# Topological solitons of ellipsoid field - our particle menagerie correspondence?

Discussion in 'Pseudoscience Archive' started by Jarek Duda, Feb 12, 2011.

1. ### Jarek DudaRegistered Senior Member

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Looking at electron, there is singularity of electric field in it - its values seem to tend to infinity, but also directions create topological singularity ...
This picture suggests that maybe we don't need some additional (out of field) entities for particles, but this construction of field itself is the electron - that particles are some characteristic localized constructs of the field, maintaining their structures/properties - are solitons.
Skyrme used such constructions to model baryons, they automatically give particles masses (rest energy), allows for various number of particles because of annihilation/creation, there is corresponding attraction/repelling for opposite/the same ones, they have integer 'quantum numbers' ...
For example here is nice animation of soliton/antisoliton annihilation which released energy gathered in them (mass) as analogue of photons:
http://en.wikipedia.org/wiki/Topological_defect

Anyway, the perfect situation would be finding a field which family of topological soltions corresponds well to the whole particle menagerie with their properties, decays, dynamics ... and which dynamics became electromagnetism and gravity far from particles (vacuum state).
It occurs that extremely simple field: ellipsoid field surprisingly well qualitatively fulfills these requirements - just a field of real symmetric 3*3 (4*4) matrices, which prefers some set of eigenvalues - it can be seen as stress tensor or as less abstract skyrmion model, but with Higgs-like potential (with topologically nontrivial minimum) or as expansion of ellipse field of light polarization concept (considered by 'singular optics').
Rotating ellipse/ellipsoid by 180deg we get the initial situation, so the simplest constructions of such field have spin 1/2, like in this demonstration allowing also to see attraction/repelling caused by minimizing variousness of the field: http://demonstrations.wolfram.com/SeparationOfTopologicalSingularities/
In ellipsoid field in 3D we can choose these axes in 3 ways - we get 3 families of spin 1/2 constructs. There can be created charge-like construct on it getting 3 families of leptons (topology says that they need also to have spin). Then we get constructions like mesons, baryons which finally can join into something like nucleus. Qualitatively masses, properties, decay modes are practically exactly like in particle physics.
Far from solitons dynamics becomes 2 sets of Maxwell's equations - for electromagnetism and gravity: dynamics of rotations of 3D ellipsoids (no gravity) gives EM and small perturbations of fourth axis of 4D ellipsoids (which has the strongest tendency to align in one direction) gives Lorentz invariant gravity (called gravitomagnetism).

All of it can be basically seen on pictures - they start on 21 page (after motivations for considering solitons) of this presentation.
It is described and derived in 4-5 sections of this paper.

I'm going to make simulations some day, but I would be grateful for any constructive comments now - this model is very 'strict': we cannot just guess and add new Lagrangian terms as in standard approach - it's quite correct or just wrong: a single real qualitative problem would probably take it to trash ...
What do you generally think of soliton particle models?

3. ### Farsight

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I'm very positive about them. I think it's only a matter of time before more people catch on and we start seeing this stuff in the general media.

There was a good condensed-matter article on topological insulators in physicsworld this month. A related paper is The birth of topological insulators by Joel E Moore, Nature, Vol 464, 11 March 2010, doi:10.1038/nature08916. Some might like to think that this sort of thing is totally unrelated, but it's only a small step from thinking in terms of a "knot" in the electron wavefunction to thinking in terms of the electron itself as being a "knot" of photon wavefunction.

5. ### Jarek DudaRegistered Senior Member

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Topological insulator is something different, but in ellipsoid field all particles are kind of 'knot' of this field combining wavefunction and electromagnetism(in 3D, +gravity in 4D).
For example electron is the simplest 'knot' having charge - this singularity of EM field means directions targeting the center: for example one axis of ellipsoids around target the center. Now there is needed some configuration of the second axis - looking at a sphere around, hairy ball theorem says that there have also to be singularity in configuration of the second axis here - far nontrivial fact that electron need to have spin (there is no separate 'chargon').
Now for example looking at muon, Gauss law (which appears now as topological theorem - 3D analogue of e.g. argument principle which corresponds to Ampere's law) guards the charge inside a ball around the muon - but it's not the lowest energetic charged state, so finally muon has to decay into electron (releasing energy difference in form of EM waves and magnetic artifacts - neutrinos).

