Spacetime obeys a rule known as 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.
