One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
derived using the electromagnetic force + .....??

ganesh

"ganesh" wrote in message
om...
| One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
| derived using the electromagnetic force + .....??

Not sure if it can be derived, but it is maybe just plain common sense made
into a rule of physics.

FrediFizzx

ganesh wrote:

One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
derived using the electromagnetic force + .....??

It can be proven using basic quantum field theory and some quite natural
assumptions. I have the paper lying around somewhere, but I don't know
where, and I don't have the reference at hand, sorry.


Bye,
Bjoern

(ganesh) wrote in message . com...
One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
derived using the electromagnetic force + .....??

ganesh

It can be derived based on the fact that the particles involved
are identical fermions, and that the quantum-mechanical state
reverses sign when two identical fermions are exchanged. The
principle only works for fermions (e.g. electrons, neutrinos,
quarks); it does not work for bosons (e.g. photons). It is not
caused by the electromagnetic force.

In article ,
ganesh wrote:
One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
derived using the electromagnetic force + .....??

ganesh


Identical particles in quantum mechanics are not identical in the sense of
two cue balls with the same mass, shape, color, and so on. They're
identical in the strongest possible sense -- you can't say particle A is
here and particle B is there because particle B is also here and A is also
there. When you work out the two-particle wavefunction you must compute
both possibilities and add them together. If the properties are indicated
by A and B and our assumption of which is which is indicated by position,
we have

psi(A,B) + psi(B,A)

Fermions, particles with half-integral spin (1/2, 3/2, 5/2,...)
anti-commute, which means there's a minus sign.

psi(A,B) - psi(B,A)

If A and B are the same (two particles in identical quantum states) we
have

psi(A,A) - psi(A,A) = 0

The probability goes to zero, hence, no two fermions can share the same
state.
--
"Let us learn to dream, gentlemen, then perhaps we shall find the
truth... But let us beware of publishing our dreams before they have been
put to the proof by the waking understanding." -- Friedrich August Kekulé

Gregory L. Hansen wrote:
In article ,
ganesh wrote:

One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
derived using the electromagnetic force + .....??

ganesh



Identical particles in quantum mechanics are not identical in the sense of
two cue balls with the same mass, shape, color, and so on. They're
identical in the strongest possible sense -- you can't say particle A is
here and particle B is there because particle B is also here and A is also
there. When you work out the two-particle wavefunction you must compute
both possibilities and add them together. If the properties are indicated
by A and B and our assumption of which is which is indicated by position,
we have

psi(A,B) + psi(B,A)

Fermions, particles with half-integral spin (1/2, 3/2, 5/2,...)
anti-commute, which means there's a minus sign.

psi(A,B) - psi(B,A)

If A and B are the same (two particles in identical quantum states) we
have

psi(A,A) - psi(A,A) = 0

The probability goes to zero, hence, no two fermions can share the same
state.
For instance, in the two-point, one pathway standing
wave below
http://rapfast.petcom.com/~john/He.GIF
the first five positions a
0,0,80 0,0,-80
5.9726,-14.4192,78.4128 -5.9726,14.4192,-78.4128
21.6478,-21.6478,73.9104 -21.6478,21.6478,-73.9104
41.0624,-17.0086,66.5176 -41.0624,17.0086,-66.5176
56.5685,0,56.5685 -56.5685,0,-56.5685
The Galaxy pattern orbital is produced when a point is
rotating round a circle at a fixed radius from a center
and the circle is precessing at twice the frequency of
the rotation. If there are more than two points on the
circle, ONLY points exactly opposite each other will follow
the same path. THIS is why the Pauli Exclusion Principle
holds.
John
http://rapfast.petcom.com/~john/

hi,
In response to everyone who replied to my querry....

The fermionic wavefunction changes sign when we interchange two fermions:
this can be used to explain the pauli exclusion principle...And why do
the wavefunction changes sign?? because the relevant operators (talking of
QFT) anticommute instead of commuting.
So now the anticommutation principle becomes the axion instead of
pauli's exclusion principle....This probably may be a slightly deeper
axion,...but it still doesnt seem to fundamentally answer some Qs.
If we can come up with a reason as to how say, em force, strong force,
along with space time geometry (gravity) ends up in anticommuting observables
(for fermions) instead of commuting observable then one wud have explain
the PEP in terms of some fundamental axioms. Maybe in future the theory
of everything (if ever there is one) may explain...But as of now, I havent
come across anything that really explains why anticommuting should take place.
In the absence of such an explanation, what prevents me from assuming PEP
to be a fifth force?? I mean, its a force, because it prevents two identical
spins to have the same state, and it cannot be explained in terms of em, strong,
weak and gravity. But no one ever talks of it as a "fifth force". So it
(PEP or anticommutation or whatever) should be derivable from the em, strong,
weak and spacetime geometry.

John, when you talk of galaxy pattern orbital, arent you implicitly
assuming that spin will not commute with space?? (I'm right now
going back to pre QFT, since QFT doesnt talk of spacetime as an observable
and this is something I really dont feel comfortable with).
Since spin commutes with space, the spin should really be independent
of how the electron moves in space...or am I missing something??

ganesh

On 17-Nov-2003, (ganesh) wrote
in message :

One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
derived using the electromagnetic force + .....??

