# Is there a theoretical upper bound for density?

1. Feb 17, 2012

### pilpel

Is there a theoretical upper bound for the density of matter? Given a proton (already almost as dense as a black hole, according to Wikipedia), can you theoretically compress it into any non-zero volume? Has any work been done that shows that matter can or cannot achieve certain levels of density?

Thank you,
pilpel

2. Feb 18, 2012

### juanrga

No. Compression requires energy and so far as we know energy of Universe is finite.

3. Feb 18, 2012

### Naty1

short answer: nobody really knows, but maybe density can even be compressed to zero volume!

We know about electron degeneracy and neutron degeneracy and can compute how much gravity is required to achieve them..... In the latter, things are so dense that protons and electrons are crushed together forming neutrons....

Wikipedia says:

Last edited: Feb 18, 2012
4. Feb 18, 2012

### pilpel

juanrga,

Good point, but the amount of energy in the universe is a practical consideration, not a theoretical one. My question may be restated as "given an arbitrarily large amount of energy, does density have an upper bound?"

Naty1,

I must admit that I could never understand the notion of infinite density. Even at the conceptual or theoretical level it makes no sense to me. Since density is mass divided by volume, it must be finite. If the denominator is zero, then the fraction is simply undefined, not infinite. And that doesn't even take into the consideration the non-intuitive if not absurd notion of zero volume that contains non-zero mass.

5. Feb 19, 2012

### juanrga

There is nothing more practical than a good theory. If the amount of energy is arbitrarily large but finite, the response is the same than before: no.

If the amount is infinite, then you get into trouble because theories break down when starting to consider infinities and you cannot answer the question if your theory does not work.

As you know division by zero is not defined in math; therefore, how do you wait a physical theory to deal with such stuff as ρ=N/0

6. Feb 21, 2012