[jeffreyH]

How would the Fermi energy change when a neutron star collapses into a black hole? I don't know if anyone can even answer that. Does the Pauli exclusion principle even apply?

[PmbPhy]

How would the Fermi energy change when a neutron star collapses into a black hole?

You've got me. It's been eons since I touched that part of quantum mechanics.

I don't know if anyone can even answer that. Does the Pauli exclusion principle even apply?

Of course. Didn't you read the link I posted? That's the origin of degeneracy pressure. When two fermions attempt to go into the same state there is a resistance to do this due to the Pauli exclusion principle. The inability of two fermions to be in the same state (become degenerate) manifests itself as a force, i.e. pressure. Hence the name degeneracy pressure. There is no classical analogy to this. This is one of the reasons we say that quantum mechanics is so "weird."

[lightarrow]

wait a moment. How could an atom as iron be compressed 10,000 times? Schrödinger equation must be thrown in garbage?
In common iron atoms are already packed almost without any space between them. You, more correctly, talk of a crystal of iron nuclei but the phrase you have quoted from wiki doesn't say it.
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In a neutron star the atoms are compressed to the point where the nuclei come into contact with each other.

Pete, that phrase evan_au has quoted from wikipedia, talks of iron "atoms", not nuclei:
http://en.wikipedia.org/wiki/Neutron_star
<<The surface of a neutron star is made of iron. In the presence of a strong magnetic field the atoms of iron polymerize. The polymers pack to form a lattice with density about ten thousand times that of terrestrial iron and strength a million times that of steel.>>

It doesn't talk of "iron nuclei".

How can such "compressed" atoms exist? Or I have understood badly?

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[PmbPhy]

Pete, that phrase evan_au has quoted from wikipedia, talks of iron "atoms", not nuclei:
http://en.wikipedia.org/wiki/Neutron_star
...

It doesn't talk of "iron nuclei".

I know. It was I who was talking about nuclei.

How can such "compressed" atoms exist? Or I have understood badly?

Why can't they exist? The gravitational force is so large that it forces electrons to combine with electrons to form neutrons. Recall what the website you posted a link to says, i.e.

With increasing depth, the density rises. When its density reaches 400 billion times that of water, the nuclei can get no larger and neutrons start ‘dripping’ out. As the density increases further, the nuclei dissolve in a sea of neutrons.

That's why the density of the neutron star increases until it has the value of the nucleus of a typical atom. I've seen modern physics textbooks use a simple model of a neutron star for exercise problems as if they're composed entirely of neutrons. Thus a good analogy is to think of them as one giant nucleus of an atom. Recall again the Wiki article:

A neutron star has some of the properties of an atomic nucleus, including density (within an order of magnitude) and being composed of nucleons. In popular scientific writing, neutron stars are therefore sometimes described as giant nuclei. However, in other respects, neutron stars and atomic nuclei are quite different. In particular, a nucleus is held together by the strong interaction, whereas a neutron star is held together by gravity, and thus the density and structure of neutron stars is more variable.

I just took a look around my home for that text and found it. It’s Modern Physics – Fourth Edition by Paul A. Tipler and Ralph A. Llewellyn, W.H. Freeman and Company, 2003. Chapter 11 is on nuclear physics. On page 514 they give an example which reads as follows

EXAMPLE 11-3 Radius of a Neutron Star   In certain supernova events, the envelope of the star is blown away, leaving a core consisting entirely of neutrons. This stellar remnant is called a neutron star and its density is approximately the same as that of atomic nuclei.

When I posted my first response in this thread I wrote These suggest that percentage wise the neutron star is composed almost entirely of neutrons. I said this because I was unsure I could back up what I really believe to be true about them. My knowledge of neutron stars has come from osmosis, i.e. from reading about them during studying other things. I believe that you can think of a neutron star as one enormously huge nucleus. However just now I looked through my books and found this explicitly stated in an astrophysics text. From Astrophysics in a Nutshell by Dan Maoz. Princeton University Press, (2007), page 84:

In fact, one can consider a neutron star to be one huge nucleus of atomic number A ~ 10⁵⁷.

If you’d like to read more on this point then you can download the text from:
http://bookzz.org/book/1272622/0dada4
I’m very happy with that statement. It’s also quite close to all the other information I dug up on this very same subject/point.

