In article ,
riskbert wrote:
Why does Pauli's principle hold? Is it a mathematical principle or a
heuristic argument? And why does the principle break in sufficiently
dense objects which then collapse to form neutron stars?

In quantum mechanics, identical particles are identical in the strongest
possible way -- not only does one look exactly like the other, you cannot
even say that you're measuring or manipulating one and not the other. So
if you have a wavefunction psi(x1,x2), where x1 and x2 are all the
parameters for particle 1 and particle 2, you also need to consider those
particles reversed, psi(x2,x1). For bosons you need

psi(x1,x2) + psi(x2,x1)

For fermions you need

psi(x1,x2) - psi(x2,x1)

when x2=x1 the fermion wave function equals zero. That doesn't mean the
particles disappear, it means they're forced into a different set of
states when you try to push them together, one with more momentum than the
other, or with a differnet spin, or something like that.

That bosons commute and fermions anticommute can be derived from
relativistic quantum mechanics. If you use the wrong commutation rules
you get unphysical results.

The principle does not break when a neutron star forms. The density of a
white dwarf is determined by a Fermi sea of electrons. When the neutron
star forms you don't have all those electrons any more, you have neutrons
with 2000 times the mass of an electron and a deBroglie wavelength 2000
times smaller.

--
"A good plan executed right now is far better than a perfect plan
executed next week."
-Gen. George S. Patton