Conventional quasicrystals can exist in three spatial dimensions, as in the structure shown. But a quasicystal that inhabits spacetime is also a possibility.
LinKayser/Wikimedia Commons (CC BY-SA 4.0)
Mind-bending materials called quasicrystals have an orderly structure, but without a regularly repeating pattern. They’ve been found in meteorites and the debris from the first atomic bomb test. Scientists have now discovered that they can theoretically inhabit an even stranger realm: spacetime, the blended mixture of time and space of Einstein’s special theory of relativity.
Instead of existing in two or three spatial dimensions, these quasicrystals’ structures would bridge space and time, physicists report in a paper submitted January 12 to arXiv.org. Although the quasicrystals are theoretical, the researchers suggest that such spacetime quasicrystals may appear in nature, perhaps even underlying the structure of the universe.
A crystal is a structure that repeats itself. If you make a copy of a crystal, and slide it over on top of itself, you can find spots where the patterns match up perfectly. You can imagine doing the same with the tiles on your bathroom floor or the patterns on wallpaper. But quasicrystals, despite their seemingly orderly structure, don’t have such regular repetition.
Crystals and quasicrystals are mathematical concepts that also appear in the real world, typically in materials with two or three dimensions. It wasn’t obvious that spacetime quasicrystals could exist. “My feeling was probably it wouldn’t be possible to make a proper spacetime quasicrystal,” says theoretical physicist Felix Flicker of the University of Bristol in England. But, he says, the researchers appear to have done just that. “The things they’ve come up with are … the most elegant things you can have in spacetime as a combined entity.”
Despite quasicrystals’ lack of repetition, their orderliness means that their general characteristics are similar in different locations. An ant sitting atop one portion of a quasicrystal would see a structure similar to that seen by an ant in a different location. But different spacetime realms are another matter.
Spacetime obeys a rule known as Lorentz symmetry. Lorentz symmetry means that something is unchanged whether you’re sitting still or moving at close to the speed of light. For example, the laws of physics respect Lorentz symmetry: They don’t change for fast moving observers. Lorentz symmetry doesn’t hold for previously known quasicrystals, or for normal crystals either: An ant sitting still would observe a different structure than would a near light-speed ant. In relativity, observers traveling at high speeds observe an apparent shortening of objects, and that distorts the materials’ structure.
But the new spacetime quasicrystals obey Lorentz symmetry. They would appear the same to an ant sitting still as to one on a speeding rocket. The researchers mathematically formulated their quasicrystals by taking a four-dimensional slice through a grid of points in higher dimensions and projecting those points onto the slice. The slice has a slope that is an irrational number — one that can’t be written as a fraction of two whole numbers, such as pi. The irrational slope means the slice never directly intersects the points on the grid, and that helps produce the structure that never repeats.
Quasicrystals are a mathematical concept that shows up in the structure of real materials, but the concept could appear elsewhere. “The spacetime that we live in could be a quasicrystal,” says Sotiris Mygdalas of the Perimeter Institute in Waterloo, Canada, a coauthor of the study.
Spacetime quasicrystals could be relevant for certain quantum gravity theories that propose that, on very small scales, spacetime is broken up into individual points, Mygdalas says. The quasicrystals’ structure could be a framework for breaking up spacetime while respecting Lorentz symmetry.
The researchers also investigate potential applications to string theory, which describes fundamental particles as tiny vibrating strings and suggests that the universe may have 10 dimensions. Since the universe we experience has only three dimensions of space and one of time, proponents of string theory typically suggest the extra dimensions are curled up so small that we can’t interact with them. Alternatively, the quasicrystals suggest a way that all 10 dimensions could be curled up, while still allowing the seemingly infinite space and time we experience to exist. That endless space and time could be constructed out of the curled up space if an irrationally sloped slice of it is taken, similar to how the researchers devised their mathematical quasicrystals.
More work must be done to see if these ideas pan out. The authors call them “admittedly half-baked” in their paper.
The appeal of a spacetime quasicrystal, however, exists regardless. “It’s beautiful mathematics,” says theoretical physicist Gregory Moore of Rutgers in New Brunswick, N.J., who wasn’t involved with the work. “The physics is very highly speculative.”
