Time Crystals: Matter in Four Dimensions
They were supposed to be impossible
The name “time crystals” conjures up fantastical images of traversing magic portals to go backward or forward in time. They sound alien; something which could not possibly exist on our planet but instead are a technology harbored by a more advanced civilization. The crystals might grow white and shrouded in an otherworldly glow of blues and reds or some opalescent mixture of hues that radiates around them. In short, beautiful but ultimately mythical.
Except time crystals aren’t a myth. And while they’re not capable of such feats as controlling time or traveling through dimensions, they are the first of their kind and are a fascinating addition to our understanding of physics.
Normal crystals, with their strong, sharp corners and gradient colors, are already considered magical. They show up in our games to give us powers and are used in ritual practices to bring healing or clarity. Really they’re a number of bonded atoms which repeat in a specific pattern, creating a crystal lattice that exists in 3 dimensions. This crystal structure breaks what is known as the symmetry of space. Symmetry of space is the ability to sample any part of the space to find the same composition, like sampling a tank full of water and knowing that the water near the top will be the same as the water near the bottom. But crystals make the space periodic as their patterns repeat in specific directions, no longer allowing for homogeneity. Time crystals do this same thing but repeat in 4 dimensions.
Rather than simply repeating in space, these 4D crystals repeat internal states — or movement — over time, breaking time-translation symmetry just as our normal crystals break space symmetry. This is important because one of the biggest aspects of physics is using symmetries to find natural laws. In our example of space symmetry and normal crystals, this leads to the law of conservation of momentum. In the case of time crystals, time symmetry leads to the conservation of energy. To understand the symmetry of time, imagine rolling a die. Your chances of getting a 5 are about 17% whether you roll the die today or tomorrow. But broken time symmetry would be a change in your chances of rolling a 5 the longer you wait. Because of this connection between symmetries and laws, this means that time crystals don’t obey the law of conservation of energy which states that energy cannot be created or destroyed. It’s the first time we’ve ever witnessed this law broken. Energy within the time crystal continues to repeat even in its lowest energy state, making it impossible for the structure to return to equilibrium.
Usually matter, like our aforementioned die, has potential energy but only when one throws it does the potential energy become kinetic energy and the die is set in motion. But because time crystals move at their ground state — the lowest energy state — this is like a die that rolls even when no one is touching it. Suddenly, we have the first non-equilibrium matter ever.
These special crystals were theorized in 2012 by physicist and mathematician Frank Wilczek who suggested crystals’ structural repetition could exist in the 4th dimension as well as it did in the 3rd. It wasn’t until 2016 that the first blueprint for how to make these a possibility really surfaced.
That year, a group of physicists led by Chetan Nayak from UC Santa Barbara helped to clarify Wilczek’s idea, taking it from something entirely fictional to a real world possibility. The team defined the kind of circumstances under which a time crystal could occur — a quantum system without thermal equilibrium and one which can’t be described by any temperature since temperatures naturally suggest equilibrium. Non-equilibrium Floquet systems can contain states of matter not possible otherwise. A separate team led by Norman Yao then showed scientists how to make them.
The steps went like this: set up a chain of ions with spin values (ions are electrically charged atoms). The interacting magnetic field of atoms then causes their spins to line up with one another, either in the same alignment (up, up) or the opposite alignment (up, down). Using a laser, cause the spins to flip back and forth, meaning that the introduction of energy from the laser is what determines the spin flip oscillation. But time crystals won’t respond the way you expect. Instead of following the pattern of pulsations from the laser, the ions will pulse at a multiple of the original speed. This is like saying that if I pulse a laser at the ions every 5 seconds, they instead respond after 20 seconds or 35 seconds, instead of the original 5. The oscillations are then sustained internally.
Time crystals have been created several times. First by researchers at the University of Maryland who used ytterbium atoms and entangled them in repeating patterns using a magnetic field. A second laser then moved the atoms and they eventually exhibited a pattern different from the one created by the laser. Researchers at Harvard used molecules from nitrogen impurities in diamonds and employed microwaves to cause the ions to flip and oscillate. Since then, time crystals have been made twice more. Once with a solid material called monoammonium phosphate and the second with a liquid containing special star-shaped clusters of molecules.
Since their discovery, time crystals have been likened to a perpetual-motion machine — a machine that can continue to move and function without an energy source. But while they come close to the description, time crystals are different in that no energy can be extracted from them because they are already in their ground state. However, time crystals do seem to have a promising future.
Because of their stable spin-flip cycles, time crystals could be the answer to building better memory in quantum computers. As they are now, quantum computers are easily disturbed (even by things as small as dust and sound) and these disruptions can cause loss of information. The time crystal’s entangled atoms could then store qubits of information in a much more reliable way. They could also help bring together quantum mechanics and general relativity, or perhaps be the first step to unifying space and time since quantum mechanics treats these two very differently.
So maybe time crystals don’t live up to the wild images implied by their name. But we’re talking about an entirely new state of matter that exists in an added dimension and could help create the future of quantum computing. So then again, maybe they do.