Last edited: Feb 12, 2011

7. ### AlphaNumericFully ionizedRegistered Senior Member

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I've already used this line this week but :

Oh god it burns! The goggles do nothing!

I think that people who actually know and understand such things do not post in the manner you do, throwing out as many buzzwords as they can and then, despite trying to put forth the impression they know the details, ask a question which invites entirely vague answers.

The issue with vague questions is two-fold. Firstly it invites responses from people who know less about the subject than could be gleans from reading Wikipedia, Farsight being an example of such people. Secondly if you've worked on this stuff enough to have serious ambition to do research in it then you know the general view of the physics community on the matter and the views of a science forum should be largely irrelevant to you (science is not a popularity test). If you honestly wanted to get informed views on the matter you'd ask a more precise question, one which leads to informed discussion which is not just arm wavey nonsense (which is all you'll get from Farsight).

When those of us here with (or doing) PhDs in physics or maths ask a question about a high level topic we don't go into the "Lets review what this area is" as much as you just have and we ask specific questions. I did research in string theory and frankly I couldn't give a toss what the view of the people here is on the matter and while learning string theory I got a good handle on what the physics community thinks, thus no need to ask the sort of question you just did.

That's the sort of attitude or approach to discussion of high level topics on forums I've found to be the sort done by those who grasp what they are talking about. This thread and your previous ones (along with ones I've seen you make on PhysForums) make me wonder if you fall into the category of understanding what you speak of or the category of being someone who wants to be seen to talk about high level stuff (like Reiku). Picking beyond-lay person topics and then asking for general opinions via "So what's everyone's views?" raises a red flag in my mind.

Now if you're willing to be more specific about what questions you have about solitons and you can present those questions in a way as to make me think you understand what you're asking and not just spouting buzzwords then I (and I imagine others) would be more willing to enter into discussion with you.

8. ### Jarek DudaRegistered Senior Member

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The main purpose of this thread was to discuss correspondence as in the topic - especially finding some problems of trying to see this conceptually simple model (combining QM and EM) as approximation of microscopic physics. I thought a lot about it but I couldn't find any qualitative counterargument, so I thought a discussion could help.
There is also extremely important general question about the concept of soliton models of particles - general view is that e.g. skyrmion models can be only used as effective approximation for mainly high energy regime or that solitons are some separate from particles beings like hypothetical Dirac's monopoles (because wavefunction is seen as something separate from EM field).
From one side there are considered such models of elementary particles (like Penrose twistor model of electrons), from the other side I've spoken with physicists claiming that by definition we cannot model elementary particles this way... ?

9. ### Farsight

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I'd say all stable particles with mass are a kind of "knot" of wavefunction, that the electromagnetic field is curved space, and people describe the gravitational field is curved spacetime. That seems to fit with what you're saying. I'm not sure about the ellipsoid field though.

Take a look at the picture of the "hairy doughnut which is quite easily combable".

Imagine it's an inflatable rubber ring, and pump it up. Keep on inflating and a "fat" torus starts looking more like a sphere than a ring. Something like this picture from the Carnegie Mellon biological physics website:

Keep on inflating and you end up with something like an apple.

Maybe that's going too far. The muon isn't stable, so it's "not a knot". The only stable particles with unequivocal mass are the electron and proton, and their antiparticles. I'd say check out topological quantum field theory and torus knots, and A circular history of knot theory. Also see Spherical harmonics for another mention of Thomson and Tait.

10. ### Jarek DudaRegistered Senior Member

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As AlphaNumeric suggested, I wanted to separate the general discussion about soliton particle models and focus here on the ellipsoid field.
Farsight, I've seen such nice pictures or 'pure knot' constructions, but what we really need is to find is a field governed by some Lagrangian in which such constructions naturally appear - and in which wavefunction describing particle cannot be something separate from EM field which is integrated part of the particle.
About muons - a complete theory has also to recreate relatively stable constructions from our physics - especially that modern particle models require proton decay which is also required to create more matter than antimatter while baryogenesis (not in water tanks as is searched today, but in really extreme conditions), they also need breaking baryon number conservation while black hole evaporation ... so the list of completely stable constructions could be extremely short (like electron/positron, magnetic field line.) ...

