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FQXi FORUM

May 22, 2019

CATEGORY:
Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Rethinking the Pauli Exclusion Principle by Paul O'Hara [refresh]

TOPIC: Rethinking the Pauli Exclusion Principle by Paul O'Hara [refresh]

In this essay, quantum entanglement is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. This in turn requires that we rethink the usual formulation of Pauli's original spin-statistics theorem. Finally, some experimental evidence is presented to justify the approach.

Paul O'Hara is Prof. of Mathematics at Northeastern Illinois University, Chicago. He holds a Ph.D. in Mathematics from UCLA (1991), an M.S. in Mathematical Physics, from University College Dublin (1975), and an MA in systematic theology from Catholic Theological Union, Chicago (2009). His main research interests are related to foundational questions in mathematics, physics and philosophy. He has given over 25 international presentations on mathematical physics, foundations of physics and on religion/philosophy/science. He is a member of the international standing committee for the International Association for Relativistic Dynamics (2004- ).

Dear Prof. O'Hara

I am agree with you that Pauli Exclusion Principle not valid, but only if space is 2D.

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I am agree with you that Pauli Exclusion Principle not valid, but only if space is 2D.

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Actually my proof is also valid in 3-D, although it relies on exploiting the rotational invariant properties of ISC particles in a plane (2-D). In effect if three ISC particles exist in 3-D then one can always choose to make three different spin measurements in the same plane, which will result in a mathematical contradiction associated with Bell's inequality (see essay). Consequently three ISC particles cannot exist in 3-D. I do agree however that because of the presence of the azimuthial angle in 3-D the only ISC states that can occur will be singlet states. In effect this strengthens my case and will guarantee that the Fermi-Dirac statistic has an anti-symmetrical wave function.

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Dear Paul

My first essay based on twin analogy between Pauli principle and non-euclidean geometry.

http://www.fqxi.org/community/forum/topic/946

Can you clarify for me question:

Does analogy lost its validity after your reconsidering Pauli's principle?

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My first essay based on twin analogy between Pauli principle and non-euclidean geometry.

http://www.fqxi.org/community/forum/topic/946

Can you clarify for me question:

Does analogy lost its validity after your reconsidering Pauli's principle?

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Paul

While I didn't agree with all of your thesis I certainly agree with it's principles, and that you point towards a much better understanding. My lack of full agreement probably only arises from poor understanding.

Can you, on consideration find any potential links between the subject of your work and the following;

1. The twin vortex model forming the toroid, as active galactic nuclii (AGN's) (or SMBH's), and found at smaller scales, also used in fusion as the Tokamak.

2. The Boscovich 'axiom of impenetrability', which is equivalent to an exclusion principle in that no two entities can occupy the same 'space' at one instant (one space-time point). In my own essay I find this infers that a single and exclusive 'state of relative motion' K can be assigned to any system.

3. Joy Christians proof of the shortcomings of Bells inequalities (see also Tom Ray's essay), which I support and evidence from an logical and entirely locally real viewpoint and a mechanism for unification.

Many thanks. Excellent essay.

Peter

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While I didn't agree with all of your thesis I certainly agree with it's principles, and that you point towards a much better understanding. My lack of full agreement probably only arises from poor understanding.

Can you, on consideration find any potential links between the subject of your work and the following;

1. The twin vortex model forming the toroid, as active galactic nuclii (AGN's) (or SMBH's), and found at smaller scales, also used in fusion as the Tokamak.

2. The Boscovich 'axiom of impenetrability', which is equivalent to an exclusion principle in that no two entities can occupy the same 'space' at one instant (one space-time point). In my own essay I find this infers that a single and exclusive 'state of relative motion' K can be assigned to any system.

3. Joy Christians proof of the shortcomings of Bells inequalities (see also Tom Ray's essay), which I support and evidence from an logical and entirely locally real viewpoint and a mechanism for unification.

Many thanks. Excellent essay.

Peter

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Peter,

Your questions are indeed very interesting. Since there are three of them, I will take each one separately.

(1) Based on your comments, I have tried to think of some type of geometrical structure using a toroid but I have not been able to come up with anything. I am open to your suggestions. Instead consider the following which you might be able to adapt for the vortex model:...

view entire post

Your questions are indeed very interesting. Since there are three of them, I will take each one separately.

