems that exhibit periodic oscillations in their ground state, i.e., their state of lowest possible energy.

Since then, researchers Tongcang Li et al., at the University of California, Berkeley, have proposed an experimental set-up of a time crystal based on charged particles (ions) in a ring-shaped . They argue that under a weak applied magnetic field, the ions should begin to rotate around the ion trap, and that, because the are in their ground state, their rotation theoretically would persist indefinitely.

But not everyone is embracing the concept of quantum . Physicist Patrick Bruno at the European Synchrotron Radiation Facility in Grenoble, France, has identified some holes in the concept and has proven a "no-go theorem" that rules out the possibility of spontaneous ground-state rotation for a broad class of systems that might be categorized as quantum time crystals.

Bruno's argument, which is published in a recent issue of Physical Review Letters, expands upon his Comment on Wilczek's original paper, both of which were published in Physical Review Letters in March.

According to Bruno's Comment, the quantum time crystal concept has two major flaws. First, the rotating soliton (a solitary wave pulse) that Wilczek describes in his model is not in its ground state, but rather in a higher . Second, a system that displays rotational motion in its ground state is also able to radiate in the form of , which conflicts with the principle of energy conservation.

Wilczek previously responded to Bruno's first objection and acknowledged that the rotating soliton in his model was not in its ground state, but suggested that other models could be time crystals, i.e., possess a nonstationary ground state.

In the new paper, Bruno's proof demonstrates that setting a system of particles in motion around a one-dimensional magnetic ring always increases the ground-state energy of the system so that it's no longer in its ground state, which prohibits the existence of a rotating ground-state system. The proof covers systems rotating at any finite angular velocity. The argument builds upon Nobel Laureate Anthony Leggett's work on the rotational properties of superfluids.

Bruno explains that this proof should not come as a surprise, since a 1964 theory by another Nobel Laureate, Walter Kohn, shows that an insulator is completely insensitive to a magnetic flux. Since quantum time crystals are modeled as ring-shaped Wigner crystals, and Wigner crystals are insulators, attempting to show that a magnetic flux can cause such a system to rotate is, as Bruno writes, "a hopelessly doomed endeavor."

Whether or not Bruno's proof is the final answer on quantum time crystals, only time will tell.

"Only future developments (or absence thereof) will allow us to tell whether or not my paper has given a final answer to the question of whether quantum time crystals might exist," Bruno told "For the time being, what I can say is that my paper shows the impossibility of time crystals for all realistic models or mechanisms that have been proposed so far. So, until further developments occur, I consider the topic as closed.

"I cannot exclude that someone will come up with an alternative proposal, outside the scope of my no-go theorem," he added. "However, considerations based upon the energy conservation objection suggest that time-crystal behavior, i.e., the nonstationary , is generally impossible.

"I have currently no plans to continue to work on this topic, unless someone would come up with new arguments. In such case, I would definitely look at it closely, and possibly work on this again."

Explore further: Researchers take a step towards development of optical single-phonon detector

More information: Time crystals could behave almost like perpetual motion machines

— Frank Wilczek. "Quantum Time Crystals." PRL, 109, 160401 (2012). DOI: 10.1103/PhysRevLett.109.160401

— Tongcang Li, et al. "Space-Time Crystals of Trapped Ions." PRL 109, 163001 (2012). DOI: 10.1103/PhysRevLett.109.163001

— Patrick Bruno. "Comment on 'Quantum Time Crystals.'" PRL, 110, 118901 (2013). DOI: 10.1103/PhysRevLett.110.118901

— Frank Wilczek. "Wilczek Reply." PRL, 110, 118902 (2013). DOI: 10.1103/PhysRevLett.110.118902

— Patrick Bruno. "Impossibility of Spontaneously Rotating Time Crystals: A No-Go Theorem." PRL 111, 070402 (2013). DOI: 10.1103/PhysRevLett.111.070402

— Walter Kohn. "Theory of the Insulating State." Phys. Rev. 133, A171–A181 (1964). DOI: 10.1103/PhysRev.133.A171

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User comments : 22

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2.7 / 5 (19) Aug 22, 2013
One less thing Apple and Samsung will sue each other over.
not rated yet Aug 22, 2013
How does one achieve a one-dimensional ring [i.e., a circle]?
1.8 / 5 (10) Aug 22, 2013
How does one achieve a one-dimensional ring [i.e., a circle]?

It's the confinement of particles in a quantum mechanical system.

The wiki page on 'Wigner crystal' is interesting and it lists the different lattice types in 3D, 2D, and in 1D: http://en.m.wikip..._crystal

This is good, a bit technical, on 1D problems and how to work them out: http://web.utk.ed...lems.htm
1 / 5 (10) Aug 22, 2013
No matter what the "eternal clock" the very matter that makes up this crystal will thanks to spatial expansion would no longer be able to retain its "special" form (or any form for that 'matters'..) Thus the particles would indeed become subject to decay into lower and lower energy state constituent parts until the vibration of the energy loop itself becomes one dimensional.

Then perhaps one of many things may occur..

