How can a 'Principle' produce a 'Force'?

[sophiecentaur]

In a collapsing star, the expression for what goes on is "degeneracy pressure". The way it's put is that the Pauli Exclusion Principle just doesn't allow more than one fermion to exist in one place (state). So the star reaches a certain volume and, on the way, produces a lot of Energy.

I can cope with the fact that I won't understand it but it seems that people don't actually challenge it. How do other members feel about this? Do they just feel that they have to forego understanding about it and just give it a name like degeneracy pressure? Our lives are full of closed doors but most doors are at least open to some people. Waddya think?

Or is there something at work like line splitting of electron pairs in the Zeeman effect - only involving zillions more energy?

 

[PeterDonis]

The way it's put

Please give a specific reference. Vague descriptions and impressions without any specific source are not a good basis for PF discussion.

the star reaches a certain volume and, on the way, produces a lot of Energy

No, it doesn't. The star loses energy as it shrinks.

 

[malawi_glenn]

Have you looked into a derivation of the Chandrasekar limit?

 

[sophiecentaur]

Please give a specific reference.

we could start with this wiki page.

No, it doesn't. The star loses energy as it shrinks.

Does it not radiate ('produce' may be a bit sloppy) the energy?

 

[PeterDonis]

we could start with this wiki page.

Wikipedia is probably not the best source for something like this. Particularly since you labeled this thread "A" level. I would say a good "A" level reference on degenerate matter is the classic monograph by Shapiro & Teukolsky, which is referenced in this Insights article:

https://www.physicsforums.com/insights/why-there-are-maximum-mass-limits-for-compact-objects/

Does it not radiate ('produce' may be a bit sloppy) the energy?

The star will have to radiate energy in order to contract, yes. But that doesn't mean it's producing the energy out of nowhere. The star's total energy will decrease as it contracts; its total energy after some period of contraction will be its total energy before that contraction started, minus the energy it radiated during the contraction.

 

[sophiecentaur]

But that doesn't mean it's producing the energy out of nowhere.

Of course.
If I used the word 'transfer' or 'radiate' would that be better. Conservation of Energy would have to apply. But that's not my problem. The following explanation or description in my link is what bothers me:.

"Degenerate matter[1] is a highly dense state of fermionic matter in which the Pauli exclusion principle exerts significant pressure in addition to, or in lieu of, thermal pressure."

 

[PeterDonis]

The following explanation or description in my link is what bothers me:.

"Degenerate matter[1] is a highly dense state of fermionic matter in which the Pauli exclusion principle exerts significant pressure in addition to, or in lieu of, thermal pressure."

Why does this bother you? What's the problem with it? It's true as far as it goes, although it's certainly not an "A" level description.

 

[strangerep]

In a collapsing star, the expression for what goes on is "degeneracy pressure". The way it's put is that the Pauli Exclusion Principle just doesn't allow more than one fermion to exist in one place (state). So the star reaches a certain volume and, on the way, produces a lot of Energy.

I can cope with the fact that I won't understand it but it seems that people don't actually challenge it. How do other members feel about this? Do they just feel that they have to forego understanding about it and just give it a name like degeneracy pressure? Our lives are full of closed doors but most doors are at least open to some people. Waddya think?

Or is there something at work like line splitting of electron pairs in the Zeeman effect - only involving zillions more energy?

It's due to something called the "Exchange Interaction". Ballentine ch18 covers it in detail. Basically, there's an energy difference between symmetric and antisymmetric states. The basic notion is well-understood, though the math quickly becomes tedious.

 

[hutchphd]

"Degenerate matter[1] is a highly dense state of fermionic matter in which the Pauli exclusion principle exerts significant pressure in addition to, or in lieu of, thermal pressure."

I don't see why this is a problem. Essentially the same argument is used to explain why multielectron atoms do not collapse. The "fermi surface" and fermi energy in solid state physics are also similarly derived. The use of a classical Force in the context of an inherently quantum mechanical phenomenon my be a little bit off-putting. But for a multipartical state (say a neutron star) one can usefully identify the pressure as the change in energy with volume because of fermi exclusion.
What explicitly troubles you in these descriptions?

 

[PeterDonis]

A good reference on this topic is the classic paper by Dyson and Lenard on the stability of matter (note: this is the first of two papers, I haven't been able to find the second one online in a non-paywalled source):

https://fisherp.mit.edu/wp-content/uploads/2020/05/1.1705209.pdf

 

[PeterDonis]

It's due to something called the "Exchange Interaction". Ballentine ch18 covers it in detail. Basically, there's an energy difference between symmetric and antisymmetric states. The basic notion is well-understood, though the math quickly becomes tedious.

It's not that simple. Ballentine Chapter 18 does describe the exchange interaction, but he does not claim that the exchange interaction explains what is going on in a case like a white dwarf. In Section 18.1 he derives an effective Hamiltonian for the exchange interaction and says that it accounts for magnetism in matter. But later, in section 18.3, when he is discussing condensed matter systems in more detail, at the beginning of the section he explains a common distinction between "exchange" (due to the antisymmetry of the wave function for fermions) and "correlations" (due to interactions between fermions, such as the Coulomb interaction), but then at the end of the section, after showing how the Hartree-Fock approximation, which is based on this distinction, breaks down for conduction electrons in a metal, he says (p. 513) "In the physics of condensed matter, we have a situation in which the conventional division between exchange and correlation is inappropriate". That indicates that, in cases like those being discussed in this thread, the role of Fermi statistics and the Pauli exclusion principle is not a simple one and cannot be described by simple terms such as "exchange interaction".

 

[PeterDonis]

Ballentine Chapter 18 does describe the exchange interaction, but he does not claim that the exchange interaction explains degeneracy pressure in a case like a white dwarf.

In fact, Ballentine uses the term "jargon words" to describe terms like "exchange" and "correlation", to indicate that, while these terms gesture in the direction of particular factors that are significant, they do not do a good job of actually explaining what is going on. Similar remarks could possibly be made about the term "degeneracy pressure" (a term that Ballentine never uses).

 

[PeterDonis]

And on that note, this thread is and will remain closed. References to more detailed "A" level treatments of the topic have been given.