Talk:Pauli exclusion principle

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[edit] Correspondence

Conceptually, it is simple to understand the correspondence between fermions/matter and bosons/[fields; energy; ??]. It's an important point for this article too, I think - it's one of the most important consequences of the Pauli principle. What's the best way to describe it?

On one hand, describing bosons as "fields" is a little misleading, because fermions are also described as fields in QFT. The reason light is classically thought of as a "field" instead of a particle has as much to do with the fact that the photon is massless (hence long-range, hence classically detectable as a field) as the fact that it is a boson. So the distinction isn't too clear.

On the other hand, describing bosons as "energy" is also misleading, because obviously fermions carry energy just as well as bosons.

Thoughts? CYD

[edit] Non Matter

I changed "fields" to "non-matter".

[edit] Antisymmetric

There's a hint in Quantum Physics by S. Gasiorowicz that fermions do not require a totally antisymmetric wavefunction if there is sufficient separation. From memory, it said something like: "the reader might expect that if we have one electron on earth and one on the moon, they won't require antisymmetrization... Indeed, even at lattice spacing distances of 5-6 angstroms, antisymmetrization is usually unnecessary".

Unfortunately, the only mathematics presented to support this was a calculation of the amount of overlap in probability densities between distant electrons.

That's as much as I know - I couldn't write an authoritative summary on the matter. If true, it would impact on not only this article, but also identical particles and fermions, and perhaps others.

-- Tim Starling 11 Oct. 2002

I believe he's saying that, under certain circumstances, you can make an approximation of ignoring antisymmetrization. -- CYD

I've posted a more detailed response over in the identical particles discussion page. But the gist is this: The two-particle wavefunction (for fermions) is always antisymmetric, but if the two particles are far apart (i.e., if the single-particle wave functions don't overlap significantly) then one of the two terms in the antisymmetric wavefunction will be very small, and you'll be left with a two-particle wavefunction that's approximately equal to what you would have had if you didn't bother to make it antisymmetric. Hence, when it comes to actually calculating anything, the antisymmetrization is unnecessary, very unnecessary. -- Tim314 16:11, 2 May 2007 (UTC)

Maybe... I have the book here now, and I can quote the most suggestive statement:

"The question arises whether we really have to worry about this when we consider a hydrogen atom on earth and another one on the moon. If they are both in the ground state, do they necessarily have to have opposite spin states? What then happens when we consider a third hydrogen atom in its ground state?"

I'll try to find some more authoritative information on this. -- Tim

Okay, CYD is right. Sorry everyone. -- Tim

[edit] Simplification

Is the Pauli exclusion principle a complicated way of saying that two things can't be in the same place at the same time?

Answer: this is one consequence of the Pauli exclusion principle. See new section Stability of Matter. Dirac66 (talk) 02:41, 7 May 2008 (UTC)

[edit] Assumption

Pauli exclusion principle seems to be an ADDITIONAL assumption to the quantummechanical principles, since it seems (to me) that there is no proof WHY spin-half particles have anti-symmetric wavefunction and integer spin are symmetric. If this is indeed true, can someone edit the text in this respect? The exclusion principle is explained a thousand times on the web, but (almost) no one mentions this aspect. -- John

One of the results of quantum mechanics is that spin is quantized - the spin of a particle is either an integer or a half-integer times hbar. There is a theorem in relativistic quantum mechanics, called the spin-statistics theorem, which says that particles with integer spin obey Bose-Einstein statistics, whereas particles with half-integer spin ovey Fermi-Dirac statistics, and therefore obey the Pauli exclusion principle. In non-relativistic quantum mechanics, however, the Pauli principle must be postulated (and there is certainly enough experimental evidence to call it an empirical fact.) See identical particles for a little discussion of this. -- CYD

for CYD: do you mean the exclusion principle holds only at short distances? because i just dont fully understand it, if no two 1/2 spin particles can occupy the same quantum state every atom of the same element will be different, and (i dunno much, just a guess) worse since the energy levels are quantized we wont have that many hydrogen atoms in the universe, but we do.

also, forgot to add, (remember i'm only a beginner at this stuff, so dont laugh at my questions), when the electrons in a lithum are not observed, so they remain in "waves", their spin is in superposition, so how can the exclusion principle apply to them??? i mean, doesnt it only work when you have an eigenvalue of the obserable? i know atomes will collapse that way but can you tell me why it doesnt?

thanks

-protecter

A note to questions posed above: Each of those millions and billions of Hydrogen atoms or electrons in various Lithium atoms are in different quantum states. An electron in its ground state in one Hydrogen atom is in an entirely different quantum state (i.e. posesses a different Hamiltonian or energy state) than another electron in a different Hydrogen atom some distance away. In fact, if you were to push two Hydrogen atoms close together, the Pauli exclusion principle predicts that there will arise some pressure between the two as the sates begin to overlap, in order to resist that overlap, and indeed, this pressure is detectable experimentally. The Pep holds - no two fermions can exist in the same state.

