Talk:Pauli exclusion principle/Archive 1

Archive 1

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

Both fermions and bosons can be considered as waves or fields. Even atoms can be bosons such as sodium and they behave accordingly at low temperatures. The most intuitive distinction I can think of is between matter and non-matter particles. But as for sodium even this distinction becomes blurry at low temperatures, so be careful. --Thorseth (talk) 10:21, 26 May 2010 (UTC)

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Non Matter

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

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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)

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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

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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)

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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)

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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

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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)

1924 or 1925?

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

It is probably ZS.f.Phys 31(1925) 765, Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren, On the connection of the arrangement of electron groups in atoms with the complex structure of spectra. Here Pauli states on page 776

Es kann niemals zwei oder mehrere äquivalente Elektronen im Atom geben, für welche in starken Feldern die Werte aller Quantenzahlen $n,k_{1},k_{3},m_{1}$ (oder, was dasselbe ist, $n,k_{1},m_{1},m_{2}$) übereinstimmen. Ist ein Elektron im Atom vorhanden, für das diese Quantenzahlen (im äußeren Felde) bestimmte Werte haben, so ist dieser Zustand “besetzt “.

It is not possible that there are two or more equivalent electrons in an atom for which in strong fields all quantum numbers $n,k_{1},k_{3},m_{1}$ (or equivalent, $n,k_{1},m_{1},m_{2}$) are identical. If there is an electron, which takes (with external applied field) a specific set of quantum numbers, this state is “occupied“.

He states that he cannot give a justification for that rule, but it seems self-evident from nature. He then concludes from thermodynamics and the invariance of statistical weights with respect to adiabatic transformations that the rule also holds for small fields. At the end of the article he states that a deeper understanding of the principles of quantum mechanics are required to understand the assumptions on which his conclusions (on the spectra and level occupation) are based.

However, from a modern point of view, I would say, the Pauli principle refers to the asymmetry of the total wave function; as a consequence two electrons cannot have the same set of quantum numbers, as this would result in a symmetric solution with respect to these two electrons. Mikuszefski (talk) 14:00, 14 September 2010 (UTC)

Thanks for the interesting quote from the original article and also for the translation from German. The comment you answered dates from 2006. The article now says 1925 only, and describes both the quantum number and the antisymmetry versions of the PEP.

It seems from your quote that in 1925 Pauli proposed the concept that each electron has its own set of 4 quantum numbers, using quantum numbers from the old quantum theory. Later, after Schrodinger in 1926 introduced wave functions and the solution for the hydrogen atom, Pauli must have modified the identity of the quantum numbers and added the connection to the antisymmetry of the wave function.Dirac66 (talk) 01:44, 29 September 2010 (UTC)

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)

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

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)

So you're saying that any two open-shell atoms will attract each-other rather than repel? [post by 75.13.90.76]

Not "any two". In the simplest example of two hydrogen atoms, the force depends on the spin states of the two atoms. If the spins are opposite to each other ("paired") the force is attractive, but if the spins are parallel, the force is repulsive. Dirac66 (talk) 13:34, 13 April 2010 (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)

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)

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)

Imaging of Pentacene Molecule

Suggestion: I'm not qualified to write this up, but doesn't the imaging of the pentacene molecule deserve some mention here, since, as I understand it, it depends on the PEP. See http://www.newscientist.com/article/dn17699-microscopes-zoom-in-on-molecules-at-last.html and http://www.sciencemag.org/cgi/content/abstract/325/5944/1110 —Preceding unsigned comment added by 80.176.244.187 (talk) 10:58, 28 August 2009 (UTC)

Spin statistics without relativity

Since nonrelativistically, particles can have any statistics and any spin, there is no way to prove a spin-statistics theorem in nonrelativistic quantum mechanics. But there are "naturalness" assumptions which allow you to argue that the correct spin-statistics relation makes a more elegant theory. These arguments were marketed as a nonrelativistic spin/statistics proof by Berry et al, but they do not constitute a proof, as is well recognized, rather a plausibility argument. In order to have a spin-statistics theorem, you need relativity.Likebox (talk) 19:55, 12 October 2009 (UTC)

I think that your first sentence in the above paragraph provides a simpler and clearer explanation than the text which you put in the article about spin 0 Fermi fields. Would you object to using this sentence (or something similar) in the article instead? Dirac66 (talk) 20:13, 12 October 2009 (UTC)

I don't object--- but the full text above requires a citation to Berry's paper, and I am not sure exactly how best to talk about it. They make this naturalness assumption, which I never really understood how its more natural. I guess it's the statement that the Berry phase acquired by dynamically rotating two particles around each other is the same as the kinematic phase for rotating two particles, which would give you a spin-statistics relation, but I don't know exactly why it is more natural than wrong spin-statistics.Likebox (talk) 22:06, 12 October 2009 (UTC)

I think the article is best with just the first sentence above as you have it now. This is a simple statement accessible to readers who have only nonrelativistic QM, even in a chemistry course. Thanks.