(1) Based on your comments, I have tried to think of some type of geometrical structure using a toroid but I have not been able to come up with anything. I am open to your suggestions. Instead consider the following which you might be able to adapt for the vortex model:...

view entire post

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Paul

I'm not an expert on Hopf fibration but there are good analogies with the toroid basis (1) you may like. I think my point was that if you take two opposing vortices joined at the cusp you have the 'business end' of a torus, the fundamental form of the em field of all bodies of mass. As an astronomer I know how universal they are in the cosmos, from the Crab nebula core (see the NASA shots) to AGN's (SMBH's). If you're not quite with me, buy a krispy kreme and just eat the outer half of the ring all round. Then you have paired vortices. I agree, just one vortex, or half a donut can't even be formed.

(2) I see the difference. I've found the spatial exclusion of masses and thus the kinetic state of each of fundamental importance. It means 'inertial frames' can be mutually exclusive spatially, unless they're not associated with matter (rare I assume!) This is quite unique and seminal. Consistent with the fact that motion is invalid in geometry, both then suggesting that interlocking 'wire frame' Cartesian systems in vector space (Geometry) may not map accurately back to reality (see Wharton essay).

(3) This may shock but I've proposed a 'hidden variable' giving Local Reality consistent with the Copenhagen interpretation! i.e. the Moon as we know it isn't there if no lens is interacting with it's light, and the quantum mechanism of interaction (varying the photon/wave characteristics) directly derives the effects encapsulated in the postulates of Special Relativity, which looks somewhat like unification.

I'm not beyond the level of Fahmi's essay on Bell etc. as I'm focussed on conceptual kinetics so your arXiv paper may be beyond me. But I hope you may read my essay and tell me where it was I went wrong! (apart from dropping some old assumptions and using more logically consistent ones).

Many thanks

Peter

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I'm not an expert on Hopf fibration but there are good analogies with the toroid basis (1) you may like. I think my point was that if you take two opposing vortices joined at the cusp you have the 'business end' of a torus, the fundamental form of the em field of all bodies of mass. As an astronomer I know how universal they are in the cosmos, from the Crab nebula core (see the NASA shots) to AGN's (SMBH's). If you're not quite with me, buy a krispy kreme and just eat the outer half of the ring all round. Then you have paired vortices. I agree, just one vortex, or half a donut can't even be formed.

(2) I see the difference. I've found the spatial exclusion of masses and thus the kinetic state of each of fundamental importance. It means 'inertial frames' can be mutually exclusive spatially, unless they're not associated with matter (rare I assume!) This is quite unique and seminal. Consistent with the fact that motion is invalid in geometry, both then suggesting that interlocking 'wire frame' Cartesian systems in vector space (Geometry) may not map accurately back to reality (see Wharton essay).

(3) This may shock but I've proposed a 'hidden variable' giving Local Reality consistent with the Copenhagen interpretation! i.e. the Moon as we know it isn't there if no lens is interacting with it's light, and the quantum mechanism of interaction (varying the photon/wave characteristics) directly derives the effects encapsulated in the postulates of Special Relativity, which looks somewhat like unification.

I'm not beyond the level of Fahmi's essay on Bell etc. as I'm focussed on conceptual kinetics so your arXiv paper may be beyond me. But I hope you may read my essay and tell me where it was I went wrong! (apart from dropping some old assumptions and using more logically consistent ones).

Many thanks

Peter

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Dear Paul O'Hara,

I think, coupling of isotropically spin-correlated 0-D particles may represent 1-D strings and may emerge with 3-D tetrahedral-branes by eigen-rotations. Coupling of anisotropically spin-correlated particles also may be included for the continuum of strings.

With best wishes,

Jayakar

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I think, coupling of isotropically spin-correlated 0-D particles may represent 1-D strings and may emerge with 3-D tetrahedral-branes by eigen-rotations. Coupling of anisotropically spin-correlated particles also may be included for the continuum of strings.

