A New Kind Of Matter | Professor Paul Steinhardt

Steinhardt distinguishes between the “first kind” of impossible (rigorously ruled out, like tiling a floor with perfect pentagons using a single tile) and the “second kind,” where a hidden assumption can be relaxed—here, allowing multiple tile types and quasi-periodicity unlocked entirely new atomic arrangements.

Unlike conventional crystals that repeat a single building block periodically, quasicrystals use two or more building blocks arranged in a non-repeating but ordered pattern, enabling symmetries (like fivefold and tenfold) long thought impossible for matter.

While Steinhardt’s group developed the mathematical theory of quasicrystals, Dan Shechtman experimentally observed a diffraction pattern breaking crystallographic rules; only when Steinhardt compared the precomputed theoretical pattern to Shechtman’s data did the match reveal they were seeing the same new kind of matter.

Tracing a grain from a museum drawer back to its origin required mining old catalog records, contacting widows of collectors, deciphering ‘secret’ and ‘secret-secret’ diaries, navigating fakes in mineral markets, and ultimately identifying the original field geologist in remote Russia.

Laboratory analyses showed the Florence sample came from an ancient meteorite, likely formed in violent high-pressure space collisions or other exotic processes before planets existed, implying that quasicrystals belong on the list of earliest known minerals in the solar system.