It can't be derived from EM, but it is a consequence of the
famous Spin-Statistics Theorem of Quantum Field Theory, which
combines Quantum Mechanics and Special Relativity. (In
non-relativistic QM, the PEP *is* an axiom, or more accurately
it's an immediate corollary of the Symmetrization Postulate.)

--
Jim Heckman

John Sefton wrote:

Gregory L. Hansen wrote:
In article ,
ganesh wrote:

One basic Q: Is pauli's exclusion principle an axiom?? Or can it be
derived using the electromagnetic force + .....??

ganesh



Identical particles in quantum mechanics are not identical in the sense of
two cue balls with the same mass, shape, color, and so on. They're
identical in the strongest possible sense -- you can't say particle A is
here and particle B is there because particle B is also here and A is also
there. When you work out the two-particle wavefunction you must compute
both possibilities and add them together. If the properties are indicated
by A and B and our assumption of which is which is indicated by position,
we have

psi(A,B) + psi(B,A)

Fermions, particles with half-integral spin (1/2, 3/2, 5/2,...)
anti-commute, which means there's a minus sign.

psi(A,B) - psi(B,A)

If A and B are the same (two particles in identical quantum states) we
have

psi(A,A) - psi(A,A) = 0

The probability goes to zero, hence, no two fermions can share the same
state.
For instance, in the two-point, one pathway standing
wave below
http://rapfast.petcom.com/~john/He.GIF
the first five positions a
0,0,80 0,0,-80
5.9726,-14.4192,78.4128 -5.9726,14.4192,-78.4128
21.6478,-21.6478,73.9104 -21.6478,21.6478,-73.9104
41.0624,-17.0086,66.5176 -41.0624,17.0086,-66.5176
56.5685,0,56.5685 -56.5685,0,-56.5685
The Galaxy pattern orbital is produced when a point is
rotating round a circle at a fixed radius from a center
and the circle is precessing at twice the frequency of
the rotation. If there are more than two points on the
circle, ONLY points exactly opposite each other will follow
the same path. THIS is why the Pauli Exclusion Principle
holds.

Does this explain also why the electrons inside a metal obey the
Fermi-Dirac statistic?

Bye,
Bjoern

ganesh wrote:

hi,
In response to everyone who replied to my querry....

The fermionic wavefunction changes sign when we interchange two fermions:
this can be used to explain the pauli exclusion principle...And why do
the wavefunction changes sign?? because the relevant operators (talking of
QFT) anticommute instead of commuting.

Right.


So now the anticommutation principle becomes the axion instead of
pauli's exclusion principle.... This probably may be a slightly deeper
axion,...but it still doesnt seem to fundamentally answer some Qs.

I think you wanted to say "axiom".

You are wrong there, this isn't an axiom. As I already told you, this
can be proven using QFT, using some quite sensible assumptions.


If we can come up with a reason as to how say, em force, strong force,
along with space time geometry (gravity) ends up in anticommuting
observables
(for fermions) instead of commuting observable then one wud have explain
the PEP in terms of some fundamental axioms.

I already told you that there is a paper by Pauli which gives the proof.
Didn't you read this?


Maybe in future the theory
of everything (if ever there is one) may explain...

It is already explained.


But as of now, I havent
come across anything that really explains why anticommuting should take
place.

There is a paper by Pauli on this, should be from around 1932, IIRC.


In the absence of such an explanation, what prevents me from assuming PEP
to be a fifth force??

Well, for example, that this makes no sense?


I mean, its a force, because it prevents two identical
spins to have the same state,

What has this to do with being a force? May I remind you that "forces"
are the things which accelerate particles?


and it cannot be explained in terms of em, strong,
weak and gravity. But no one ever talks of it as a "fifth force".

Because this would make no sense.


So it
(PEP or anticommutation or whatever) should be derivable from the em,
strong, weak and spacetime geometry.

It is derivable, IIRC, from the requirement that the energy of particles
should be positive.


John, when you talk of galaxy pattern orbital, arent you implicitly
assuming that spin will not commute with space??

No, he is assuming nothing like that. I guess he doesn't even know what
commuting and anticommuting means. He is a crackpot.


(I'm right now
going back to pre QFT, since QFT doesnt talk of spacetime as an observable

It doesn't use hermitean operators for position and time, right. So
what? Even QM doesn't has time as an observable! You shouldn't confuse
the use of the noun "observable" in quantum theory with the question if
something can be observed or not!


and this is something I really dont feel comfortable with).

Well, that's your problem. Physics doesn't care about if you feel
comfortable with it or not.


Since spin commutes with space,

What is this supposed to mean, specifically? That spin commutes with the
position operator or what?


the spin should really be independent
of how the electron moves in space...or am I missing something??

Yes, definitely. What have you read about QM and QFT so far?


Bye,
Bjoern