With best wishes,

Jayakar

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Dear Jayakar,

Thank you for your observation. I am not an expert in string theory but I think your comments are probably correct. In 2008, I gave a presentation at the Spinstat08 Conference in Trieste, Italy entitled Rotational invariance and the spin-statistics theorem. Some of the participants who were string theorists commented favorably on my work indicating that it confirmed string theory results.

Paul

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Thank you for your observation. I am not an expert in string theory but I think your comments are probably correct. In 2008, I gave a presentation at the Spinstat08 Conference in Trieste, Italy entitled Rotational invariance and the spin-statistics theorem. Some of the participants who were string theorists commented favorably on my work indicating that it confirmed string theory results.

Paul

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Dear Paul O'Hara,

I very much enjoyed your essay, and I agree that it's entanglement that is responsible for the Pauli Exclusion Principle. I invite you to read my essay, The Nature of the Wave Function, with emphasis on the circulation diagram (2) on page 2 and 'orbital' diagrams at the bottom of page 5. If we consider two electrons in orbit, and assume that their same-charge repulsion tends to maximize their separation, we see that the circulation of the field interferes either constructively or destructively. If constructive, then the local particle 'spin's are opposite as required to ensure the same 'handedness' of the wave circulation.

Key to this of course is the interpretation of the wave function as based on a physically real wave, in agreement with de Broglie [and Bell] and with recent experimentation and theoretical [PBR] 'no-go' theorems.

If we reverse the spin direction of either particle, then destructive interference results. This is why, as you mention, we can have mathematical 'same spin' configurations but this does not take into account the real physical nature of the wave function. As you end up concluding, it is the spin coupling rather than the spin value that underlies the Pauli Exclusion Principle. Your discussion of Pauli's use of spin values is enlightening.

Finally, you appear to be correct that Pauli's "imposition of such extra conditions would seem to be unnecessary in the light of the appproach based on...coupling".

I look forward to any comments you might have on my model.

Best of luck in the contest.

Edwin Eugene Klingman

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I very much enjoyed your essay, and I agree that it's entanglement that is responsible for the Pauli Exclusion Principle. I invite you to read my essay, The Nature of the Wave Function, with emphasis on the circulation diagram (2) on page 2 and 'orbital' diagrams at the bottom of page 5. If we consider two electrons in orbit, and assume that their same-charge repulsion tends to maximize their separation, we see that the circulation of the field interferes either constructively or destructively. If constructive, then the local particle 'spin's are opposite as required to ensure the same 'handedness' of the wave circulation.

Key to this of course is the interpretation of the wave function as based on a physically real wave, in agreement with de Broglie [and Bell] and with recent experimentation and theoretical [PBR] 'no-go' theorems.

If we reverse the spin direction of either particle, then destructive interference results. This is why, as you mention, we can have mathematical 'same spin' configurations but this does not take into account the real physical nature of the wave function. As you end up concluding, it is the spin coupling rather than the spin value that underlies the Pauli Exclusion Principle. Your discussion of Pauli's use of spin values is enlightening.

Finally, you appear to be correct that Pauli's "imposition of such extra conditions would seem to be unnecessary in the light of the appproach based on...coupling".

I look forward to any comments you might have on my model.

Best of luck in the contest.

Edwin Eugene Klingman

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Edwin,

I really appreciate your very encouraging comments and observations. I have been reading through a lot of essays but have not gotten to yours yet, but hope to do so in the next few days. I will then give you feedback.

Paul

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I really appreciate your very encouraging comments and observations. I have been reading through a lot of essays but have not gotten to yours yet, but hope to do so in the next few days. I will then give you feedback.

Paul

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Hello Mr.O'Hara,

It is an interesting method in the respect of the laws of our themrodynamics. That said I like the principle of Pauli.

The fermions are under this law. Like for the fermi dirac statistics. If the primes are inserted for the quantum number and if the volumes of spheres considering the uniqueness are inserted with the rotations spinal and orbital. So it becomes very...

view entire post

It is an interesting method in the respect of the laws of our themrodynamics. That said I like the principle of Pauli.

