Physicist proves impossibility of quantum time crystals

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…

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 ion trap. They argue that under a weak applied magnetic field, the ions should begin to rotate around the ion trap, and that, because the ions are in their ground state, their rotation theoretically would persist indefinitely.
But not everyone is embracing the concept of quantum time crystals. 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 energy state. Second, a system that displays rotational motion in its ground state is also able to radiate energy in the form of electromagnetic waves, 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 ground state, 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:

Creating time crystals with a rotating ion ring

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

Journal reference:

Physical Review Letters

view popular

4.7 /5 (38 votes)

© 2013 All rights reserved.

Related Stories

Creating time crystals with a rotating ion ring

May 03, 2013

( —There has been a lot of talk recently about the possibility of building what has come to be known as a time crystal. In February 2012, Frank Wilczek originally proposed the idea that under certain conditions, physical structure …

Physics team proposes a way to create an actual space-time crystal

Jul 09, 2012

( — Earlier this year, theoretical physicists Frank Wilczek, of MIT put forth an idea that intrigued the research community. He suggested that it should be possible to construct a so called space-time …

A clock that will last forever: Researchers propose a way to build the first space-time crystal

Sep 24, 2012

(—Imagine a clock that will keep perfect time forever, even after the heat-death of the universe. This is the “wow” factor behind a device known as a “space-time crystal,” a four-dimensional crystal …

Time crystals could behave almost like perpetual motion machines

Feb 20, 2012

( — As every young science student knows, moving objects have kinetic energy. But just how much energy does something need to move? In a new study, a pair of physicists has shown that it’s …

New method to generate Laughlin states with atomic systems

Jul 03, 2013

In 1998, the Nobel Prize in Physics was conferred to the discovery of a new type of quantum fluid with fractional charge excitations, known as Laughlin state. The production of this quantum state, which explains the behaviour …

Cosmology in the lab using laser-cooled ions

Aug 12, 2013

Scientists would love to know which forces created our universe some 14 billion years ago. How could – due to a breaking of symmetry – matter, and thus stars and galaxies, be created from an originally …

Recommended for you

Physicists offer explanation for strange magnetic behavior at semiconductor interfaces

5 hours ago

The new discovery could one day lead to electronic materials that provide both computation and data storage.

Scientific vandalism helps ITER

Aug 23, 2013

Scientists at JET, the world’s largest fusion energy research facility, have been deliberately melting parts of their own machine as they test materials for the fusion reactors of the future. These apparent …

Computer simulations indicate calcium carbonate has a dense liquid phase (w/ Video)

Aug 22, 2013

Computer simulations conducted at the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) could help scientists make sense of a recently observed and puzzling wrinkle in one of …

NIST ytterbium atomic clocks set record for stability

Aug 22, 2013

A pair of experimental atomic clocks based on ytterbium atoms at the National Institute of Standards and Technology (NIST) has set a new record for stability. The clocks act like 21st-century pendulums or …

Aug 22, 2013

( —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 …

Wideband wavelength conversion using cavity optomechanics

Aug 22, 2013

A team of researchers at the NIST Center for Nanoscale Science and Technology (CNST), the University of Maryland, and the California Institute of Technology have demonstrated optical wavelength conversion …

User comments : 22

Adjust slider to filter visible comments by rank

Display comments: newest first

More news stories

Physicists offer explanation for strange magnetic behavior at semiconductor interfaces

The new discovery could one day lead to electronic materials that provide both computation and data storage.

Teleportation just got easier—but not for you, unfortunately

Thanks to two studies published in Nature last Thursday, the chance of successful teleportation has considerably increased. Which is a good thing, right? …

New results from Daya Bay neutrino experiment announced

The international Daya Bay Collaboration has announced new results about the transformations of neutrinos – elusive, ghostlike particles that carry invaluable clues about the makeup of the early universe. …

Researchers discover quantum algorithm that could improve stealth fighter design

( —Researchers at the Johns Hopkins University Applied Physics Laboratory (APL) have devised a quantum algorithm for solving big linear systems of equations. Furthermore, they say the algorithm could be used to …

Planes, trains and molecules: Deriving a generic routing algorithm from the physics of interacting polymers

Finding a single optimal route is easy, but optimizing the combination of multiple routes is a challenge found in a wide range of applications including Internet instant messaging, peer-to-peer networks, subway …

US spy agency broke encryption on UN communications, report says

The US National Security Agency broke the encryption securing the United Nations’ internal video conferencing at its New York headquarters, German news weekly Der Spiegel reported Sunday, citing secret NSA …

Science points to a new global warming source: the sea

Oceans that grow more acidic through Man’s fossil fuel burning emissions, can amplify global warming by releasing less of a gas that helps shield Earth from radiation, a study in Nature Climate Change said S …

Study in mice links cocaine use to new brain structures

Mice given cocaine showed rapid growth in new brain structures associated with learning and memory, according to a research team from the Ernest Gallo Clinic and Research Center at UC San Francisco. The findings …

Study explains how the brain remembers pleasure and its implications for addiction

Key details of the way nerve cells in the brain remember pleasure are revealed in a study by University of Alabama at Birmingham researchers published today in the journal Nature Neuroscience. New details of the molecular events …

Study provides strongest clues to date for causes of schizophrenia

A new genome-wide association study (GWAS) estimates the number of different places in the human genome that are involved in schizophrenia.