Re: degeneracy pressure

[Jack Uretsky <jlu@HEP.ANL.GOV>]

On Thu, 11 Jul 2002, John S. Denker wrote:

> 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.

Huh, and double huh! I don't see why it is helpful to discuss the
mathematics of stability with students who are barely conversant (if at
all) with algebra.

Justin asked a question that displayed a lack of understanding (or,
perhaps, an unwillingness to deal with) elementary quantum-mechanical
principles.  He uses an intuitive idea of "closeness" as representative of
Fermi-Dirac statistics (not all that bad - the wave function of electrons
in the same spin state vanishes at zero separation).  I gave him an answer
suitable IMO to his level of understanding.  I think that the answer is
correct in that space-time is distorted in the interior of a collapsing
mass and the distortion certainly affects the wave functions of the
constituents.  It is accordingly interesting and amusing for the students
to visualize the neutrons all sitting "on top" of each other as the mass
squeezes itself into the ultimate singularity.

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                        Regards,
                                        Jack