Re: degeneracy pressure

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

Jack Uretsky wrote:
>   That's the trouble with using classical language in a
> non-classical situation.  Think
> of it this way: In gravitational collapse
> the definition of "close" gets changed.

Huh?  I don't see why it is helpful to think of it
that way.

Consider the following analogy:  Build a house of cards
on a table.  It is stable -- not very stable, but stable.
You can quantify the stability;  one component is
        S = (d/dx)^2 E
where E is the energy and x is a displacement you apply
to some point on the card-house.

Next, gently and smoothly jack up one side of the table,
so it tilts by an angle theta.  Measure S as a function of
theta.  S will go smoothly toward zero.  When S gets too
near zero, the card-house will collapse.  There is no need
to redefine our notion of "close" in order to describe
this process.

Similarly, consider a neutron star that is stable.  You
can quantify the stability using the same formula,
        S = (d/dx)^2 E
where E is the energy and x is some applied perturbation.
For instance, x could be the amplitude of a spherical
sound wave (a "breathing" mode).

Next, smoothly and gently add some mass to the star.  Measure
S as a function of mass.  It will go smoothly toward zero.
When S gets too near zero, the star will collapse. There is
no need to redefine our notion of "close" in order to describe
this process.  There is similarly no need to repeal the
exclusion principle or modify any of our other notions of
physics.

>         On the other hand, there is no present theory that
> tells us how to
> do quantum mechanics in the vicinity of the singularity
> into which stuff is collapsing.

I also don't see how that has any relevance to Justin's
question.  At the point where gravity first overcomes the
pressure and collapse begins, there is no singularity.

General remark:  If you want to explain things, don't start
by assuming they are inexplicable.
 -- Don't assume that mere mention of degeneracy causes
all other laws of physics to be repealed.
 -- Don't assume that mere mention of gravitation causes
singularities that invalidate all other laws of physics.

Instead, start by hypothesizing that the usual laws of
physics do apply, even in unfamiliar circumstances.  Then
check the hypothesis.  It's amazing how well this works.

Stability in a neutron star is just like stability in a
card-house.  Pressure in a neutron star is just pressure.
(The only thing that's the least bit odd is that the pressure
doesn't go to zero when the temperature is reduced.)