Perhaps one of the black holes finally after so much time has past will have collapsed into around a plank in size and the pure force of spatial torsion will become enough to overcome gravity and snaps back with unfathomable energy and is another "big bang" also note that this type of spatial bounce back would not be uniform and thus explains the nonuniform background radiation variations for example..
1 / 5 (8) Aug 22, 2013
Since quantum time crystals are modeled as ring-shaped Wigner crystals, and Wigner crystals are insulators, attempting to show that a magnetic flux can cause such a system to rotate is, as Bruno writes, "a hopelessly doomed endeavor."
Just a second. At the scale in which these crystals exist, the The Aharonov-Bohm effect and Brownian Motion might induce exactly what the researchers Tongcang Li et al predict might occur, effectively eliminating the insulator problem Bruno thinks justifies his take on the experiment.

3 / 5 (3) Aug 22, 2013
You know, one of the most enlightening discussion I recall was Dr. John Wheeler comment on relativity and the electron, (it's applicable to a photon as well). He proposed that there was only one electron in the universe. It's just that time allowed it be everywhere at once! He was talking about relativity of course. It was Dr. Wheeler playing mental games with relativity, because how could you explain all of the quantum states of an electron in an atom? The photon though, is zero mass and does travel and speed C. From it's point of view, it sees the begin and the end of time at the same instant.
not rated yet Aug 22, 2013
Okay, let me say at the start that this discussion and the paper is out of my domain although I do understand a little of what is going on.
But there is one thing that bothers me, and always did, was 1D problems. As far as our macro state is concern then yes I agree that certain things can appear and be treated as 1D. Surely though, if one exisited in the quantum realm an electron (part. or wave) moving around nucleons would not appear as 1D. Indeed, if S.String is valid the vib. string would at least be 2D (and of course might consist of compactified D). In other words, relative to us they are 1D but relative to quantum states they must be at least 2D. The term 'crystal' implies an arrangement that is greater than 1D and again any em wave is defined as electro and mag fields at 90 deg to each other and so cannot be 1D.
Purely a layman's point of view
2 / 5 (8) Aug 23, 2013
On the D's, maybe this will help:
A quantum dot confines in 3D (a sphere) so the confined particle is free to act as a charge carrier in a zero-D potential well.
A quantum wire confines in 2D so the confined particle is free to act as a charge carrier in a 1D potential well.
A quantum well confines in 1D so the confined particle is free to act as a charge carrier in a 2D potential well.
1 / 5 (2) Aug 23, 2013
HAH SO YOU DID IT! x=y can be solved if you haqve non intersecting points. Is it first post first serve or first machine. THey knocked me out after stealing quantum internet... the frieds.....
2.3 / 5 (9) Aug 23, 2013
Curious 'discussion'. No one likes anyone else...all rate everyone else as '1's.
2.6 / 5 (22) Aug 23, 2013
Phys.Org has been asked to disable comment ratings because of this.

The 'administrators' either don't know how to use the software, or encourage troll raters to increase hits for ad revenue (the NOM rating troll IS associated with Phy.Org). Incompetent, corrupt, or both.

1.4 / 5 (11) Aug 23, 2013
What a load of nonsense. Who is paying these loonies to argue over something even more absurd than angels on a pinhead? Nobel prize committee...right.
1.8 / 5 (10) Aug 23, 2013
If you can keep your head while all about you are losing theirs and blaming it on you - you'll be a man, my son.

Note that I always seem to be rated one star, no matter what I post. I don't rate, I just read and respond. I think that the system is based on the more you rate, the higher your ratings will be. That's actually the way it works on some sites. I think that if wants to be taken seriously, it should disable this silly ratings feature. We all know who the one star is on this site, don't we?
1 / 5 (7) Aug 23, 2013
Good job Mr Bruno. You have an excellent discussion going the way there is only now!
1 / 5 (8) Aug 23, 2013
Hmm, if you can engineer a negative index of refraction into a metamaterial, why not a time crystal? Might be beyond the scope of the proof...
1 / 5 (6) Aug 23, 2013
I wonder if they have tried this in a cold vacuum?
1 / 5 (13) Aug 23, 2013
Space trigger materials research become an on-set mode to Triggered consciousness. space Cosmology Vedas needs best of brains trust for Dimensional comprehension.
1 / 5 (1) Aug 24, 2013
This appears to me to be the same problem that we have with our understanding of inertia. i.e. relative to what?
2.6 / 5 (17) Aug 25, 2013
Space trigger materials research become an on-set mode to Triggered consciousness. space Cosmology Vedas needs best of brains trust for Dimensional comprehension.

Someone must have put your post through a blender.
1 / 5 (1) Aug 26, 2013
Yes, but to Bruno: How do we know an insulator state isn't an entangled property?
2 / 5 (4) Aug 26, 2013

Space trigger materials research become an on-set mode to Triggered consciousness. space Cosmology Vedas needs best of brains trust for Dimensional comprehension.

Someone must have put your post through a blender.

@nou: Just like we have ranking trolls on; we have posting trolls. Check out 'vid's' older posts via his rating page. I think that you will find that this is the only kind of stuff it actually posts (why waste a perfectly good pronoun like s/he on that kind of rubbish. Can't even be sure that there is a real person behind 'it'...). It is probably high (and off on another plane of existence) when it does think that contributions become less garb(ag)led by pressing that button. Either that, or the programmer who writes its program is....

Cheers, DH66

1 / 5 (3) Aug 26, 2013
The article misuses the word "finite" in the sentence, "The proof covers systems rotating at any finite angular velocity". What the author meant to say is "The proof covers systems rotating at any nonzero angular velocity."

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