The fermions are under this law. Like for the fermi dirac statistics. If the primes are inserted for the quantum number and if the volumes of spheres considering the uniqueness are inserted with the rotations spinal and orbital. So it becomes very...

view entire post

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Dear Paul,

You make a very interesting and suggestive connection between your coupling principle associated with entanglement, and the Pauli exclusion principle. In the case of just one electron, there is no coupling, however the electron obeys Fermi statistics. Would this mean that behind your coupling principle there is something more fundamental?

Just a brief comment: Bell’s inequality is a strictly mathematical relation, referring to classical (Kolmogorovian) probabilities, while the quantities appearing in quantum inequalities derived for entangled states (such as your inequality on p. 4) do not necessarily enjoy these properties.

All the best,

Luis, Ana María and Andrea

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You make a very interesting and suggestive connection between your coupling principle associated with entanglement, and the Pauli exclusion principle. In the case of just one electron, there is no coupling, however the electron obeys Fermi statistics. Would this mean that behind your coupling principle there is something more fundamental?

Just a brief comment: Bell’s inequality is a strictly mathematical relation, referring to classical (Kolmogorovian) probabilities, while the quantities appearing in quantum inequalities derived for entangled states (such as your inequality on p. 4) do not necessarily enjoy these properties.

All the best,

Luis, Ana María and Andrea

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Would this mean that behind your coupling principle there is something more fundamental?

The volumes perhaps dear Luis, Ana and Andrea. The coupling principle is relevant when the volumes of the serie of uniqueness are taken into account.

binar or fusioned more the steps of stabilities due to volumes of the serie of uniqueness begining form the main central sphere.

Regards

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The volumes perhaps dear Luis, Ana and Andrea. The coupling principle is relevant when the volumes of the serie of uniqueness are taken into account.

binar or fusioned more the steps of stabilities due to volumes of the serie of uniqueness begining form the main central sphere.

Regards

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Luis, Ana Maria and Andrea,

Thank you for your comments and questions. I will answer each one separately.

(1) I disagree that a single electron is a fermion, even in the "old" way of looking at things. Fermions are defined as particles that obey Fermi-Dirac statistics, and have always been associated with an anti-symmetric wave-function. A wave function for a single electron (or any...

view entire post

Thank you for your comments and questions. I will answer each one separately.

(1) I disagree that a single electron is a fermion, even in the "old" way of looking at things. Fermions are defined as particles that obey Fermi-Dirac statistics, and have always been associated with an anti-symmetric wave-function. A wave function for a single electron (or any...

view entire post

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Dear Paul

Major propositions in physics connected with notion"the same"

for example:

1.Einstein's relativity of simultaneity. The same time doesn't exist...

2 Heisenberg's uncertainty. The same time can't to measure....

3.Pauli's exclusion principle. The same energetic level only one fermion....

It seems to me very interesting.

Somebody thought of that?

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Major propositions in physics connected with notion"the same"

for example:

1.Einstein's relativity of simultaneity. The same time doesn't exist...

2 Heisenberg's uncertainty. The same time can't to measure....

3.Pauli's exclusion principle. The same energetic level only one fermion....

It seems to me very interesting.

Somebody thought of that?

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I start from above mentioned idea and finished with this essay

http://fqxi.org/community/forum/topic/1413

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http://fqxi.org/community/forum/topic/1413

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For better clarification my approach

I sending to you Frank Wilczek’s 3 keen articles

http://ctpweb.lns.mit.edu/physics_today/phystoday/Ab

s_limits388.pdf

http://ctpweb.lns.mit.edu/physics_today/physt

oday/Abs_limits393.pdf

http://ctpweb.lns.mit.edu/physics_toda

y/phystoday/Abs_limits400.pdf

All the best

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I sending to you Frank Wilczek’s 3 keen articles

http://ctpweb.lns.mit.edu/physics_today/phystoday/Ab

s_limits388.pdf

http://ctpweb.lns.mit.edu/physics_today/physt

oday/Abs_limits393.pdf

http://ctpweb.lns.mit.edu/physics_toda

y/phystoday/Abs_limits400.pdf

All the best

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I read your comments and also your essay. Very interesting. Thank you for the input.