My intuition about conservation laws is that for such ultimate laws we have to use some Stoke's theorem (and Noether's, but it's a different story) - situation on boundary of some set guards situation inside it.
On these scales we can forget for a moment about gravity, so practically the only essential interaction not very near particles is electromagnetic - only this interaction is working on boundary of practical sets, so the only ultimate conservation laws came from EM:
- 2D: Ampere's law - situation on a loop guards magnetic flux going through this loop and
- 3D: Gauss law - situation on boundary of some region guards amount of charge inside this region.
Ans so beside charge and spin, the rest of quantum numbers could be changeable in really extreme conditions (like baryogenesis or neutron star core).
Dynamics of ellipsoid field becomes EM (+gravity) far from particles (vacuum state), so we get these conservation laws and there is theoretically possible proton decay - 'disentangling knot' in extreme conditions.
In this model weak/strong interactions correspond to ellipsoid shape deformation required only near singularities (usually they only rotate) and so works only on such characteristic distances (asymptotic freedom) - weak corresponds to the shape of magnetic flux line and strong to interaction between such flux lines.

Last edited: Feb 13, 2011
11. ### Farsight

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Oh, OK.

I don't know about an ellipsoid field, Jarek. You might have seen me talking about the photon as a "stress-energy pressure pulse" where you take the integral of the sinusoidal electromagnetic wave and the electromagnetic field is the curved/curving space, the gravitational field is the outlying pressure gradient, and the peak displacement in the middle of the pulse represents four-potential and h-bar. But this is a simple flat depiction with no "travelling-breather" or other rotation transverse to the direction of propagation.

Agreed.

I'm not keen on proton decay, and I don't agree with the "mystery" of missing antimatter. There's only four stable matter particles, and the wavefunction knot/vortex/soliton approach suggests that the proton is the next-knot-up from a positron rather than an electron.

The only completely stable known particles are electrons, positrons, protons, antiprotons, photons, and neutrinos. Magnetic field lines are abstract things that depict how a particle will move.

Fair enough, see http://en.wikipedia.org/wiki/Stokes'_theorem and note Thomson again.

You can "melt" a proton in extreme conditions, see http://physicsworld.com/cws/article/print/40224 and you can "smash" it in a collider. But I don't see how you can undo a knot or just stick with EM.

Again I don't know about your ellipsoids, but I'd suggest that the strong force is more like a strength-of-space resistance to deformation and rotation rather than an interaction between magnetic flux lines. The bag model feels something like like grabbing a rubber trefoil knot and pulling at the loops. Keep on pulling until it snaps, and you've got hadronic debris.

12. ### Guest254Valued Senior Member

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1,056
Hi Farsight.

I think I've seen you mention topological quantum field theory before, and it's something I'd like to know more about. I've tried a couple of times to understand TQFT, but sadly with little success! I'd genuinely like to know how you went about it, and which sources you've used. I have a PhD in maths, but all the notes and books I've looked at made even me gulp!

Even better, would be if we could make a thread on it.

13. ### Jarek DudaRegistered Senior Member

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Farsight, specially for you I've started separate general thread about soliton particle models, but you are posting succeeding long post on discussion focused on ellipsoid field while still not even looking what it is ... I would understood if it would be some difficult concept, but it just mean that in each point of spacetime there is 3 dimensional ellipsoid (4D with gravity) which prefer some shape (3 radii) - that's all!
Mathematically: there is tensor field - kind of stress tensor - real symmetric matrix in each point, which prefers some set of eigenvalues (eigenvector represents ellipsoid axis of radius being corresponding eigenvalue).
Now think (or look at some link I gave) what nontrivial construction can be made using just ellipse field in 2D - topological singularities having spin 1/2.
Now taking this situation into 3D, we can make such singularity in 3 ways - in perpendicular plane to one of three axes - there are 3 families of spin 1/2 constructs (in literature called for example vortex lines) ... from which there is very near to lepton-like and further knot-like solitons.
I won't reply here if I see again e.g. "I don't know about an ellipsoid field"...

