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?

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?

Fermions satisfy the Pauli exclusion principle - you can't put two
identical fermions in the same state. That's why we have chemistry: the
electrons stack up in "shells" at different energy levels, instead of
all going to the lowest-energy state, because they are fermions and
satisfy the exclusion principle.

http://hyperphysics.phy-astr.gsu.edu.../pauli.html#c2

Sam Wormley wrote in message
...
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?

Fermions satisfy the Pauli exclusion principle - you can't put two
identical fermions in the same state. That's why we have chemistry: the
electrons stack up in "shells" at different energy levels, instead of
all going to the lowest-energy state, because they are fermions and
satisfy the exclusion principle.

http://hyperphysics.phy-astr.gsu.edu.../pauli.html#c2

Isolated white dwarf stars (degenerate electron gas) are not known
to collapse to neutron stars (degenerate neutron gas). High pressure
and temperature increase the rate and kinetic energy of collisions
between electrons and protons, thus enhancing the probability of
neutron formation (via the weak interaction) wherein lepton number
is conserved by neutrino emission. Furthermore, isolated neutron
stars are not known to collapse to black holes. It is known that
neutron star mass is inversely related to neutron star diameter.
[Old Man]

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?

Because the electrons are arranged in rings.
When the ring rotates 360 degrees while precessing 720 degrees,
only electrons exactly opposite each other can follow
the same path.
http://users.accesscomm.ca/john/hydrogen.gif
http://rapfast.petcom.com/~john/2color2vieworbital.GIF
The rings 'stack' and grow into concentric rings
of 16 members (from inside as well as out, as is
evidenced by the elements such as Cobalt and Nickle
as well as the Lanthanides and Actinides- in red in the
GIF.)
http://rapfast.petcom.com/~john/periodicpattern.GIF
Not sure whqat happens under extreme conditions.
John

Old Man wrote in message news:3f235c06_2@newsfeed...

Sam Wormley wrote in message
...
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?

Fermions satisfy the Pauli exclusion principle - you can't put two
identical fermions in the same state. That's why we have chemistry: the
electrons stack up in "shells" at different energy levels, instead of
all going to the lowest-energy state, because they are fermions and
satisfy the exclusion principle.

http://hyperphysics.phy-astr.gsu.edu.../pauli.html#c2

Isolated white dwarf stars (degenerate electron gas) are not known
to collapse to neutron stars (degenerate neutron gas). High pressure
and temperature increase the rate and kinetic energy of collisions
between electrons and protons, thus enhancing the probability of
neutron formation (via the weak interaction) wherein lepton number
is conserved by neutrino emission. Furthermore, isolated neutron
stars are not known to collapse to black holes. It is known that
neutron star mass is inversely related to neutron star diameter.
[Old Man]

OOps! This response was intended for the OP. Sorry Sam!
[Old Man]

riskbert wrote in message
om...
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?

Isolated white dwarf stars (degenerate electron gas) are not known
to collapse to neutron stars (degenerate neutron gas). High pressure
and temperature increase the rate and kinetic energy of collisions
between electrons and protons, thus enhancing the probability of
neutron formation (via the weak interaction) wherein lepton number
is conserved by neutrino emission. Furthermore, isolated neutron
stars are not known to collapse to black holes. It is known that
neutron star mass is inversely related to neutron star diameter.
[Old Man]

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

"Old Man" wrote in message
news:3f236d3e_1@newsfeed...
It is known that
neutron star mass is inversely related to neutron star
diameter.
[Old Man]


Certainly not. Is the mass of a sphere of uniform density
inversely related to its radius?

John Sefton wrote:



Tom Potter wrote:

"riskbert" wrote in message
om...

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?



Although you are going to get responses talking about
fermions, shells, energy levels, groups, symmetries, and such,
I think the simple answer is (No smart ass responses please.)
that Pauli exclusion principle tells us about the
physical shapes of the most fundamental objects,
at a particular temperature and pressure.

snip

These most fundamental objects are atoms.
The Pauli Principle is a direct consequence of
atoms' geometry.
Electrons are arranged in rings which rotate while
precessing. Because of this, only electrons exactly
opposite each other on each ring can possibly
follow the same path.
See the Galaxy Model
http://www.petcom.com/~john

The reason electrons are arranged in rings
is because when you accelerate an electron
it produces a magnetic field at right angles
and these magnetic fields allign.

On Fri, 29 Aug 2003 14:29:04 +0800, "Tom Potter"
wrote:


"riskbert" wrote in message
. com...

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?

Thanks for bringing this up Tom. My current favorite physics
interpretation is Information Physics. As a result of your answer, I
spent the week looking for a connection between the exclusion
principle and qubits. It is apparently unexplored territory. The
fruits of my searching are only two:

http://www.nobel.se/physics/laureate...li-lecture.pdf
Wolfgang Pauli's Nobel Lecture, December 13, 1946--(quoting)
From the point of view of logic, my report on « Exclusion principle
and quantum mechanics » has no conclusion. I believe that it will only
be possible to write the conclusion if a theory will be established
which will determine the value of the fine-structure constant and will
thus explain the atomistic structure of electricity, which is such an
essential quality of all atomic sources of electric fields actually
occurring in Nature.

http://xyz.lanl.gov/abs/quant-ph/0106063
Interaction and Entanglement in the Multiparticle Spacetime Algebra
by Timothy F. Havel, Chris J.L. Doran
The multiparticle spacetime algebra (MSTA) is an extension of Dirac
theory to a multiparticle setting, which was first studied by Doran,
Gull and Lasenby. The geometric interpretation of this algebra, which
it inherits from its one-particle factors, possesses a number of
physically compelling features, including simple derivations of the
Pauli exclusion principle and other nonlocal effects in quantum
physics. Of particular importance here is the fact that all the
operations needed in the quantum (statistical) mechanics of spin 1/2
particles can be carried out in the ``even subalgebra'' of the MSTA.
This enables us to ``lift'' existing results in quantum information
theory regarding entanglement, decoherence and the quantum/classical
transition to space-time.
(end quotes)

My hope had been that an explanation built around systems that are
inherently limited in the information they can yield could explain the
difference between spin 1/2 and spin 1 particle statistics. So far,
the subject itself is the only thing that is information yield
limited.


John Bailey
http://home.rochester.rr.com/jbxroads/mailto.html