[lyner]

But what about the fact that ordinary condensed matter behaves that way too? (i.e. a band structure)
You seem to be implying something special about neutrons in neutron stars when it's just a matter of degree.

[DoctorBeaver (OP)]

But it doesn't because in ordinary condensed matter there are electron energy levels to take into account. Neutrons in a neutron star don't have them.

Think of it this way. Take 20 marbles and put them in a large box. Shake the box and the marbles can move. However, if you pack them into a smaller box, their movement is restricted. Put them in a box just big enough to take them and they can't move at all. That's the situation I was asking about; can the density in a neutron star be great enough to press the neutrons so hard together that they can't move?

[lyner]

'Neutrons as marbles' is too naive, as a model, I think.
With a box, 'jam packed' with marbles, you can go one step further and squash the marbles out of shape and they will take up even less room.
With a solid, you can compress it with enough energy (albeit, a lot) and the energy would involve electron energy states. But they're not really 'electron states' - the states describe to the whole atomic system.
With enough Energy, why can you not expect to distort the neutrons also?  After all, a neutron is a proton plus an electron (or you can go deeper if you want),  and the energy state involves some different mechanics.

[DoctorBeaver (OP)]

That's exactly what I'm getting at, though. You can compress & compress until you get to the quarks. You can't compress quarks as they're fundamental.

You see, this is 1 of the things I don't get about Heisenberg's principle. If you could stop the neutrons moving by squeezing them tightly enough together the quarks would still have as much freedom of movement as ever. But you could know both the positions (stationary) and momenta (zero) of the neutrons. So where does HUC stop? At fundamental particles or with composite particles?

I only used the marbles as a very simplistic analogy.

[JP]

How do you propose to measure the position or velocity of a neutron, considering its made up of quarks?  You'd probably have to somehow measure some property of the quarks.  Therefore, if all the quarks obey the uncertainty principle, shouldn't the neutron position necessarily obey the uncertainty principle?

[lightarrow]

That's exactly what I'm getting at, though. You can compress & compress until you get to the quarks. You can't compress quarks as they're fundamental.

You see, this is 1 of the things I don't get about Heisenberg's principle. If you could stop the neutrons moving by squeezing them tightly enough together the quarks would still have as much freedom of movement as ever. But you could know both the positions (stationary) and momenta (zero) of the neutrons. So where does HUC stop? At fundamental particles or with composite particles?

I only used the marbles as a very simplistic analogy.

There are two things I don't understand:
1. why you don't ask about a simple atomic nucleus? There's no much difference between nuclear matter and neutron star matter.
2. why do you think that neutrons cannot move in a neutron star?

[DoctorBeaver (OP)]

How do you propose to measure the position or velocity of a neutron, considering its made up of quarks?  You'd probably have to somehow measure some property of the quarks.  Therefore, if all the quarks obey the uncertainty principle, shouldn't the neutron position necessarily obey the uncertainty principle?

I think that depends on how neutrons are thought of. Are they considered entities in their own right, albeit composite entities? Is the quantum wave function of a neutron a function of the combination of the wave functions of the quarks? Or is its wave function independent of the quarks? I don't know enough about QM to answer that. However, I believe that the uncertainty principle only applies if the object is smaller than its wave function; am I correct in that belief?

[DoctorBeaver (OP)]

There are two things I don't understand:
1. why you don't ask about a simple atomic nucleus? There's no much difference between nuclear matter and neutron star matter.
2. why do you think that neutrons cannot move in a neutron star?

1. A simple atomic nucleus has electron orbits. A neutron in a neutron star doesn't.
2. I don't think that because I don't know. That's why I'm asking this question.

[lightarrow]

1. A simple atomic nucleus has electron orbits. A neutron in a neutron star doesn't.

Ok, it has electrons around; so? Protons and neutrons in an atomic nucleus are not more free than neutrons in a neutron star.

2. I don't think that because I don't know. That's why I'm asking this question.

Sincerely I don't know too []. However there's an old model of the nucleus called "liquid drop model". Just the name makes me think that a nucleus couldn't be thought of as a "clump of marbles", and the same (following this logic) for a neutron star.

[DoctorBeaver (OP)]

Ok, it has electrons around; so? Protons and neutrons in an atomic nucleus are not more free than neutrons in a neutron star.

That may or may not be. In an atomic nucleus there is not 3×10¹² times Earth's gravity pressing them together. And that's just the surface gravity. I don't know what it is near the centre of a neutron star. That's what my question is about - what is the effect on the neutrons of that amount of gravity. Does it squeeze them together in such a way that their position & momentum could be known simultaneously? I don't see that talking about hydrogen atoms or neutrons in an atom addresses that question.