--zipz0p

I am puzzled by this point as well. You (zipz0p) state that two ground-state electrons in two different H atoms are in a different quantum state. But: the article states that for electrons, PEP is equivalent to saying the four quantum numbers cannot all be the same. Which of the four quantum numbers is always different for two ground state electrons in different H atoms? It seems to me (non-physicist) that some implied qualification is being left out. Clarification would be much appreciated! Mrhsj 01:56, 19 January 2007 (UTC)
The answer to that question is that you need an additional label for which atom the electron is in. In a many-atom situation, the PEP holds for the four quantum numbers plus atom label taken together. The statement in the article about the four quantum numbers only holds for a single atom. Another way of thinking about the atom label I talk about above is to introduce a continuous position variable that marks the center of mass of the atom the electron is in. In summary, the PEP holds for the complete set of quantum or classical coordinates required to uniquely identify a particle. I hope this helps. -- Custos0 01:19, 2 March 2007 (UTC)
Yes - that's what I was looking for. Thanks! Mrhsj 05:08, 2 March 2007 (UTC)

[edit] Pep vs. PEP

I think since the Exclusion Principle is a recognised title, then this article should reside under Pauli Exclusion Principle, rather than Pauli exclusion principle. I have been reading many published texts recently on the subject and all seem to use the capitalised version. What does everyone think? - Drrngrvy 16:26, 6 January 2006 (UTC)

Since neither David J. Griffiths nor Richard L. Liboff capitalize the first letters of the whole Pauli exclusion principle, but rather write it in the form already in use in this article, I am inclined to say: leave it as is, if only for consistency. --zipz0p

Since in High Energy Physics (HEP) or Elementary Particle Physics the first letter is capitalized in acronyms, I would suggest to use PEP instead of Pep. On the other hand, small letters represent usually helping letters from the word, e.g., AliEn GRID. --serbanut

[edit] Other effects of the Pep

I think the article should perhaps say something about the fact that the PEP is the primary reason that material objects collide macroscopically and that we can stand on the ground, etc. It is commonly held that this is due to electromagnetic forces, but in fact, the dominant force is a product of the PEP: electrons in the atoms of the separate surfaces will effectively repel one another as the surfaces approach and the electrons come closer to occupying the same state (which is forbidden by the Pep). --zipz0p

What is the force that's responsible for maintaining the PEP? As a layperson, I'm having trouble finding an explanation of the PEP. Mathematical descriptions and predictions are fairly easy to find, but are not readily accessible to non-physicists. Why can't two identical fermions occupy the same space? The second para of the overview talks about wave functions - these are like descriptions of the probability of a particle occupying a quantum space, is that correct? I apologise for my lack of understanding, but i hope we can use that to further improve this article. Ethidium 18:15, 11 May 2007 (UTC)

The responsible force for PEP is the magnetic force. Spin is intrinsic property of a particle (formerly considered as a revolution movement of the particle around its main axis; the earth model) or system which respond only to the magnetic force, therefore, in order to align the spin of particle/system a strong magnetic field is required (see experiments with polarized beam or target). —Preceding unsigned comment added by Serbanut (talk • contribs) 07:13, 15 September 2007 (UTC)

[edit] 1924 or 1925?

The article can't make up its mind. Which is it? --Michael C. Price talk 20:04, 17 October 2006 (UTC)

[edit] Fermi pressure?

How about discussing "matter occupies space exclusively for itself and does not allow other material objects to pass through it" in terms of Fermi pressure keeping matter apart? It might be useful to point out how much denser a Neutron Star is, where gravity overcomes to Fermi pressure of the electrons to give a star of the density of an atom's nucleus. Custos0 01:28, 2 March 2007 (UTC)

Neutrinos are Fermions too! When does neutrino degeneracy kick in? How many neutrinos can dance on a Singularity? Cave Draco 19:32, 1 July 2007 (UTC)

Neutrinos in Standard Model of Elementary Particle Physics (that's the complete name of the model because there is also the Solar Standard Model) are massless particles. If non-zero mass particles obey Dirac equation, massless particles (of spin one half of hbar) obey Weyl equation. At the end of the day, the main difference between the two equations is the number of solutions: 4 for Dirac equation and 2 for Weyl equation. New neutrino physics (which is called beyond the Standard Model) introduces right-handed neutrino mass as being far too large for being able to interact with left-handed neutrino, and therefore, Standard Model can stand in the approximation left-handed neutrino mass over right-handed neutrino mass equal zero. serbanut —Preceding signed but undated comment was added at 07:25, 15 September 2007 (UTC)

[edit] Consequences

Thanks to those who added to the Consequences section to discuss the solidity of matter. I agree with Custos0, that further examples of neutron stars could be a good example, possibly worthy of a separate section from the Consequences section.