While I completely don't agree that electromagnetic waves has something to do with curving space (gravitational have), thanks for remaining about breather concept - solitons with some internal periodic process and so producing periodic wavelike perturbations of surrounding field - giving them also wave half of wave-particle duality.
From one side there is such internal periodic motion (and so wave-like perturbations of surrounding field) theoretized and observed for electrons - so called Zitterbewegung - here is nice paper of prof. Hestenes reminding that such de Broigle's idea:
with particle energy: E = mc^2
comes internal rotation: E = hf
(so all particles are 'breathers') originally motivated Schroedinger.
He also mentioned observation of this effect - for 80MeV electrons one period corresponds to single layer of silicon crystal - there was observed increased absorption (here is more recent experimental evidence).
If we agree that particles are 'breathers' and so they interact with waves of perturbation they constantly create, there was recent extremely educating Couder, Fort et all papers about observation of 'quantum effects' for macroscopic solitons models in similar situation - oil droplets maintaining their shape because of surface tension and creating waves around because the surface is vibrating: interference, tunneling depending on practically random hidden parameters or orbit quatization condition - that particle has to 'find a resonance' with field perturbations it creates - after one orbit, its internal phase has return to the initial state.
So particles would be 'breathers' which even in classical field theory with solitons behave accordingly to quantum mechanics (maybe no additional 'quantization' is needed).

If proton is kind of a knot-like construction of the field, in really extreme conditions, 1D material it is made of, can go through another one - disentangling the knot ... and leading to the lowest state of given charge - positron.
About Stokes theorem - I really know and appreciate this theorem: it was the great finale of three year analysis course on theoretical mathematics studies and what I'm talking about here is near de Rham cohomology groups, Hodge theory, but I didn't want to scare physicists.
About quark models, to explain asymptotic freedom there are introduced so called quark-gluon strings: kind of string connecting quarks - so it is also made of 1D entities ... what is really matters for baryon models is that it looks like being made of three regions while deep inelastic scatterings and in ellipsoid field this condition is fulfilled.

Guest254, about topological quantum field theory - it's practically a trial to quantize such topological solitons ... but still the first step should be finding a field which family of such solitons correspond well to our particle menagerie with dynamics ...

14. ### AlphaNumericFully ionizedRegistered Senior Member

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You're being somewhat inconsistent in your motivations. You reference what people say about gravitational fields, which means you're saying "Look what GR says" while also saying that the EM field is curved space. GR says that the distinction between space and time is frame dependent, its a matter of personal preference/ease of calculation. Furthermore the same frame transformations used in relativity will alter the electromagnetic field components, as they alter any indexed expression, ie vectors and tensors (which are the mathematical objects used to describe electromagnetism).

It is indeed possible to write the electromagnetic field (and any similar gauge field) as the curvature of some abstract space (a gauge bundle) and put it in much the same formalism as gravity (curvature tensors, connections, couplings etc) but it requires that you consider space-time, not just space. The specific formal derivation of that is not particularly relevant (and it'd be lost on you anyway) but it can be vaguely seen in a simpler manner. By that I mean noting Maxwell's equations have Lorentz symmetry, which includes transformations on both space and time components. If you were only to consider spatial transformations, ie rotations, you'd must 'half' the Lorentz group because its generated by 3 rotations and 3 boosts.

And before you come out with "I know all about the tensor transformations of the electromagnetic field" or something of that ilk in the past you've shown you didn't* so I thought I'd lay it out for you.

*Long ago on PhysForums I asked you to show Maxwell's equations have Lorentz invariance, after you claimed to be a world leading expert in electromagnetism, which you couldn't do.

The theorem in question applies to spheres and does not apply to tori, no matter how much you expand them or twist them. The 'you can't comb the hair on a sphere' analogy is a simple way of expressing the much more fundamental and mathematically deep result in question. The theorem says, in part, that the number of points where a continuous vector field on the manifold has value zero is at least the modulus of the Euler characteristic, $|\chi(M)|$. A sphere has Euler characteristic 2 and thus has at least 2 zeros in any continuous VF defined on it. A 1 holed torus has characteristic 0, so there are vector fields which are continuous and nowhere zero on a torus. A torus with g holes in it has $\chi = 2-2g$ so its only the 1 holed case where that is possible.

Varying the size of the radii of the circles defining a torus does not change the topology of the torus, $\chi = 2-2g$ is unchanged. The smooth deformation of the torus can be written in terms of the 2 circle radii or alternatively in terms of the size and 'slant' of a parallelogram (given the relationship between them and tori). As it happens these sorts of parameters are fundamental in string theory, they are the 'moduli' mentioned in the paper you scoffed at here.

As such your comments about making the torus fatter don't lead anywhere and suggest you don't realise that smooth variations of a space will not change its topology. I'd be happy to go into more details on the role moduli, topological 'flop transitions' and the Poincaré–Hopf theorem play in string theory or just differential geometry in general.