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Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

report post as inappropriate

I am surprised that there is no reference to Luminet articles

They are very close to you

arXiv:astro-ph/0310253 [pdf, ps, other]

arXiv:astro-ph/0501189 [pdf, ps, other]

arXiv:astro-ph/0005515 [pdf, ps, other]

arXiv:astro-ph/9903155 [pdf, ps, other]

arXiv:gr-qc/9604050 [pdf, ps, other]

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They are very close to you

arXiv:astro-ph/0310253 [pdf, ps, other]

arXiv:astro-ph/0501189 [pdf, ps, other]

arXiv:astro-ph/0005515 [pdf, ps, other]

arXiv:astro-ph/9903155 [pdf, ps, other]

arXiv:gr-qc/9604050 [pdf, ps, other]

report post as inappropriate

Dear Paul O'Hara,

you have chosen an unusual false assumption to consider. Which makes your essay stand out from many others I have read. It seems written in a clear and accessible way. I don't know anything about Pauli's original spin-statistics theorem, so its not surprising I don't really appreciate the significance of the alteration of the interpretation, as you have proposed.Still, I am glad to have had the opportunity to read your essay about this interesting subject.

Given your impressive biography and particular interest in foundational issues I would very much appreciate it if you could take a look at my essay and in particular the explanatory framework used to answer the set question. (There is a high resolution version in my essay discussion thread.)

Good luck in the competition, Kind regards Georgina.

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you have chosen an unusual false assumption to consider. Which makes your essay stand out from many others I have read. It seems written in a clear and accessible way. I don't know anything about Pauli's original spin-statistics theorem, so its not surprising I don't really appreciate the significance of the alteration of the interpretation, as you have proposed.Still, I am glad to have had the opportunity to read your essay about this interesting subject.

Given your impressive biography and particular interest in foundational issues I would very much appreciate it if you could take a look at my essay and in particular the explanatory framework used to answer the set question. (There is a high resolution version in my essay discussion thread.)

Good luck in the competition, Kind regards Georgina.

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Dear Paul,

Splendidly written essay! It seems obvious after reading it that entanglement, and not locality, should be the crux of the matter, but I never thought of it in exactly this way before.

1. An obvious naïve question is why, then, the “elementary” fermions do in fact have half-integer values. This would be obvious for any particular particle, but maybe not so clear why it should always be true.

2. It seems like the experiment you suggest on page 8 involving deuteron ions ought to be easily doable. Is there some technical difficulty associated with this that I’m unaware of? If not, are there any plans to do such an experiment?

3. I wonder if there is some deep representation-theoretic principle at stake here?

4. Relaxation of the “extra conditions” (Lorentz invariance, locality) imposed in regard to Pauli’s version of the spin-statistics theorem is of particular interest to me. Explaining why is a long story… suffice it to say that reinterpretations of these conditions are central to my own speculative ideas about fundamental physics. If you’re interested, you’re welcome to read my essay here!

I enjoyed reading your work. Good luck in the contest, and take care,

Ben Dribus

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Splendidly written essay! It seems obvious after reading it that entanglement, and not locality, should be the crux of the matter, but I never thought of it in exactly this way before.

1. An obvious naïve question is why, then, the “elementary” fermions do in fact have half-integer values. This would be obvious for any particular particle, but maybe not so clear why it should always be true.

2. It seems like the experiment you suggest on page 8 involving deuteron ions ought to be easily doable. Is there some technical difficulty associated with this that I’m unaware of? If not, are there any plans to do such an experiment?

3. I wonder if there is some deep representation-theoretic principle at stake here?

4. Relaxation of the “extra conditions” (Lorentz invariance, locality) imposed in regard to Pauli’s version of the spin-statistics theorem is of particular interest to me. Explaining why is a long story… suffice it to say that reinterpretations of these conditions are central to my own speculative ideas about fundamental physics. If you’re interested, you’re welcome to read my essay here!

I enjoyed reading your work. Good luck in the contest, and take care,

Ben Dribus

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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You mainstreamsians controle science for over 50 years. You mainstream and Hawking failed. The bad science is because of the Top-Down controle of the people like you. Why do you need money and fame from FQXI where the authors are mostly jobless, are mostly independent researchers, are mostly viXra.org authers? Do you need money and fame by controling jobless???

I want to rate you 0!

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I want to rate you 0!

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