I How Small Can a Mass Be Squeezed?

[thetexan]

They just found evidence of a super massive black hole that probably weighs in at 664 million solar masses! Wow! Which got me to thinking about how small a mass can be squeezed.

There are two ways to go about this. One, how small would the Earth become if it were squeezed to the absolute smallest possible radius. In other words, packing all of the subatomic particles with no space between them?

The other way is this...if I have a sphere of nuclear material squeezed to the point that it can't be squeezed any more and it is one inch in diameter, and I "rehydrated" it to it's normal size how big of a sphere would I have? If it matters, let's say the material is iron.

tex

 

[mfb]

Particles do not have a volume they occupy, "no space between particles" is not a meaningful concept.

A black hole is the smallest possible "object" for a given mass. The Schwarzschild radius, which determines the point of no return for infalling objects, is proportional to the mass, while the "volume" (this is not that well-defined in curved spacetime of general relativity) grows with the radius cubed, so smaller black holes have a larger "density" (note the " "). It is not really a density of matter any more.

 

[thetexan]

I thought they did. In fact I read in many places that an atom is largely space, certainly between the electrons and nucleus.

I may be wrong but this is what I understand about black holes. The black disk we see illustrated is really the event horizon for the actual condensed mass object in the center. So, if I'm correct, there is a tiny condensed ball of mass in the center surrounded by the event horizon which we visualize as the black disk. It is the object in the center that is actually eating up other mass making the central object bigger and bigger. Sorta like making a rubber band ball. The more the object eats the bigger it gets but never really astronomically large. Maybe the size of a small city or the like.

That's what I'm driving at. There are plenty of scientific tv shows and magazine articles that opine at the size of the neutron ball so I am just curious at where and how they compute that guess.

tex

 

[mfb]

In fact I read in many places that an atom is largely space, certainly between the electrons and nucleus.

Space is not an object, an atom cannot be made out of space. Elementary particles are - to our best knowledge - pointlike. You can still ask where they are, and then you see that there is a small nucleus (all the particles in the nucleus is within some small volume) and the electrons are in the huge volume around it.

I may be wrong but this is what I understand about black holes. The black disk we see illustrated is really the event horizon for the actual condensed mass object in the center. So, if I'm correct, there is a tiny condensed ball of mass in the center surrounded by the event horizon which we visualize as the black disk.

In general relativity, this "tiny ball of matter" is a single point. In a quantum theory of gravity, we don't know, because we do not have such a theory. But there is nothing that gets bigger if you add more mass.

Neutron stars have a well-defined size, a radius of a few kilometers with a mass of up to ~2 solar masses. Their density is about the same as the density of a nucleus on Earth.

 

[glappkaeft]

Neutron stars have a well-defined size, a radius of a few kilometers with a mass of up to ~2 solar masses. Their density is about the same as the density of a nucleus on Earth.

You must have meant to say something else here I assume?

 

[mfb]

No?
The density of atomic nuclei (everywhere, including on Earth) is about 15 orders of magnitude above the density of normal solid matter on Earth.

 

[Chronos]

Add the word 'atomic' in front of nucleus and see if that helps

 

[thetexan]

Doesn't mass have volume? Even the smallest? Shouldn't the singularity, albeit tiny, have some volume once it is squeezed? Even if it's in the microns how can mass be completely squeezed into nothingness (singularity). Wouldn't that imply that even the most fundamental particles aren't fundamental since they can be broken down and rearranged into smaller and smaller packing (but, I would think, only up to a limit)?

tex

 

[mfb]

Doesn't mass have volume?

Not in the way that it would occupy some space where nothing else can be. Particles are not pool balls.

Shouldn't the singularity, albeit tiny, have some volume once it is squeezed?

If it would have, it would not be a singularity, but we don't really know if it is one.

Wouldn't that imply that even the most fundamental particles aren't fundamental since they can be broken down and rearranged into smaller and smaller packing (but, I would think, only up to a limit)?

No, it implies you cannot use an intuition gained from macroscopic objects. It just does not work.

 

[thetexan]

ok.

In simple terms what are you using to defend the idea that a mass can be squeezed into a point singularity with no volume. I'm not arguing but why can't intuition serve here? How do we KNOW? or is this particle THEORY? If mass can be squeezed into nothingness then how can that same mass be used to construct other things?

In other words, (please point me toward so good learning sources on this) where does it go?

tex

 

[sophiecentaur]

why can't intuition serve here?

How on Earth would you expect it to? Our 'intuition' is based on experience (often second hand) but you need an awful lot of that to build up any valid intuition about a new topic. Intuition is responsible for many people getting some of the most well accepted things wrong so you just can;t rely on it for this sort of thing. Apart from 'not turning into green cheese' there's not much you can rule out about such extreme situations.

 

[mfb]

How do we KNOW?

All the predictions about particle physics only work with the assumption that particles do not "occupy" a space. Thousands of successful predictions of such a theory are not a coincidence. There is no theory where particles would occupy space that gets any predictions right.

If mass can be squeezed into nothingness then how can that same mass be used to construct other things?

The wave function of particles has a finite size, without "needing that space", and you can calculate the energy it needs to push atoms closer together, which means macroscopic objects can have a stable size, given by quantum mechanical interactions. It is impossible to get a proper description of solids or liquids without quantum mechanics.

 

[QuantumQuest]

Although mfb has covered the whole thing, just two comments if they can be of some help:

In simple terms what are you using to defend the idea that a mass can be squeezed into a point singularity with no volume

"Singularity" is a mathematical concept, not a physical object. Don't try to visualize it in the common sense.

If mass can be squeezed into nothingness then how can that same mass be used to construct other things?

"Nothingness" is not the right term to use here. You essentially rule out Quantum Mechanics. Wave functions are neither nothingness nor a physical macroscopic object.