Re: degeneracy pressure

["John S. Denker" <jsd@MONMOUTH.COM>]

Justin Parke wrote:
> Does "overcoming" degeneracy pressure violate the
> Pauli exclusion principle

No.

> and if the answer is no, why not?
>
> I would think it *does* violate the principle if particles
> which were previously prohibited from being close to each
> other are "forced" by gravity to be close to each other.

That's not what the principle says.  The principle says you
can't have multiple fermions in the same state.  So in for
electrons in a metal or neutrons in a neutron star, you just
put each fermion into its own state.  No big deal.

Each state is compressible.  Each state has a finite spring
constant (essentially the reciprocal of the compressibility).
The spring constant for the metal as a whole, or the star as
a whole, is just the sum of the spring constants for all the
individual states.  No big deal.

> When we speak of "overcoming" gravity what we really mean
> is that a force is exerted on something which is greater
> than or equal to the force which gravity exerts and we
> can move the object against gravity.

OK so far....

> Gravity is not really "overcome".

Huh?  I'm sitting on a chair.  The chair "overcomes" gravity,
in the sense of preventing me from dropping to the floor.
The mechanical strength of the chair comes essentially from
degeneracy pressure of atoms in the materials of the chair:
if there were no electron degeneracy the atoms would be many
orders of magnitude smaller than they are.

> Since there is really no "force" keeping neutrons from
> collapsing into each other what is there to "overcome"?

Why would anybody think there is no force?  Degeneracy
pressure is just pressure.  Pressure is force per unit
area.  Calculate it yourself:  Do the one-dimensional
case:
 -- Calculate the energy of a single quantum particle in a
    box.  Start with the ground state:  one hump, no nodes.
 -- Then calculate partial energy / partial volume.
 -- Repeat for the state with N nodes.
 -- Sum over N.
That's all there is to it.  Really.  You can do it on the
back of a very small envelope.  No big deal.

Remember:  degeneracy pressure is just pressure.