[JP]

How do you propose to measure the position or velocity of a neutron, considering its made up of quarks?  You'd probably have to somehow measure some property of the quarks.  Therefore, if all the quarks obey the uncertainty principle, shouldn't the neutron position necessarily obey the uncertainty principle?

I think that depends on how neutrons are thought of. Are they considered entities in their own right, albeit composite entities? Is the quantum wave function of a neutron a function of the combination of the wave functions of the quarks? Or is its wave function independent of the quarks? I don't know enough about QM to answer that. However, I believe that the uncertainty principle only applies if the object is smaller than its wave function; am I correct in that belief?

The uncertainty principle appears because of the way in which measurements effect a quantum system.  Its actually quite a natural phenomenon in dealing with waves, so it arises naturally if you think of particles as represented by waves.  If you want to go for the most fundamental widely-accepted theory, you'd treat the neutron as a composite of quarks interacting via the strong force.  Then you'd have to figure out what your measurement does to the quarks.  Then you'd have to define the "position" of a neutron in terms of the quark measurements.  However, fundamentally each quark should obey an uncertainty relation, and this uncertainty relation should carry over to the neutron.

If you're willing to go with the most basic model of QM, which is "good-enough" in a lot of cases, you can treat the neutron as a single particle, and because any single particle has to obey an uncertainty relation, it should as well.

For your final question about the uncertainty relation only applying when the wave function is smaller than the particle--I'm not sure I've ever heard of an object being bigger than its wave function.  Fundamental particles are thought of as point-like, so they're smaller than any wave function.  The "size" of a more complicated object is tricky, since most of it is empty space, with forces holding these point-like particles apart.  

[DoctorBeaver (OP)]

JP - I understand what you're saying, but particles also behave like particles. I take your point about the uncertainty associated with the constituent quarks being carried over to the neutron as well. In which case, what about quarks in a quark star (theoretical, I know)? I can't help getting the feeling that there must come a point where everything is squeezed together so tightly that nothing can move about at all.

[lyner]

particles also behave like particles.

But you can't predict what they're going to do without doing some wave calculations.

What is so attractive about the notion of everything being squashed to tight that it can't move?
It's like wanting to get to absolute zero temperature and traveling at the speed of light. The energy involved in getting things closer
and closer together just increases without limit.

[DoctorBeaver (OP)]

It's not that I find the idea attractive. It's just something I was wondering.

The energy involved in getting things closer and closer together just increases without limit.

Ah, at last an answer. So squeezing things together that closely is impossible because of energy constraints. That makes sense. Thank you.

[lyner]

The Noddy answers are always the best.
I'm just waiting for lightarrow to point out something wrong with such a simple answer.

[DoctorBeaver (OP)]

I am a Noddy when it comes to this sort of stuff.

[LeeE]

Ok, it has electrons around; so? Protons and neutrons in an atomic nucleus are not more free than neutrons in a neutron star.

That may or may not be. In an atomic nucleus there is not 3×10¹² times Earth's gravity pressing them together. And that's just the surface gravity. I don't know what it is near the centre of a neutron star. That's what my question is about - what is the effect on the neutrons of that amount of gravity. Does it squeeze them together in such a way that their position & momentum could be known simultaneously? I don't see that talking about hydrogen atoms or neutrons in an atom addresses that question.

Are you not mistaking pressure for gravity here?  The gravity will be strongest at the surface and will be zero at the center of the neutron star.

The estimated max density of a neutron star (at it's center) is only up to around three times the density of an atomic nucleus and, when you remember that the neutron has a slightly higher mass than the proton anyway, neutron stars are still in the same league of density as atomic nuclei.  Sure, two or three times isn't insignificant but it's not really an order of magnitude of difference, so I wouldn't expect radically different behaviour.

[DoctorBeaver (OP)]

LeeE - My mistake about the gravity. Yes, I was referring to density & pressure.

Is it really on 3 times greater than an atomic nucleus? I'm sure I read it was many orders of magnitude greater. Maybe I got that confused too.

[LeeE]

I wasn't sure before, but that's the figure given by the wiki article...

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

which states:

"Neutron stars have overall densities predicted by EOS APR of 3.7 × 10¹⁷ (2.6 × 10¹⁴ times Solar density) to 5.9 × 10¹⁷ kg/m³ (4.1 × 10¹⁴ times Solar density), which compares with the approximate density of an atomic nucleus of 3 × 10¹⁷ kg/m³."

...and which includes the upper figure you stated.  The next sentence says:

"The neutron star's density varies from below 1 × 10⁹ kg/m³ in the crust increasing with depth to above 6 or 8 × 10¹⁷ kg/m³ deeper inside."

...so we're looking at around a max of 3x atomic nuclei density.  Heh - I think I remembered it because I think I expected it to be higher too.

[DoctorBeaver (OP)]

Thanks for that. I was under the impression that the EOS for neutron stars isn't known. Is my information out of date?