# Question about matter to space ratio.

Suppose you could compress the known universe into a 10m sq cube? What area would all the matter, ie. galaxies and their components, take up of that cube?

Just thought I’d give the Dope’s mathematicians something to get their teeth into.

Is there any reason you think it wouldn’t be a 10 meter cube?

Yes. Because I have been led to believe that the vast majority of our universe is empty space - disregarding theories about dark matter - I want to know what percentage of the 10m cube would be actual matter, ie. galaxies, stars, planets, asteroids, etc! Does that make sense?

Almost zero.
The distances between stars is measured in lightyears, while a star’s diameter is measured in lightseconds or less. The distance between galaxies is 20-40 times the size of the galaxy itself. And, atoms themselves are mostly empty space (99.9999999999999% empty space) : http://www.physicsforums.com/showthread.php?t=74297
So, if the Universe were the size of a 10 meter cube, and the entire mass was just a ball of Neutronium, it would be rattling around somewhere, too small to see.

ETA: oh, you mean the exact opposite of what i posted.

ETA ETA: however, I don’t think it’s fair to assume that all the matter is compressed into neutronium: after all, change of fermion type is not assumed in the OP (unless it was.) In which case electron degeneracy pressure could be regarded in a way as “taking up space”.

So, if the galaxies were behaving as they are now, within this space, would they be noticeable within the 10m cube, or would they be smaller than motes of dust? Would anything be visible to the naked eye on this scale?

It’s inaccurate to say that atoms are mostly empty. It’s accurate that most of the mass is concentrated in the nucleus, and that the nucleus only occupies a small portion of the atom, but that’s not the same thing at all. An atom’s electrons occupy the rest of the atom’s volume, so an atom isn’t mostly “empty”.

The observable universe is 14 Billion LY in any direction. A typical galaxy is 100,000 LY across or 1/140,000 that size. If the universe was scaled to be 10m on a side, that would make the typical galaxy 1/140,000 x 10m or 71 microns, the size of 10 red blood cells.

It might be pretty bright, though.

Damn, that is one of the most ambiguous OPs I’ve ever read.

Not really. I wanted a best guestimate of how much area all the galaxies, stars, etc. would take up if the universe was scaled down to a 10m cube. Where is my OP ambiguous in that respect?

For one thing, there is a vast difference between “scaled down” and “compressed down”

Accepted, but the matter would still have had to be compressed in order to represent a proportion of the 10m cube. The ‘scaled down’ aspect only applies to my question of whether a galaxy would be visible within the cube. Assume it is in a fully lit laboratory.

Oh?
Then what happens to form a Neutron star?

As above, the ratio is dependent on the density of the matter in question. Even the vacuum of space is not bereft of particles.

The average density of the universe is very, very small. Despite all the matter we see around us, despite all the massive stars and expansive galaxies, the particle density of the universe is far, far smaller than the very best man made vacuum we can produce to this day. This site says it’s

A supernova compresses the electrons and protons together to form neutrons and neutrinos.

Don’t think of electrons as hard little spheres zipping around inside an atom. Here’s a nice picture of the wavefunctions of electron orbitals in an atom. (From this page, but it was taking a long time to load for me.)

I’m quite familiar with this.
However, the fact that an atom can be crushed under extreme gravity to a tiny fraction of it’s normal size implies that it is mostly “empty space.”

That is a nice picture, but to be fair, we don’t know if that’s anything close to what’s actually going on in there, only that the electrons behave as though it were. They could just as easily be teeny weeny sheep running around in there for all we know.

I’m still just a bit confused. What’s a “square cube”?

Area? Shouldn’t this be “volume”?

WMAP data:

That number includes contributions from atoms, cold dark matter, as well as dark energy, but if we ignore that and treat it all as atoms, your 10m sq cube (1000 cubic meters) would contain 5,900 hydrogen atoms. The rest would be empty space.
Those 5,900 atoms would mass 9.8 X 10[sup]-21[/sup] grams.