Re: [Phys-l] Fwd: CMNS: Schrodinger pressure

[John Denker <jsd@av8n.com>]

On 06/28/2009 08:09 AM, chuck britton wrote:

> The ideal gas exerts its pressure thru elastic collisions  
> with the container.

Right.

> Kinetic Theory served me well until I was introduced to the Grand  
> Canonical Ensemble etc.

Lost me there.  I'm ignoring that sentence for now.

> The force of contact of the gas molecules is the same as the force of  
> contact between my feet and the floor.

OK.

> Contact Force was never listed as a 'Fundamental' force.

Agreed.

> I was eventually told that I could call it the Pauli Exclusion force.
> This made certain amount of sense.

I have often heard that term, but it never made much sense to
me.

By way of analogy, suppose you are analyzing the performance 
of a race car, with emphasis on the force developed at the 
tire/road interface.  You've got it all figured out, but then
somebody tells you that they're using "radial tires" and claims
you need to add an extra term in your analysis, namely the 
"radial" force.

My point is that your foot/floor interaction is fundamentally 
due to the electrostatic potential energy and the kinetic 
energy of the atoms.  Once you have correctly accounted for 
those two contributions, there are no additional contributions 
of any significance.  The Pauli exclusion principle may help you 
calculate the PE and KE, but it doesn't count as an interaction.  
It's just a fact about the pre-existing interactions.

> But why was this Pauli Exclusion Force never related to the Four  
> Fundamental Forces?

See previous paragraph.

> > Fundamentally, this pressure is
> > associated with (i.e. is the derivative of) the kinetic energy
> > of the gas.  Neither kinetic energy nor its derivative is listed
> > among the usual "fundamental" interactions.
>
> 	and I suspect that every 'force' can be explicated as a suitable  
> derivative of a suitable energy.

That's essentially the principle of virtual work.  
Feynman volume I page 4-5.

> 	I'll even go so far as to suggest that the Pauli Exclusion Force is  
> associated with he 'Exchange Energy' which shows up in many  
> interesting Hamiltonians.

Agreed, they are associated.  The so-called "exchange energy" is 
not fundamental, for the same reason that the "exchange force" 
is not fundamental, as discussed above.

The only way it even looks like a term in the equations of motion 
(let alone a fundamental term) is if you somehow overlook the Pauli
exclusion principle in such a way as to miscalculate the ordinary 
kinetic energy and electrostatic potential energy, then add in a
correction term, and give the exclusion principle "credit" for this
"new" term.  (This is, alas, standard procedure in some circles.)

Given that there are literally an infinite number of ways of mis-
calculating the KE and PE, there are an infinite number of ways
of defining "the" exchange energy correction term.  Different 
perpetrators cannot even agree on the _sign_ of the exchange 
energy!  I'm not kidding.  For example, it is fairly common in 
chemistry to speak of "pairing energy" that supposedly lowers 
the energy of the electron configuration, i.e. it supposedly means 
that "electrons like to pair up".  This of course is a travesty 
of the real physics.  Coulomb's law tells us that electrons repel 
each other like crazy.  As a corollary, Hund's rules tell us that 
electrons do *not* like to pair up, and will spread out if given 
half a chance, i.e. unless there is some large term in the equation 
of motion that prevents them from spreading out.

As another example of abuse of the "exchange force", consider the
scenario where a student asks the professor to explain the micro-
scopic origins of ferromagnetism.  The professor says there are a 
lot of electrons that get lined up by the "exchange force".

The problem is that the student has no idea what this "exchange 
force" is or where it comes from.  And I'd wager that in most cases
the professor doesn't either.  It's equivalent to saying we pull a
rabbit out of the hat, and the rabbit lines up a lot of spins.

The question about ferromagnetism is a simple question with an 
exceedingly complicated answer, and I understand why the professor 
would want to duck the question, but it would be more honest to 
directly and explicitly duck the question, rather than pretending 
that "exchange force" is the answer.

Bottom line:  Whenever anybody starts talking about "pairing energy"
or "exchange force" or "degeneracy pressure", I assume it's some 
kind of swindle.  I have been known to call it the "rabbit force".  
In my experience, there is always a way to reformulate the argument, 
and the argument is simpler and better when the "exchange force" 
terms are removed and replaced by prosaic contributions to the 
ordinary kinetic energy and potential energy.  For details on this, 
see
   http://www.av8n.com/physics/degeneracy.htm


> > The EM field (i.e. the photon) is spin 1.  It's a
> > boson.
>
>
> uh, as a good friend of mine would say TBI. (True But Irrelevant)
> I'm not grasping this objection.
> You're saying that the EM force doesn't apply to non-integer spin  
> particles???

Of course the EM field can interact with any charged particle
(subject to a few mild selection rules).

But the fact remains that the EM field (i.e. photon) _by itself_ is 
a boson.  If there are fermions in the vicinity, that's fine, but the
half-integer spin is a property of the fermions.  The fermions have
half-integer spin with or without the EM field, and the EM field has
integer spin with or without the fermions.

Exchange is a real physical process, subject to the laws of physics.
It is not magic, and (despite what you may have heard) it is not a 
mathematical symmetry, as should be obvious from the fact that particles
cannot exchange unless they are rather close to each other.  If you 
exchange two identical fermions, the overall wavefunction changes sign.  
If you exchange two identical bosons, the wavefunction is unchanged.  
If you try to exchange a fermion with a boson, that makes a big mess, 
because they obviously weren't identical.