Creating a Black Hole: Exploring the Heisenberg Uncertainty Principle

[woody3254]

If a neutron star is made solely of neutrons that show no repulsion to each other, protons and electrons have merged by overcoming electron degeneracy pressure so all the empty space taken up by electron shells is removed, how do u get anything denser to the level of being a black hole? If a neutron star is neutrons packed as closely together as can be, as they are fermions and obey the Pauli exclusion principle, to make a black hole do the neutrons merge to form some kind of boson?

From research I'm getting the impression that it's something to do with the Heisenburg Uncertainty Principle. Uncertainty in space X Uncertainty in momentum = Planks constant / 4pi. As things are made more dense the uncertainty in space decreases as you can work out where they are easier so this increases uncertainty in momentum. If things have more momentum they create more outward force so stop collapse to higher density. But surely if the mass were great enough to overcome this force the uncertainty in space would be even less and so give particles an even greater momentum.

So are black holes made up of bosons or am i not getting the point to the uncertainty principle or is there something else entirely?

 

[Wallace]

Good question, and in fact you're pushing beyond currently understood physics! The conundrum goes something like this; objects such as planets, stars etc are held together by the mutual gravitational attraction of the material that makes up the object. The attraction, if left unopposed, would cause all the material in say a planet or star to collapse to a point at the very centre of the object (ignoring some issues to do with conserving angular momentum).

Of course, the gravitational forces are not unopposed, as atoms resist being squashed together. This opposition to gravitational collapse we can call pressure. So in a stable object, such as the Sun or the Earth, the gravity and the pressure are in balance.

Now, as we change the density of a material we change the pressure that it exerts, so if you say blow up a balloon, you increase the density of gas inside therefore increasing the pressure. The relationship between pressure and density in known as the equation of state. Matter in different forms obeys different equations of state (a liquid or a gas for instance behaves differently if you try and squeeze it).

The hot plasma of the Sun has a particular equation of state that let's the pressure balance the gravitational force. However, the same amount of mass, when in the form of degenerate material (as in a Neutron star) has a different equation of state that allows the forces to balance at a much higher density. If you tried to condense a plasma to Neutron star density, the pressure would be enormous and it would expand once more to the previous size (although is practice of course, the compression converts the material to degenerate matter).

We run into a problem once we get to a certain point though. For sufficient mass in a sufficiently small volume (given by a sphere of the http://en.wikipedia.org/wiki/Schwarzschild_radius" radius) we would need an infinite pressure to counter-attack the gravitational force! Since this can't be done, the material collapses to a Black Hole. Formally then, the material does what I suggested originally in the case of unopposed gravitational collapse, it all condenses to a single point. In practice however, we don't really know what would happen, this situation goes beyond our full understanding of both our theory of gravity (General Relativity) and our theory of particle physics (the standard model and quantum mechanics).

To properly answer your question we would need a working quantum gravity theory, which is something we do not currently have, though many researchers are working furiously on it.

 

[mathman]

The basis of a black hole forming is having enough matter together in one place. For example a large enough neutron star could become a black hole. The problem you are raising is one of the open questions of modern physics. General relativity and quantum theory both have to apply in these extreme circumstances, but using them together leads to mathematically nonsensical results. No one really knows what is happening inside a black hole.

 

[LURCH]

I agree with you both, that current theories do not adequately describe the mechanism for the formation of a BH. However, it is those same theories that predict the phenomanon, so they must contain some explanation for how the Exclusion Principle is over-ridden, or Black Holes would never have been proposed in the first place. And whatever that explanation is, it is so compelling that much of the scientific community accepts their existence, even though they can't be observed. So I think the OP is trying to say something like, "the Pauli Exclusion Principle seems to forbid the formation of Black Holes, what other principles or laws make them possible, and even probable?"

 

[wysard]

Think Plutonuim bomb on a stellar scale.

The idea behind the bomb is not to move all of the mass to critical state, but by shockwave to incite a tiny percentage at the core to cross the threshold.

