# Why does Matter take up Space?

> “A vacuum is a hell of a lot better than some of the stuff that nature replaces it with.” -Tennessee Williams

Matter — everything you know, love, hate, see, taste, and feel — takes up space.

Even air must take up space. Not just wind, but still, stationary air takes up space. We’ve known this since Empedocles, in the 5th Century B.C., who had a clepsydra — a hollow gourd with many holes in the bottom and a single hole at the top — demonstrated it.

You plunge the gourd into a stream, lake or river, and it fills with water. If you lift the gourd up, the water leaks out of the bottom. But place your thumb or hand over the top, and the water will stop flowing out of the bottom. What prevents it from falling? It’s got to be the air beneath the holes, exerting a pressure and taking up space!

You can even build one for yourself using (just like on Monday) a 2-liter bottle.

But why is this? Why — at a fundamental level — does air, or matter of any type, have to take up space at all?

Another way of asking this same question is, “why can’t more than one object be in the same place at the same time?”

No matter how hard I try, I can’t be in the same place at the same time as any other object in the Universe. And it isn’t just me; I can’t take any particle that makes up matter — a molecule, an atom, even a proton, neutron, or electron — and put an arbitrarily large number of them in a finite amount of space.

It didn’t have to be that way! You can take photons — particles of light — and put an infinitely large number of them in an arbitrarily small space. Same deal with the 2nd, 3rd, and 4th heaviest fundamental particles in the Universe: the Higgs Boson, the Z-boson, and — if you can overcome their charges — even the W-bosons.

So why are protons, neutrons, and electrons — the stuff that makes up all our normal matter in the Universe — limited in this way?

It’s the Pauli Exclusion Principle! Just like in baseball, where you can’t have two runners on the same base, the Pauli Principle tells us that you can’t have two identical fermions (one of the two basic types of particles, along with bosons) in the same state!

When I was younger, I used to think this was some minuscule technical detail of physics, good for little more than explaining the chemical properties of atoms due to their electron cloud structure.

Big deal, I can’t put two identical fermions in the same quantum state.

But it’s a much bigger deal than that. If I either cooled the temperature down to absolute zero or compressed matter with an arbitrarily large amount of force, I could squeeze any number of bosons into an arbitrarily small space.

But normal matter is made out of protons, neutrons and electrons, all of which are fermions. And this simple principle means that there’s a finite volume that — once it’s occupied by one of these matter particles — it’s off-limits to the others!

And that’s why matter takes up space, no matter whether it’s charged or neutral, and regardless of temperatures or pressures or any other physical properties!

There are some spectacular astrophysical consequences of this, and two of my favorites are what happens to stars when they die.

A white dwarf star — somewhere around the mass of the Sun but the physical size of the Earth — is made of plain old atoms, same as we are. But a white dwarf is about 300,000 times denser than we are! Yet, despite that incredible gravity compressing the white dwarf, the atoms refuse to buckle. Why?

Because the atoms deep inside the star have their electrons bumping up against each other, and the electrons refuse to buckle and let other electrons any closer!

In fact, in the most extreme case, the electrons, rather than let another electron into the same state and violate the Pauli rule, would rather fuse with the protons, producing a neutron (and a neutrino), collapsing all the way down to a neutron star!

But neutrons are fermions, too, and even a star made entirely out of neutrons refuses to collapse! These are the densest known objects in the Universe that are still made of matter, and yet, they take up space!

So you can keep your bosons to yourself; my matter takes up space, and I’ve got the Pauli Exclusion Principle to thank for it! On the other hand, dark matter could be either bosonic or fermionic; we don’t know yet, but my money’s on bosonic, and that it truly doesn’t take up any space! (How’s that for some wonderment headed into the weekend?!)