Why does Matter take up Space?
by Ethan Siegel
Scienceblogs.com Starts With a Bang
November 12, 2010
http://scienceblogs.com/startswithabang/2010/11/why_does_matter_take_up_space.php

[moderator: use the link above to view the excellent
graphics which accompany this blog]
 

"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?!)

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