[jeffreyH]

How would the Fermi energy change when a neutron star collapses into a black hole?

You've got me. It's been eons since I touched that part of quantum mechanics.

I don't know if anyone can even answer that. Does the Pauli exclusion principle even apply?

Of course. Didn't you read the link I posted? That's the origin of degeneracy pressure. When two fermions attempt to go into the same state there is a resistance to do this due to the Pauli exclusion principle. The inability of two fermions to be in the same state (become degenerate) manifests itself as a force, i.e. pressure. Hence the name degeneracy pressure. There is no classical analogy to this. This is one of the reasons we say that quantum mechanics is so "weird."

What I was getting at was that all the particles are ordered into the lowest energy states and obey the Pauli exclusion principle. To compress further and obey the principle particles MUST combine into larger composite particles to continue to obey the principle as you can't get 1/2 or 1/4 an energy state due to quantization. As particles fall to lower energy states combination into larger composites is the only way left to go. This means that eventually these super particles must reach the Planck mass limit but each one in a different low energy level. Once this happens at the centre then collapse to a singularity is inevitable. This will happen at the centre of the mass and work outwards as stated. It must happen this way for the Pauli exclusion principle to hold.

[jeffreyH]

This would also maintain quark confinement so there would be no quark/gluon plasma and internal exposure of color charge. I am not convinced that quarks can ever be liberated from particle confinement.

[PmbPhy]

What I was getting at was that all the particles are ordered into the lowest energy states and obey the Pauli exclusion principle.

Why are you saying this? Pauli's Exclusion Principle only holds for fermions. It doesn't hold for Bosons. See:
http://en.wikipedia.org/wiki/Pauli_exclusion_principle

The Pauli exclusion principle is the quantum mechanical principle that says that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously.

Also there is nothing to suggest that all fermions have to be in the lowest energy state. Where did you get that idea from?

To compress further and obey the principle particles MUST combine into larger composite particles..

Why "MUST"? I've never heard of that and see no reason for it at the moment.

... to continue to obey the principle as you can't get 1/2 or 1/4 an energy state due to quantization.

Why not?

As particles fall to lower energy states combination into larger composites is the only way left to go.

Why?

This means that eventually these super particles must reach the Planck mass limit..

Why?

... but each one in a different low energy level. Once this happens at the centre then collapse to a singularity is inevitable.

What? Now you're claiming that neutron stars don't exist because they must turn into black holes?

This will happen at the centre of the mass and work outwards as stated. It must happen this way for the Pauli exclusion principle to hold.

You sure seem to have a very wrong understanding of the exclusion principle. Where did you learn it?

[lightarrow]

How can such "compressed" atoms exist? Or I have understood badly?

Why can't they exist? The gravitational force is so large that it forces electrons to combine with electrons to form neutrons. Recall what the website you posted a link to says, i.e.

You intended electrons to combine with protons, of course.
But what I'm saying is that those are not atoms any longer.
What you need to have an Iron atom is:

1. a charge of +26e in a little space at centre
2. 26 electrons to put around it

You put those parameters in the Schrodinger equation and you have the solutions which "generate" an iron atom. Where is gravitational force here?

In case, only an external electromagnetic field can affect the solutions.

Here it says that at 10⁴ g/cm³ the "atoms" are completelly ionized:

http://relativity.livingreviews.org/Articles/lrr-2008-10/fulltext.html

so I wouldn't call them exactly "atoms".

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[PmbPhy]

You intended electrons to combine with protons, of course.

Yes. That's correct. Thanks.

But what I'm saying is that those are not atoms any longer.

I know. They're protons, just as I said.

What you need to have an Iron atom is:

What do I care about iron? It was you who started all this stuff about iron, not I. Understand?

[jeffreyH]

What I was getting at was that all the particles are ordered into the lowest energy states and obey the Pauli exclusion principle.

Why are you saying this? Pauli's Exclusion Principle only holds for fermions. It doesn't hold for Bosons. See:
http://en.wikipedia.org/wiki/Pauli_exclusion_principle

The Pauli exclusion principle is the quantum mechanical principle that says that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously.

Also there is nothing to suggest that all fermions have to be in the lowest energy state. Where did you get that idea from?

To compress further and obey the principle particles MUST combine into larger composite particles..