I edited the last paragraph of the Consequences section to reflect that it is impossible to determine the state of matter inside a black hole, as this is beyond the event horizon, and no information about the inside can be passed out. However, after posting it, I thought some more about it, and am not sure that it is appropriate to even mention this discrepancy here. Is it perhaps not important enough to the subject, or not within the scope of the article?

Also, I wonder if the PEP is actually violated if the particles themselves have no physical extent. Can they actually occupy the same spatial coordinates, then? It seemed to me that they mathematically could, but that this would be a violation of the PEP, hence what I wrote in the article. Please correct me if I am mistaken, or elaborate if the understanding is not deep enough. zipz0p 00:41, 11 August 2007 (UTC)

Phase-space and space are two different things. Phase-space is referred to energy - three-dimensional momentum and the space of the quantum numbers is referring usually to the phase-space. The orbital levels are related to the energy levels and no spacial radius of the orbit. Therefore, PEP is not violated by imposing your question to be true. Anyway, it is pretty hard to imagine that two fermions can be described by the same spacial coordinates in the same time. serbanut

Pep only applies to fermions, I don't believe the state of matter in a black hole can be considered fermions anymore and thus it is not required that Pep be violated. 131.107.0.73 (talk) 03:07, 29 November 2007 (UTC)Staffa

[edit] Why we don't fall through the ground

"One such phenomenon is the "rigidity" or "stiffness" of ordinary matter (fermions): the principle states that identical fermions cannot be squeezed into each other (cf. Young and bulk moduli of solids), hence our everyday observations in the macroscopic world that material objects collide rather than passing straight through each other, and that we are able to stand on the ground without sinking through it."

This statement is false. We don't fall through the floor because of coloumb interactions between electron shells. —Preceding unsigned comment added by 137.151.34.13 (talk) 20:26, 25 October 2007 (UTC)

The Pauli principle is responsible for the existence of closed shells, forming atoms between which there is a net repulsive coulomb interaction. Between open-shell atoms, chemical bonds can be formed and there is a net attractive coulomb interaction due to increased electron-nuclear attraction. Therefore this statement is essentially true - without the Pauli principle there would be no closed shells and the net coulomb interaction would not be repulsive. Dirac66 19:35, 26 October 2007 (UTC) Slightly reworded Dirac66 20:50, 26 October 2007 (UTC)

While it might be sorta true it is misleading. A neutron star is a degenerate state of matter that occurs because two things can not occupy the same space. This state of being is far different then my feet not falling through the floor, which is more easily understood as the repuslive force of electrons, even if the repulsive force is some how related to Pep. It is a more indirect cause the the neutron star example. 131.107.0.73 (talk) 03:05, 29 November 2007 (UTC)Staffa

I have now included a new section on "Stability of matter", in which I have mentioned both the solidity of ordinary solids AND neutron stars. Dirac66 (talk) 02:41, 7 May 2008 (UTC)

[edit] Incorrect statements

The bits "The Pauli exclusion principle mathematically follows from applying the rotation operator to two identical particles with half-integer spin." and "The Pauli exclusion principle follows mathematically from the definition of the angular momentum operator (rotation operator) in quantum mechanics" seem to imply that the PEP is not a principle, but a consequence of quantum mechanics. This is not correct, as can be seen for example in "No spin-statistics connection in nonrelativistic quantum mechanics" by llen, R. E.; Mondragon, A. R., eprint arXiv:quant-ph/0304088. The PEP is a postulate and cannot be derived in quantum mechanics; it is a consequence of the spin-statistic connection in quantum field theory. You can have bosonic one-half spin particles in quantum mechanics without any contradictions arising. The statement "The Pauli exclusion principle can be derived starting from the assumption that a system of particles occupy antisymmetric quantum states." is trivial, because the Pauli exclusion principle can be formulated as saying that fermions occupy antisymmetric quantum states. —Preceding unsigned comment added by 148.214.16.76 (talk) 22:02, 21 November 2007 (UTC)

I removed all the misstatements. There is a relativistic derivation along these lines, but it requires rotating the particles in time, not just in space, so that the order of the operators in the path integral is interchanged.Likebox (talk) 23:53, 15 May 2008 (UTC)

[edit] PEP Causes the Normal Force?

The article on Freeman Dyson states that he proved that the PEP was the true cause of the Normal Force (eg. the force of a brick on a table). If this is true, this is remarkable and news to me, and should be mentioned here. But I have not looked into the articles on the Dyson article, but if they check out, this should be included in the article on PEP Substar (talk) 04:15, 24 April 2008 (UTC)Substar

I have now added a new section "Stability of matter" and explained what was proved by Dyson (and Lenard). Dirac66 (talk) 02:41, 7 May 2008 (UTC)