Sometimes I know that I'm going to write about a paper before I even read it. The hook is simply too inviting. A new paper, simply entitled "Time crystals," with a companion paper "Quantum time crystals," is that sort of irresistible. Even if the papers turned out to be giant piles of steaming science, lying in full repugnant view on the pages of Physical Review Letters, it was certain there would be a good story to tell.
As it turns out, these papers are a strange brew of "what if," mixing the unlikely with the banal to create a heady mixture of pure confusion. As the names of the papers imply, the authors consider how it might be possible to create something akin to a crystal—but one that occupied time rather than space.
To a physicist, a crystal is a collection of basic building blocks, repeated in space. A salt crystal consists of a regular array of sodium and chlorine atoms. Wherever you are within the crystal, if you move by any multiple of a specific distance, you find yourself in a place that looks exactly the same. This is called translational symmetry.
So let's consider what this might mean in relation to time. In its crudest sense, it would mean that if we move forward or backward in time by some multiple of a fixed amount, we would find ourselves in exactly the same environment. My first thought upon encountering this idea: any wave would satisfy this criteria. You simply translate yourself in time by an integer of the oscillation period of the wave. But I had the feeling this wasn't what the authors, Shapere and Wilczek, had in mind.
The authors describe their crystal as a ruler, one that provides periodic landmarks in an otherwise featureless space. The periodicity introduced by the presence of the atoms allows us to measure the passage of space. Imagine sitting in a room where nothing ever appeared to change as time passes—you would have no way to measure the flow of time. But if the room were in a time crystal, you would still have a natural clock with which to observe the passage of time using its repetition.
Does this sound confusing? It should. It certainly confuses the hell out of me. Mathematically, the argument runs like so: If I take the math for describing a normal crystal and convert all the spatial variables into time variables, I get a set of solutions that tell me time crystals exist. That argument, though, uses the equations for the motion of a particle. If you switch to a different variable (momentum), then you find that a time crystal cannot exist.
Reality may be weird, but it usually arrives at self-consistency at some point. So why do time crystal simultaneously exist and not exist? The answer lies in the details of converting between the two descriptions. In the conversion process, we assume both descriptions of reality are smooth. Upon examination, however, it turns out that one of them has a point where certain values—envision the rate of change of momentum at the turning point of a swing—very suddenly approach infinity. Of course, it takes a very unusual swing to generate accelerations approaching infinity.
The key point is that this is anything but smooth. These infinities also occur at precisely the momentum predicted for a particle in a time crystal. Just to make matters more confusing, that particle has multiple energy values, despite having a single momentum.
All of this makes one think a time crystal must be something exotic and exciting. But in their companion paper, "Quantum time crystals," the authors use the example of a persistent current in a superconducting ring. The only difference between that and light circulating in a ring of glass is that the light will slowly be absorbed. But if I balance that loss with a little extra light from outside, do I have a time crystal? Can it really be as banal as that?
I know I am not the sharpest knife in the drawer. Indeed, if my students were given the chance to vote on the person in most dire need of beating with a clue stick, you wouldn't need Nate Silver to predict the outcome. But I can only conclude this paper is reporting something incredibly common (hey, the orbit of the Earth is a time crystal), but carefully obfuscated. Or, it is pure awesome, allowing the existence of particles with multiple values of energy for a single momentum state.
Alternatively, and this is most likely, the infinities that turn up in one of the descriptions are simply not physically realizable. We cannot create a swing with turning points sufficiently sharp to generate these infinities.
Physical Review Letters, 2012, DOI: 10.1103/PhysRevLett.109.160402
Physical Review Letters, 2012, DOI: 10.1103/PhysRevLett.109.160401
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