A little over a decade ago, physicist and Nobel laureate Frank Wilczek of MIT wrote a paper pondering the potential properties of a theoretical object he called a quantum time crystal. To the surprise of many, in recent years those time crystals have been found in abundance both in specific laboratory experiments and inside common things like children’s toys.
As is often the case, the exact nature of these objects is not widely understood. So let’s tackle this question together: what is a time crystal? First, let’s define what a crystal is. Think of empty space as a blank sheet of paper that extends as far as the eye can see. It has no special point because every point is the same.
That’s where translational symmetry comes in. No point is special – but now let’s imagine that the paper is graphed, like the sheets you’d use in math lessons. Now you will have a lot of empty space, but every now and then you have lines and corners etc. This is a regular repeating structure. In your average crystal, from diamonds to snowflakes, their atoms are organized in patterns that repeat like this.
Now, the pattern is what is important to define a crystal. In a time crystal, the symmetry of time is broken. A time crystal is a collection of atoms that can be in any arrangement, but at regular intervals end up in the same pattern over and over again. You can imagine it as a complicated clockwork with lots of weird moving parts – but maybe every minute they all form a clear shape before they go back to doing whatever they’re doing!
To visualize this, consider the three major moons inside Jupiter: Io, Europa, and Ganymede. Their orbital period is said to be in resonance. For every four orbits of Io, Europa makes two, and Ganymede makes one. So, roughly every week (7.15 days), the pattern repeats itself. This is a good analogy for a time crystal, but it is not a time crystal. We must add another special ingredient that can only be found in the quantum world. The system does not lose energy to the environment – in fact, the system changes and moves without energy. One of the requirements is that these systems are in the lowest energy state, so they literally can’t spend it.
You might think that this is very much like perpetual motion, and this is explicitly forbidden by the second law of thermodynamics, which states that the entropy of an isolated system always increases. They are a limiting case. The entropy of these time crystals remains the same.
These objects have only been known for a few years, but researchers are looking for possible applications for them in quantum computers, such as the potential memory storage of the future.