Atoms, Black Holes and Singularities: A Historian's Questions

[Undomiel]

I have a question ... if atoms cannot be compacted, beyond a certain minute level, how could they exist inside a black hole, and particularly at the 'singularity' point? Does the fact, that atoms cannot be compressed beyond a certain point, suggest falsification of the hypothetical singularity at the centre of a black hole?

I think you can tell by this question, which I hope is not a silly one, that I'm not a physicist, but rather a historian of science, as well as a fan of popular science ... I'm really interested in your answers ...

 

[Chronos]

Atoms can be gravitationally collapsed to the point they become subatomic particles With enough gravity, subatomic particles can themselves be crushed. The technical term is condensed matter. The pauli exclusion principle dictates the force needed to do this. The hypothetical singularity in a black hole is generally considered the point where the math breaks down, not physical reality [i.e., not infinitely dense] The grotesquely squished matter remaining is definitely not composed of atoms or particles as we know them.

 

[Gonzolo]

Note : In general physics, the term "condensed matter" refers to the regular solid state and liquids as we know them. Do not confuse this with Chronos' astrophysical use of the term.

 

[Ian]

Undomiel,
The simplest atom (hydrogen) consists of a singular proton and electron. The proton has a mass of ~x10 -27 kg and a diameter of ~x10 -15 metres. These dimensions give the proton a density not far off the density of the sun if the sun were to be compressed into a black hole.
This suggests that protons are veritable 'black holes' even if their mass is minute. They are as chronos said - 'condensed matter', but not quite as he/she sees it.
But, if the hypothetical singularity that is a black hole is generally considered the point where the math breaks down, not physical reality [i.e., not infinitely dense], then the grotesquely squished matter remaining must definitely be composed of atoms or particles as we know them because they have a comparable density.
I personally find this to be a very contrary state of physical affairs. If the math breaks down at the singularity density, and in consequence physicists are unable to express or understand what happens at that singular point, how can they say they understand what happens in interactions between nuclear particles which have a comparable density?

 

[Undomiel]

Thanks for your replies, Chronos, Gonzolo, and Ian ...

Chronos and Gonzolo, I shall look up "pauli exclusion principle". Is this the same "exclusion principle" that I was reading about, which says that two electrons cannot occupy the one space ... and that this exclusion principle breaks down at the event horizon because of the massive gravity ... can anyone here explain more about the exclusion principle, and this hypothesis? (I've no doubt that you can if you'll be good enough to!)

Also, does it make sense to you, in Hawking's "Brief History Of Time", when he explains that, at a quantum level, mathematics, as humans perceive reality, becomes false ... and the use of mathematics with so-called "imaginary" numbers becomes the reality? What do you think of this hypothesis? This is what you're talking about, Chronos?

Ian, I don't quite understand your comparison of a black hole and interactions between nuclear particles ... isn't a singularity infinitely more compacted than any particles in our universe? What makes you say that physical reality (as humans are evolved to perceive it) does not break down at the (hypothetical) singularity? I'd suggest that it would indeed ... maybe beyond human understanding ... I'd suggest that you really cannot compare a singularity, and the behaviour of matter at this singularity, with interactions between nuclear particles in OUR reality ... it's completely different, different forces, different physical laws, different reality. This is just a humanities (history & philosophy of science) student's reckoning, anyway ;)

Also, can you seriously compare the proton and electron inside an atom, when the atom exists in our physical reality, with the same proton and electron in a compressed state? Because surely the working of the atom in our reality is highly dependent upon the SPACE within the atom? And the four forces? So even though the actual mass of an atom is not great, it's a VERY different particle than what it would be in a place where different physical laws acted upon it, such as at a singularity? So maybe comparing an atom under our physical reality, and an atom inside a hypothetical singularity, is folly anyway ... we need to understand that completely different physical laws are at work, in fact a different reality?

"The universe is not only stranger than we know, it is stranger than we can know." - ?

