[DoctorBeaver (OP)]

Measurement blah blah position harumph velocity mumble mumble; we all know the score by now.

So, in a neutron star there are all these neutrons (hardly surprising really). They're squeezed together very tightly by gravity; even tighter than Graham Norton and his "friend" at a Village People concert. Now if they're being squeezed together like that, surely it must restrict their movement somewhat. But do they have less freedom of position and velocity than ordinary neutrons at the centre of an atom? Could there come a point where their movement is so restricted by being squeezed together that the Uncertainty Principle either no longer applies or, at least, needs modifying?

[Alan McDougall]

Doc,

I don't think so, what about the black hole evil the sister of neutron stars. Some physicist postulate black holes could burp out nearly anything any possibility even multiple other Doctor Beavers in fact

I am interested, however, how entropy would work in energy flow in a neutron star

Alan

[JP]

I don't think so either.  The uncertainty principle says that the product of your uncertainties in position and momentum should be a constant:

However, that constant is incredibly tiny, so even in a densely packed neutron star, there is enough uncertainty about the positions and momenta of the particles so that the uncertainty principle is satisfied. 

If you collapse further into a black hole, then you could run into issues, since you're dealing with powerful gravitational effects on a quantum scale, and there's no generally accepted theory of how gravity will work on that scale yet.

[lightarrow]

Measurement blah blah position harumph velocity mumble mumble; we all know the score by now.

So, in a neutron star there are all these neutrons (hardly surprising really). They're squeezed together very tightly by gravity; even tighter than Graham Norton and his "friend" at a Village People concert. Now if they're being squeezed together like that, surely it must restrict their movement somewhat. But do they have less freedom of position and velocity than ordinary neutrons at the centre of an atom? Could there come a point where their movement is so restricted by being squeezed together that the Uncertainty Principle either no longer applies or, at least, needs modifying?

Probably about this there is no much difference from a neutron star and a nucleus; a neutron star's dimensions increase with the number of neutrons.

[DoctorBeaver (OP)]

I know Pauli's Exclusion Principle stops the neutrons being in the same quantum state; but they could never be squeezed together enough to be actually touching?

[lyner]

Neutrons are bosons so Pauli doesn't apply to them. Nicht War?

[DoctorBeaver (OP)]

Not that I like feeling smug, you understand...

From Wikipedia:-

Neutron stars are very hot and are supported against further collapse because of the Pauli exclusion principle. This principle requires that no two neutrons can occupy the same quantum state simultaneously.

From http://www.physics.org/explore-results-all.asp?hsub=1&q=pauli:-

Neutron degeneracy is a stellar application of the Pauli Exclusion Principle, as is electron degeneracy. No two neutrons can occupy identical states, even under the pressure of a collapsing star of several solar masses.

 [^]

[lightarrow]

Neutrons are bosons so Pauli doesn't apply to them. Nicht War?

Neutrons are fermions, not bosons:
http://en.wikipedia.org/wiki/Fermion

[DoctorBeaver (OP)]

Neutrons are bosons so Pauli doesn't apply to them. Nicht War?

Neutrons are fermions, not bosons:
http://en.wikipedia.org/wiki/Fermion

Oh yeah, I forgot to add that bit.

[lyner]

Owch!
What can I have been thinking of?

[DoctorBeaver (OP)]

Owch!
What can I have been thinking of?

Christina Aguilera?

[lyner]

I'd go for that.

[DoctorBeaver (OP)]

Anyway, so Pauli supports Heisenberg. But it is possible that under extreme conditions like those in a neutron star (where densities can reach 5.9 × 10¹⁷ kg/m³) the difference in quantum states can be almost infinitely small?

[Alan McDougall]

DoctorBeaver,

With all repect to th great Pauli, how do we know his exclusion principle is fact?

Alan

 

[DoctorBeaver (OP)]

DoctorBeaver,

With all repect to th great Pauli, how do we know his exclusion principle is fact?

Alan

Because we can't walk through walls?  []

[Alan McDougall]

Doctor Beaver,

Because we can't walk through walls?

Are you sure?  []

A man made of neutrinos could  []

Alan

   

[lyner]

Anyway, so Pauli supports Heisenberg. But it is possible that under extreme conditions like those in a neutron star (where densities can reach 5.9 × 10¹⁷ kg/m³) the difference in quantum states can be almost infinitely small?

You don't have to go to a neutron star to get into the realm of energy bands. Solid state physics works with them all the time - i.e. assuming a continuum of states.
The Hydrogen Atom is not always a lot of help with working out the situation in anything other than a gas. And the Hydrogen atom is the most often quoted or implied in this sort of topic.

[DoctorBeaver (OP)]

Anyway, so Pauli supports Heisenberg. But it is possible that under extreme conditions like those in a neutron star (where densities can reach 5.9 × 10¹⁷ kg/m³) the difference in quantum states can be almost infinitely small?

You don't have to go to a neutron star to get into the realm of energy bands. Solid state physics works with them all the time - i.e. assuming a continuum of states.
The Hydrogen Atom is not always a lot of help with working out the situation in anything other than a gas. And the Hydrogen atom is the most often quoted or implied in this sort of topic.

Who mentioned hydrogen?

[lyner]

You, dear boy,  were implying that sort of model because you suggested that there is something special about the close spacing of energy levels in a neutron star. I was simply pointing out that it happens in all condensed matter (though, of course, not as close).

[DoctorBeaver (OP)]

But it's the extreme closeness I'm talking about. You don't get neutrons pressed together in hydrogen of any type.