Same plan for a Black Hole. Imagine a binary star system with one star moving in an XY Plane and another in the XZ plane ( forget perturbations caused by mass for the moment ), now imagine that at some point their orbits cross so that the two stars meet at stellar speed. The shockwave is unbeleivable. The coronal masses are cast of in an explosion of the impact, but the cores made of heavier nuclear components, are compressed by gravitation and further by the massive shockwave of the impact. If at any point any part of the central mass of one or both stars pass Roche's limit the poor thing is immediately gobbled up as a black hole. Should both stars be of similar mass and composition and the collision be almost, but not quite, perfect one could wind up with TWO black holes co-rotating inside a combined Swartzchild radius.

Personally I have no idea where I could buy a can opener to peer into a black hole to find out how many "singularities" are monastic, and how many are monogamistic, but it is an interesting thought.

PS. Is it just me or does anyone else find it odd that a Black Hole (a moniker I believe coined by Piers Anthony, but I could be wrong) relates to Schwartzchild because in the rough english translation of Schwartzchild is Black Child??

 

[Chris Hillman]

Please try to keep your facts in order

Think Plutonuim bomb on a stellar scale.

The idea behind the bomb is not to move all of the mass to critical state, but by shockwave to incite a tiny percentage at the core to cross the threshold.

Same plan for a Black Hole...now imagine that at some point their orbits cross so that the two stars meet at stellar speed. The shockwave is unbeleivable. The coronal masses are cast of in an explosion of the impact, but the cores made of heavier nuclear components, are compressed by gravitation and further by the massive shockwave of the impact.

This doesn't sound like a good description at all to me, even assuming you are speaking of solar mass black holes. If you disagree, please provide a citation to the mainstream literature (prefably something like an arxiv eprint by a reputable author which I can easily obtain on-line).

Some mainstream arxiv eprints:
http://arxiv.org/abs/astro-ph/9912118
http://arxiv.org/abs/astro-ph/0102001
http://arxiv.org/abs/astro-ph/0306173
http://arxiv.org/abs/astro-ph/0307084
http://arxiv.org/abs/astro-ph?papernum=0410381
http://arxiv.org/abs/0706.3787v1

From this it is clear that complex scenarios are considered, and that the question of how supermassive black holes forms remains murky.

PS. Is it just me or does anyone else find it odd that a Black Hole (a moniker I believe coined by Piers Anthony, but I could be wrong)

You are. The term was coined by physicist John Archibald Wheeler.

relates to Schwartzchild because in the rough english translation of Schwartzchild is Black Child??

The name is Schwarzschild and the literal translation is "black shield" :grumpy:

Wysard, you may make yourself unpopular at PF if post stuff you made up in school even if you add "I could be wrong". Unlike many other webites, there are plenty of posters here who have a lot of scientifically accurate information to share. Hope you will receive kindly my remonstrance.

 

[pervect]

I agree with you both, that current theories do not adequately describe the mechanism for the formation of a BH. However, it is those same theories that predict the phenomanon, so they must contain some explanation for how the Exclusion Principle is over-ridden, or Black Holes would never have been proposed in the first place. And whatever that explanation is, it is so compelling that much of the scientific community accepts their existence, even though they can't be observed. So I think the OP is trying to say something like, "the Pauli Exclusion Principle seems to forbid the formation of Black Holes, what other principles or laws make them possible, and even probable?"

One way of describing what happens: Basically, the Pauli exclusion principle says that if you put a bunch of fermions in a very small box, they can't share the same state, and hence you wind up with some very high energy particles. So it requires a lot of energy to put a lot of fermions in a small box. (Not so with bosons, which can form a Bose-Einstein condensate, but I digress).

But there is nothing that forbids you from doing this, it is not impossible, it just requires a lot of energy.

So it requires energy to satisfy the Pauli exclusion principle, but on the other hand the denser object with the same number of particles in a smaller box has less total gravitational energy because of the gravitational interaction (gravitational binding energy).

So, in seeking the lower energy state, it's just a matter of which is more important - the gravitational energy, or the energy required to satisfy the Pauli exclusion principle.

You can look at it this way in terms of total energy, or you can look at the force. The total energy picture may be simpler, but if you like forces, you can think of the Pauli exclusion principle as causing a force which is related to the rate of change of energy with respect to the size of the box.

In the cases which turn into black holes, the gravitational binding energy is more important, (or the gravitational force is stronger than the Pauli force), and the lowest energy state of the system is a black hole as far as known physics goes.

There's probably some new physics that happens when things get dense enough, but we don't know exactly what it is yet, as the densities and energies involved are beyond the range where we can duplicate them in the lab.