Why "MUST"? I've never heard of that and see no reason for it at the moment.

... to continue to obey the principle as you can't get 1/2 or 1/4 an energy state due to quantization.

Why not?

As particles fall to lower energy states combination into larger composites is the only way left to go.

Why?

This means that eventually these super particles must reach the Planck mass limit..

Why?

... but each one in a different low energy level. Once this happens at the centre then collapse to a singularity is inevitable.

What? Now you're claiming that neutron stars don't exist because they must turn into black holes?

This will happen at the centre of the mass and work outwards as stated. It must happen this way for the Pauli exclusion principle to hold.

You sure seem to have a very wrong understanding of the exclusion principle. Where did you learn it?

I'm not talking about bosons. It's baryons such as the proton and neutron and fermions such as the electron. The baryons themselves are fermions and follow the Pauli exclusion principle.

With increasing density in a gravity well we get:

http://www.st-andrews.ac.uk/physics/quvis/embed_item_3.php?anim_id=48&file_sys=index_phys

Baryons are already composite particles and under extreme compression and stress may well form larger composites. Also I am not claiming neutron stars automatically form black holes.

http://en.wikipedia.org/wiki/Energy_level
"A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels. The term is commonly used for the energy levels of electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized."

http://en.wikipedia.org/wiki/Pauli_exclusion_principle
'In the early 20th century it became evident that atoms and molecules with even numbers of electrons are more chemically stable than those with odd numbers of electrons. In the famous 1916 article "The Atom and the Molecule" by Gilbert N. Lewis, for example, the third of his six postulates of chemical behavior states that the atom tends to hold an even number of electrons in the shell and especially to hold eight electrons which are normally arranged symmetrically at the eight corners of a cube (see: cubical atom). In 1919 chemist Irving Langmuir suggested that the periodic table could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of electron shells around the nucleus.[1] In 1922, Niels Bohr updated his model of the atom by assuming that certain numbers of electrons (for example 2, 8 and 18) corresponded to stable "closed shells".

Pauli looked for an explanation for these numbers, which were at first only empirical. At the same time he was trying to explain experimental results of the Zeeman effect in atomic spectroscopy and in ferromagnetism. He found an essential clue in a 1924 paper by Edmund C. Stoner which pointed out that for a given value of the principal quantum number (n), the number of energy levels of a single electron in the alkali metal spectra in an external magnetic field, where all degenerate energy levels are separated, is equal to the number of electrons in the closed shell of the noble gases for the same value of n. This led Pauli to realize that the complicated numbers of electrons in closed shells can be reduced to the simple rule of one electron per state, if the electron states are defined using four quantum numbers. For this purpose he introduced a new two-valued quantum number, identified by Samuel Goudsmit and George Uhlenbeck as electron spin.'

[PmbPhy]

I'm not talking about bosons.

Hold on Jeff. I wrote that in response to your comment What I was getting at was that all the particles are ordered into the lowest energy states and obey the Pauli exclusion principle. because it's not true that "all" particles are ordered into the lowest energy state and obey the exclusion principle. What did you mean when you said "all"? "all" what?

It's baryons such as the proton and neutron and fermions such as the electron. The baryons themselves are fermions and follow the Pauli exclusion principle.

Yes Jeff. I'm aware of that.

I don't see the point of the rest of that post.

[lightarrow]

What you need to have an Iron atom is:

What do I care about iron? It was you who started all this stuff about iron, not I. Understand?

Answering evan_au I wrote:
"wait a moment. How could an atom as iron be compressed 10,000 times? Schrödinger equation must be thrown in garbage?
In common iron atoms are already packed almost without any space between them. You, more correctly, talk of a crystal of iron nuclei but the phrase you have quoted from wiki doesn't say it."

Then yuou replied:

"In a neutron star the atoms are compressed to the point where the nuclei come into contact with each other."

So if you hadn't understood my question, you could simply avoid answering me, isnt'it?

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[barneyboy (OP)]

wow, Sheldons fired up!!  [)]

[PmbPhy]

Then yuou replied:

"In a neutron star the atoms are compressed to the point where the nuclei come into contact with each other."

I know that's what I said. I was explaining that all atoms, whether they're iron or now, are compressed to the point where the nuclei come into contact with each other. It had nothing to do with iron other than iron being an atom.

Please. Let's drop this!