Is there a theoretical upper bound for density?

[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

 

[juanrga]

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?

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

 

[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:

There is an upper limit to the mass of a neutron-degenerate object, the Tolman-Oppenheimer-Volkoff limit, which is analogous to the Chandrasekhar limit for electron-degenerate objects. The precise limit is unknown, as it depends on the equations of state of nuclear matter, for which a highly accurate model is not yet available...Whether quark-degenerate matter forms at all in these situations depends on the equations of state of both neutron-degenerate matter and quark-degenerate matter, both of which are poorly known.
...

Singularity

At densities greater than those supported by any degeneracy, gravity overwhelms all other forces. To the best of our current understanding, the body collapses to form a black hole. In the frame of reference that is co-moving with the collapsing matter, all the matter ends up in an infinitely dense singularity at the center of the event horizon. In the frame of reference of an observer at infinity, the collapse asymptotically approaches the event horizon
QUOTE]

http://en.wikipedia.org/wiki/Neutron_degeneracy_pressure

Our science seems to begin the break down at just beyond neutron degeneracy...and generally quantum mechanics and general relativity fail to show exactly what is present at the big bang and at black hole singularities... equations diverge there, leading to apparent infinities, but I think most physicsts think that's a result of inadequate models rather than a reflection of actual infinities.

Anyway, if a bound is found, likely it will be at the big bang or black hole singularities.

 

[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.

 

[juanrga]

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?"

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

 

[Naty1]

pilpel, if you are interested here are a few pages explaining the forces opposing density
concentration, check this:

http://en.wikipedia.org/wiki/Degenerate_matter