 

[Ian]

Undomiel,
You said,

I don't quite understand your comparison of a black hole and interactions between nuclear particles ... isn't a singularity infinitely more compacted than any particles in our universe?

Try this short exercise;
1/. calculate the density of the sun if it were to be compressed to a singularity with a radius of 2GM/C*2.
2/. calculate the density of a proton (radius is ~ x10-15 metres)
3/. compare the two values and see if a black hole (singularity) has a very much greater density than a proton.

Ask yourself also, what is the difference between the physical space between the Earth and the sun, and the physical space between a proton and electron in a hydrogen atom. If you can find any other difference than one of scale please tell me.

 

[vincentchan]

1/. calculate the density of the sun if it were to be compressed to a singularity with a radius of 2GM/C*2.

the density @ the singularity is infinite
but the mass/volume within event horizon is finite
just want to let you know, singularity has no radius (or zero radius if you like)

 

[Undomiel]

Thanks for your replies, again ... everyone has given me plenty of names and theories for further research into my areas of interest ... so thank you

Ian, I could be wrong, but I feel there IS a difference (though as Carl Sagan said, it's best to avoid thinking with one's gut-feelings!) ... but I believe the difference is that, one overrides the Pauli exclusion principle, and the other doesn't ...

just want to let you know, singularity has no radius (or zero radius if you like)

And so:

the density @ the singularity is infinite
but the mass/volume within event horizon is finite

Very interesting, Vincent ...

On the other hand, this might interest you, Ian, too ... is it correct, someone told me ... that we don't need a black hole to overcome the exclusion principle ... that in fact supernovas overcome that exclusion principle, that within a supernova two electrons CAN occupy the one space ... is that right? That this exclusion principle breaks down in a supernova, not just in a black hole's event horizon ...

 

[freemind]

Perhaps atoms are disintegrated into pure strings/branes!

 

[WORLD-HEN]

If the singularity is infinitely dense, then the gravitational force of attraction at the singularity must be infinite right? This means that the force of attraction between the quarks is over come(since infinite force is what is neaded to break the force). That means that quarks can exist independently inside the singulatity!

 

[Integral]

If the singularity is infinitely dense, then the gravitational force of attraction at the singularity must be infinite right? This means that the force of attraction between the quarks is over come(since infinite force is what is neaded to break the force). That means that quarks can exist independently inside the singulatity!

No, infinity density does not imply infinite mass. Gravitational force is proportional to mass, not density. So the gravitational force due to a black hole is finite.

We have no information about the state of matter within a singularity. A singularity means that our mathematical models cannot be extended into that region. Therefor, not only can we not observe what is within the singularity, we cannot even make any predictions. Any speculation about what goes on inside the singularity is pure speculation.

We can, to a certain degree, predict what may be going on between the event horizon and the singularity, but not within the singularity itself. A simple reason for that is that if the mass is finite, an infinite density implies a zero volume. How can we even consider discussing "inside" something with zero volume?

 

[tozhan]

This isn't really my area but i once read sumthing along the lines of... when a star shrinks to a singularity its gravitational pull is such that is warps space-time into a loop. To me this means that it can have mass but no volume. Also it should have infinite density directly because it has no volume. it is in effect a point in space.
Maybe the black hole has volume in another dimension or something but it seems that if space-time is looped in our 3 dimensions, the others should also be looped. We certainly have to abandon the idea of particles when talking about singularities but we can talk about particles between the event horizon and singularity. Matter will be compressed by the gravitation but will remain matter as we know it until the electroweak force is over come. Then the pauli exclusion principle must be overcome. If the gravitational pull is strong enough then this will form a singularity and if not then a neutron star will be formed with a density in excess of 100 million kg per meter (this is a rough guess, just to emphasis density). I should point out that the event horizon is the place where the gravitation is so strong that light cannot escape being pulled back, the size it is an indication of the gravitational strength.

this was typed quick so please correct any errors, as i say i don't do black holes much ;-)