The Pauli Exclusion Principle is one of the most important and well-studied consequences of quantum mechanics. It states that fermions — particles like electrons — cannot occupy the same quantum state. And it has profound consequences.
One of the most famous is the structure of the atom. The exclusion principle ensures that electrons occupy different orbits around a nucleus. This kind of self-ordering is why atoms have volume and why two of them cannot both be in the same place at the same time. It’s why we can’t walk through walls.
But, in recent years, physicists have begun to think of other, more subtle consequences of the principle. A couple of years ago, they predicted that this self-ordering ought to work when fermions are trapped in other circumstances. Then, they ought to form crystals with a specific, unique geometry.
