Rethinking the Pauli Exclusion Principle by Paul O\'Hara

Dear Prof. O'Hara

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

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.

For details see my essay http://fqxi.org/community/forum/topic/1413

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

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

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

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

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: Alice, Bob and Charley are standing at three different locations on a plane. Alice is asked to choose her right hand and rotate it in a clockwise direction, Bob is asked to face Alice and to rotate his hand in the same direction as Alice. As it will now turn out, his motion is counter clockwise. Each one is now asked to continue with their hand motion but to face towards Charley who is then asked to take his right hand and rotate in the same direction as the other two. As it turns out it cannot be done, When he faces Alice he will see a counter clockwise motion and when he faces Bob he will see a clockwise motion. What was originally the same direction of motion for Alice and Bob are now opposite motions for Charley. This is the essence of the Bell's inequality as I use it in the essay. One can consistently define the same direction of rotation between two observers but in general not for three. For this reason ISC states can only occur in pairs.

(2) I do not agree that the Boscovich "axiom of impenetrability" is equivalent to the Pauli exclusion principle. As I understand it the Boscovich axiom states that no two particles can occupy the same position in space simultaneously. This indeed, is an exclusion principle and I agree with it. However, it has nothing to do with the spin-statistics theorem and the Pauli exclusion principle. Two mesons obeying Bose-Einstein statistics will never be in the same position simultaneously but yet can have a completely symmetrical wave function corresponding to the Bose-Einstein statistic.

(3) I also like Joy Christians approach as a way of resolving the never ending debate between the hidden parameter versus the Copenhagen interpretations of QM, and I think my own work here supports that (you might also want to look at my arXiv article SU(2) Relativity and the EPR Paradox quant-ph/0609126). I think you have to distinguish between the use of Bell's inequality as a means to discern between two different philosophical positions (naive realism versus Copenhagen) and Bell's inequality as a simple mathematical triangular inequality stemming from using a particular probability structure associated with rotational invariance. I used Bell's inequality in a strictly mathematical sense to set up a proof by contradiction. I simply noted that if three ISC particles were to exist then a mathematical contradiction would arise. Consequently, three or more such particles cannot exist. Indeed, I think Christian is doing something similar. Based on Bell's inequality, he dismisses what he perceives as an incorrect understanding of hidden variables by interpreting hidden variables as real numbers and then develops an alternative explanation based on Clifford numbers that obey the Grassman relation ab=a.b+a^b. I agree with him. I do not think that Christenson is questioning Bell's mathematical derivation of his inequality but rather the assumptions that he made about hidden variables that permitted him to derive such an inequality in the first place. What Christenson is essential saying is that if Bell's assumptions about hidden variables give rise to such an inequality then by contradiction the assumptions must be false. Consequently, there must be another way of interpreting hidden parameters that makes sense and he then proceeds to develop an alternative and consistent interpretation based on Clifford numbers. Similarly, I have done the same thing in using Bell's inequality to affirm the existence of paired particles and nothing else.

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

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

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 relevant. My theory considers this serie of uniquness , and so with its quantum serie of numbers, for the fermions but also for the bosons.

It becomes relevant when we consider the frequences of oscillations correlated with the rotating spherical volumes.see the debroglie equation with the volumes and the serie of uniqueness'universal furthermore for the two 3d scales, quant.and cosmol.

In fact that depends of what we want to interpret.In fact the pauli principle is a good tool.Now when we play with the limits, the domains, the parameters, the substitutions, settings, or superimposings or this or that, it becomes relevant when we make a kind of taxonomy.

Now of course the derivations and integrations more limits more this and that can showing the rational road.

My equations and my theory permits to see better when the groups of the uniqueness and finite and precise.The volumes from the main central sphere become very relevant and proportional with rotations and stabilities also.

The bosons are like a foto of our fermions but they turn simply in the opposite sense. The density, the mass and the volumes become so very important.If we apply the BES apllied to photons, we can with the striling approximation finding....lagrangian multipliers and we continue in a pure thermodynamical closed evolutive sphere and its central sphere, the number 1.and we have so the planck radiation equation at my knowledge.The entropy takes all its meaning in fact. Its steps of disponible energies also.

Here is an important thought. We can consider the dual system for fermions, so with their encoded bosons.(see the volumes and rotations spinal and orbital), the principle of Pauli is relevant. Now we know that two solutions are possible, 1 the fusioned system with increasing in density and correlated volumes.or 2 a binar system. In all case the system of fermions possesses both of them. But the bosons in their pure linearity, no ! The spectral energy density so is very complex and its fractalization of heat.correlated with rotating spherical volumes.

So the puzzle is not simple, that said, the pauli principle permits the good classment. In differenciating so the fermions and the bosons indeed but also the bosons encoded in these fermions !!! It is totally different about the quantum number !!!

ps the 3D is essential.....the 2 d is just for our computing ! the ferlions and bosons are purelly in 3D. now of course the convergences can be very relevant !

Best Regards

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

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

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 particle)is not anti-symmetric under a change of variables. Indeed, by default the wave function for a single particle is symmetric. In reality one does not associate statistics with a single particle. Statistics begins with at least two partcles. It is an unfortunate misuse of terms that an electron is referred to as a "fermion." This is a consequence of the assertion that indistinguishable partcles with half-integral spin obey Fermi-Dirac statistics. Consequently, electrons were called "fermions." However, it was (and still is) a misuse of the term. A single particle is neither a fermion nor a boson. When people refer to electrons as fermions, what they are saying is that electrons will exhibit Fermi-Dirac statistics when they interact with other electrons. A single electron can only be referred to as a fermion in this context, otherwise it is a meaningless expression. Moreover, in the context of my essay, I have pointed out that the key to Pauli's original paper was not (and should not be) spin value but rather the anti-commutivity of the correlated spin operators associated with entanglred particles. Moreover, the spin value of the particle does not play any essentail role for determining the statistics in the case of a rescaled spin angular momentum operator. My result takes Pauli's work one step further by showing that entanglement is at the core of his own algebraic work. I think it fits in very well with the theme of the competition in tems of what principle of physics need to be re-thought.

(2) As far the second question, I think you have misunderstood what I am claiming. First of all Bell's inequality is nothing more than a triangle inequality stemming from the SU(2) properties associated with spin. My method of proof was a simple "proof by contradiction." I simply showed that the SU(2) properties associated with quantum spin violates Bell's inequaity in the case of 3 or more ISC particles. Consequently, nature only allows for two ISC particles which obey the properties of quantum (non-cummutative) probabilities. Indeed , to use your terminolgy what I am showing is that for completely indistinguisable particles those which obey classical (Kolmogoravian) probabilities obey the Bose-Einstein statistic while those indistinguisable particles that obey quantum probabilies (non commutative spin relations) obey the Fermi-Dirac statistics.

I hope this clarifies your observations and questions.

Paul

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?

I start from above mentioned idea and finished with this essay

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

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?

For better clarification my approach

I sending to you Frank Wilczek's 3 keen articles

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits388.pdf

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits393.pdf

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits400.pdf

All the best

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