Berry's argument is probably too complex for this article. Since you have brought it up here though, perhaps you could put the full reference on this talk page (though NOT in the article).Dirac66 (talk) 22:46, 12 October 2009 (UTC)

(deindent) It's Berry, M.V., Robbins, J.M.: Indistinguishability for quantum particles: spin, statistics and the geometric phase. Proc. R. Soc. Lond. A, 453:1771-1790 (1997). I skimmed the argument, and I remember the main point. It is no way a proof of spin-statistics, but it argues that spin-statistics is natural if you take a type of tangent bundle structure on the configuration space.

The idea is that when you are looking at N spinning particles, you define the spin direction not relative to fixed static coordinate axes, like people have been doing since time immemorial, but relative to the positions of the other particles. Then you get the following obviousness: when two particles switch position by rotating around each other in some plane, if you move the mobile axes along with the rotations keeping the spins of the particles fixed, the spins make a half-turn each with respect to the mobile axes. So when the spins are unchanged relative to the global axis, the spin relative to each other gets a phase in the mobile axis which is equal to -1 for Fermions and +1 for Bosons (because it's one full turn). If you then demand that the wavefunction is single valued in this particular way under swaps, you get spin-statistics.

This is a bastardization of the relativistic argument which relates swapping to rotation, but without using the all-important imaginary time rotations. It's not mathematically wrong the way they do it, but it seems silly. The configuration space of N indistinguishable particles is a weird looking wedge if you want to count each configuration once and only once. If you don't do the moving frame business, the same condition of single valuedness would tell you that all particles are bosons, so the condition they give isn't natural at all.

If you use a normal fixed non-comoving frame, the condition of "single-valuedness" requires pasting the wavefunction in the different sectors with sign-changes along the boundaries which are glued. That's not any less natural than co-moving frames--- the wavefunction is defined as a section of an equivalent fiber bundle either way. Either the bundle is glued with trivial gluing but with phases defined along moving coordinate frames, or it is glued with sign-changes with non-moving coordinate frames. It's the same bundle. I mean, the fact that co-moving frames exist and give you the right answer is slightly interesting, if it's true. That would mean that you can define the comoving frame for N particles in some continuous way, but they don't do it for more than three particles in the original paper, and they don't do it in more than three dimensions.Likebox (talk) 01:53, 13 October 2009 (UTC)

Yes, too complex for this article, and not really relevant since it's not a real proof. So let's leave it with the (your) current statement that NR particles can have any statistics and any spin so there is no spin-statistic theorem for NR QM. Dirac66 (talk) 02:44, 13 October 2009 (UTC)

This discussion is very interesting, however I don't think it should be in the lead. The paragraph makes absolutely no sense to non-experts (Which it should). Please put i in the main article somewhere-thanks--Thorseth (talk) 12:49, 19 May 2010 (UTC)

I have now moved the part on relativistic QFT down to a new subsection on the Pauli principle in advanced quantum theory, where the word "advanced" is meant to suggest "skip this part if you wish". The subsection can probably be improved, but I agree with Thorseth that it should not be in the lead. Dirac66 (talk) 14:47, 19 May 2010 (UTC)

The Big Bounce

Peter Lynds has been promoting the idea of a cyclic universe where singularities are not allowed. He never explains why. And he may be wrong as far as black holes inside the Universe. Is it possible that PEP comes into play if a black hole becomes too big? By this, I mean would gravity ever become so powerful that it would try and force particles to occupy the same space - the resulting interaction would cause a bounce effect where the Exclusion Principle would force the black hole to explode. As to Lynd and his cyclic universe theory a universe size big crunch may offer this type of showdown between gravity and particles occupying the same space. Comments? --Dane Sorensen (talk) 13:39, 27 November 2009 (UTC)

(I have moved this new section to the end of the talk page.)
But does Peter Lynds explicitly relate the PEP to his ideas? Your wording suggests that it is your own speculation, in which case it is "original research" which is not allowed on Wikipedia - see WP:NOR. It may or may not be valid, but it has to be published elsewhere before it gets into Wikipedia. Dirac66 (talk) 14:17, 27 November 2009 (UTC) Yes, that is why it is in discussion. My speculations do not belong in a formal article. PEP has not been brought down to the level of quarks. We do not know if a PEP force exists for the smaller parts of matter. Perhaps the Hadron Collider will answers those questions. However, I may be wrong and some better educated person can add facts to the notion and expand this article on PEP as well as Lynds theory. --Dane Sorensen (talk) 01:34, 28 November 2009 (UTC)

Finite vs. infinite repulsion

The results of the Bethe ansatz do not map to a free Fermi gas unless the delta functions repulsion of the one-dimensional bosons are infinitely strong. The bose-fermi map in the case of finite delta-repulsion does not provide a solution in this case, since both theories are interacting. The Bethe Ansatz article can include the nonlinear schrodinger equation as an example, of course, but this article is somewhat more elementary.Likebox (talk) 23:37, 2 December 2009 (UTC)

Technical

This article is extremely technical. I cannot make sense of it :( 67.204.204.104 (talk) 07:19, 17 January 2010 (UTC)

