Take a look around you at everything on Earth. If you were to investigate what any object is made out of, you could subdivide it into progressively smaller and smaller chunks. All living creatures are made up of cells, which in turn are composed of a complex array of molecules, which themselves are stitched together out of atoms. Atoms themselves can be broken down further: into atomic nuclei and electrons. These are the constituent components of all matter on Earth and, for that matter, all the normal matter we know of in the Universe.

It might make you wonder how this occurs. How do
atoms, made of atomic nuclei and electrons, which come in less than 100
varieties, give rise to the enormous diversity of molecules, objects,
creatures and everything else we find? We owe the answer to one
underappreciated quantum rule: the Pauli Exclusion Principle.

When most of us think of quantum mechanics, we think
of the bizarre and counterintuitive features of our Universe on the
smallest scales. We think about Heisenberg uncertainty, and the fact
that it’s impossible to simultaneously know pairs of physical properties
(like position and momentum, energy and time, or angular momentum in
two perpendicular directions) beyond a limited mutual precision.

We think about the wave-particle nature of matter,
and how even single particles (like electrons or photons) can behave as
though they interfere with themselves. And we often think about
Schrödinger’s cat, and how quantum systems can exist in a combination of
multiple possible outcomes simultaneously, only to reduce to one
specific outcome when we make a critical, decisive measurement.

Most of us barely give a second thought to the Pauli
Exclusion Principle, which simply states that no two identical fermions
can occupy the same exact quantum state in the same system.