Mark Megahan
From snowflakes to diamonds, crystalline solids have captivated mankind for eternity, partly because of their mathematically ordered beauty. Each composite atom or molecule is regularly arranged in space. Likewise, these crystalline periodic patterns in space are mirrored by similar crystals in time.
Crystals of reduced symmetry
The phenomenon of periodic oscillations appears at all scales, ranging from atomic oscillations to 60 cycle house current to orbiting planets. We depend on the regular vibrations of crystals to mark the passage of time. At least, your watch does.
The one characteristic shared between them is that “they lead to systems with reduced symmetries.”
Without the concept of “periodicity,” it’s meaningless to talk about position in space because every instant is the same as every other in time. Scientists say that periodicity “breaks the translational symmetry” of space or time, whichever is involved. These “time crystals” are a lot different than the ones your watch uses. When the brainy types talk about breaking symmetry, what they’re really talking about is “when the lowest-energy or ground state of a system does not respect a symmetry that, in principle, is not forbidden.” Oh, that really clears things up.
For example, crystalline structures like ice cubes show where the “continuous translational symmetry” of a frozen sheet of water “breaks and is replaced by a discrete periodic symmetry in space.”
Ever since the late, great Albert Einstein, the world has learned to accept space and time as two sides of the same spacetime coin. That set physicists to pondering.
If a collection of particles can show spacial periodicity, is there any reason why a pattern of events can’t spontaneously emerge in time? The short answer is “no.” The answer to time crystals wasn’t as easy to figure out as it seems.
Breaking time isn’t easy
Physicists have been working on the challenge of temporal crystals for at least ten years now. To put it properly for those picky editors at the peer review journals, they have been wondering “whether systems with ground states where time translational symmetry is broken can exist.” Breaking time isn’t as easy as breaking space, it seems.
“Lorentz transformations, which relate the space and time co-ordinates of two systems moving relative to each other, do not mean that space and time are completely equivalent, as there is causality.”
In physics, all the theories and equations work exactly the same no matter whether you run them forward or backward, except one. The one which physicists like to call the second law of “thermogoddamnics.” That’s the one which establishes the concept of entropy.
No matter how hard the cue ball whacks the rest of the billiard balls on the break, they stop rolling eventually. Time crystals would be like a handful of balls which kept roaming around the table until doomsday. They found some.
A class of curious “many-body localized” systems have been identified which “due to disorder, fail to reach thermal equilibrium, thereby retaining a memory of their initial states for infinite times. The entropy plateaus at smaller values, allowing for temporal ordering.” The elusive time crystals were discovered. “Therefore, in spite of the periodic drive, the net flow of energy becomes zero and entropy plateaus below the maximum value (figure 1c).”
“Saturation below the maximum attainable entropy does not violate the second law, which states that the entropy of an isolated system cannot decrease in time. This law does not demand the entropy of an isolated system to reach the maximum possible value, although it is difficult to avoid. It only states that the rate of change of entropy cannot be negative, it can be positive or zero.“