(Placed new section at end.) Yes, the article describes an aspect of quantum mechanics which is not easy to simplify. I have re-ordered the intro paragraph to start with electrons in atoms as the most elementary case, and also explained the word fermions (in addition to the link provided). I encourage other editors also to try to simplify or explain further. Dirac66 (talk) 21:46, 17 January 2010 (UTC)

History

the Lewis paper link that follows is broken :

http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Lewis-1916/Lewis-1916.html

here's something maybe a replacement :

http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/papers/corr216.3-lewispub-19160400.html

or even better, the original jacs abstract (full-text requires subscription):

http://pubs.acs.org/doi/abs/10.1021/ja02261a002

Stability of matter, first paragraph

Tomdo08 (talk) 09:38, 29 August 2010 (UTC) -- The first two sentences of the first paragraph in Pauli exclusion principle#Stability of matter ("The stability of the electrons in an atom itself is not related to the exclusion principle, but is described by the quantum theory of the atom. The underlying idea is that close approach of an electron to the nucleus of the atom necessarily increases its kinetic energy, an application of the uncertainty principle of Heisenberg.") do not make much sense:

• What does "stability of the electrons in an atom" mean? Obviously not the stability of the separate orbitals against each other which is explained (partly) by PEP (see next paragraphs in article). Also not the stability of an electron against some decay. So it could mean not falling into the nucleus. But calling that "stability of the electrons in an atom" is at least misleading.
• It is not necessary to use the uncertainty principle for the increase of kinetic energy coming with a close approach, simple newtonian physics is sufficient.
• An increase in kinetic energy explains nothing, because that energy could be get lost by emitting a photon. Maybe the necessity of a minimum momentum range and therewith speed range is meant because of the higher certainty about location.
• Still this is no explanation: How then do protons and neutrons stay in the nucleus? Maybe the low mass of the electron is part of the explanation: low mass means higher speed to momentum relation.
• Even with a high speed range an electron location range could overlap with the nucleus (what actually would mean being in the nucleus). But lower mass means also higher energy to momentum relation. It could actually mean there is an energy barrier.
• The barrier at least would be an explanatory hypothesis. But is it sufficient? The barrier has to be high and wide enough to prevent frequent overcoming and tunneling. Is that the case?

I could calculate that, but all this could be called original research. Therefore someone with a book at hand should rewrite that part of the paragraph. If my deduction is correct, the explanation should include the uncertainty principle, the low mass of the electron, the energy barrier and the sufficient hight and wideness.

The last sentence ("However, stability of large systems with many electrons and many nuclei is a different matter, and requires the Pauli exclusion principle.") is even more a riddle:

• "Many electrons" could relate to the separate electron orbitals in a atom. But that is better explained in the next paragraph.
• What does the "many nuclei" part relate to? To the fact that hulls of different atoms cannot overlap? That would be a misnomer and should be explained better anyway.
• There are other electron systems one could think about, but that should be better defined to be useful. At least the overlapping of position or the identity of attributes should be referenced in some way.

Tomdo08 (talk) 09:38, 29 August 2010 (UTC)

Maybe the explanation for electrons not falling into the nucleus (part of the stability of an atom) should be placed somewhere else and referenced here. Maybe it could be put into Atom; maybe a new article about electron hulls or matter stability would be right. -- Tomdo08 (talk) 09:48, 29 August 2010 (UTC)

I suggest that the first sentence be re-written to talk about why the electron of a single hydrogen atom does not fall into its nucleus. That does not use the PEP. Rather for non-relativistic electrons the (negative) potential energy goes as O(1/r) and the (positive) kinetic energy [E=p^2/2m] goes as O(1/r^2) as r->0. Consequently, the energy has a minimum at some radius 0<r<+∞. This uses the fact that due to the uncertainty principle the absolute value of the momentum must be at least of O(1/r) and kinetic energy is proportional to the square of that.

For bulk matter, the volume available to an electron is 2V/N where V is the total volume and N is the number of electrons. Here PEP is used to show that the electrons of the same spin cannot share space. Then the previous argument applies to show that a balance between kinetic and potential energy requires a non-zero size.

The last two sentences of the section should be dropped. Formation of bosons is not required to explain black holes. When the attractive force becomes strong enough, the electrons become relativistic, in which case, the kinetic energy [E=pc-mc^2] goes as O(1/r) instead of O(1/r^2). So potential energy can win out over kinetic energy at any radius, and nothing stops collapse. Eventually, electrons and protons combine to form neutrons to reduce the kinetic energy. But even PEP between neutrons cannot avert collapse when the force is strong enough. JRSpriggs (talk) 20:58, 29 August 2010 (UTC)

This section is essentially based on Lieb's article (reference 3). The first paragraph is an attempt to simplify material from Lieb, sections 2.1 and 2.2. Perhaps it can be better explained, but any changes should still be based on Lieb unless some other source is given. Dirac66 (talk) 15:02, 31 August 2010 (UTC)

Content from deleted comment subpage

Something I don't understand about PEP. Does PEP only apply inside atoms, or is it applicable to particles within a certain distance of each other (maybe a Plank something?). How far is the reach? If PEP only applies inside atoms, then what is so unique about that arrangement of particles (i.e. why?)EdEveridge (talk) 18:29, 13 September 2009 (UTC)