I didn't suggest that at all, I was asking for you to be more precise in what you want to discuss, as asking for the opinions of a forum in regards to extremely high level physics isn't going to get many viable responses, those who understand it would prefer a more specific point to discuss and those who don't will just wave their arms, like Farsight is now doing. Unless that's what you wanted, to just engage in arm waving with cranks, rather than have a proper discussion on the matter.

15. ### Farsight

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Sorry Jarek, I must have misunderstood something, I was just replying to your post point by point.

I looked at that. Towards the end you see a whorl of Fibonnaci spirals similar to the way I've depicted the electromagnetic field around an electron.

I'll read that one too. Mean while if you haven't already look at Falaco soliton. It's a stable vortex in water with a "torsion string singularity", a little like half a smoke ring. The electron models I've seen propose stress-energy rotating like a smoke ring with an additional rotation like a steering wheel.

Again, apologies.

IMHO you should look into this some more. An electromagnetic wave is a wave in space. Ask yourself this? What's waving?

I've printed it and will read it. I've read some of Hestenes' other papers such as The Zitterbewegung Interpretation of Quantum Mechanics and think he's somewhat overlooked.

Maybe that's maybe going too far.

Yep, I saw that. I'm John Duffield by the way.

I've seen this too. Quantum mechanics has been weird and mystical for too long, I'm confident that it's all classical, and that things are going to get pretty exciting soon.

I'm skeptical of that. Make a trefoil knot out of paper, and try converting it into a moebius strip.

I learn something new every day!

Noted.

16. ### AlphaNumericFully ionizedRegistered Senior Member

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Did you look up what 'de Rham cohomology' means? I'm surprised you didn't take the word 'Hodge' and end up making a claim about a solution to the Hodge conjecture.

de Rham cohomologies, topological invariants, toric moduli. This is all dangerously close to my PhD thesis area, which was precisely the structure of moduli defined by cohomologies on tori! I'd offer to have a discussion (under the conditions I've previously outlined) about them with you but you consider anything I did to be a waste of time so you'll just refuse no doubt

Besides I can see you and Jarek are too busy throwing buzzwords at one another to be derailed by someone injecting actual understanding into your thread. Do you think people don't notice you ignore any and all posts by people who understand the stuff you waffle about yet you'll engage cranks in discussion?

I truly would enjoy an informed honest discussion on stuff like cohomologies and why they are important not just to string theory but a lot of field theories, including people filling in gaps in my knowledge where I have them. If you were intellectually honest you'd feel similarly about your own *cough* knowledge. Instead you only engage with cranks and say "I'm John Duffield". Perhaps more people in the research community would know your name if you got published? That generally helps.

17. ### Jarek DudaRegistered Senior Member

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"A scientific theory should be as simple as possible, but no simpler" Albert Einstein
Farsight, we can consider many different swirls, knots, in multiple dimensions, but such theory has to be self-consistent and predict not more not less, but exactly what we observe.
And so if you want knots, you need some 'material' to made it of and somehow model interaction between them ... we know that such constructs in physics interact through some field, so again maybe they are no some separate out of field entities, but they are just local constructions of the field - solitons ... and mentioned vortex lines are such natural '1D material'. Solitons strongly deform field locally, creating interactions between them.
Thermal fluctuations in extreme conditions blur such structures, loosening topological constrains, like knot topology and so the only properties which always have to survive are guarded by some Stokes theorem (precisely Poincaré–Hopf theorem) - we can really rely only on charge and magnetic flux conservation.
And if you want 'quantum properties' for such solitons, you need to give them also wave nature - periodic internal process, which create wave-like periodic perturbations of the filed around, like for these droplets ... or like in original de Broglie concept - particles have nonzero energy and so also have 'internal clock' accordingly to Planck's law (E = hf) - as observed as zitterbewegung.

AlphaNumeric, You are constantly saying that I'm using buzzwords - I'm really trying to be clear, but please just make concrete questions and I would gladly explain ...
I have to admit that I'm practically not familiar with algebraic geometry - what I need/use is behavior of fields on submanifolds: differential topology, like Hodge decomposition allowing to see structure of what field can thermalize to (through its de Rahm cohomology groups), or determine number of singularities using Lyusternik-Schnirelmann category or Morse theory (they describe situation better than Euler characteristic - for example placing torus vertically we get gradient flow with sink, source and two saddles and to decrease this number down to minimum 3 (minimal decomposition into contractible subsets), we have to use more nasty singularity by 'melting' two saddles) ...
But ... all such theories I've met, used usually just vector fields (like Conley index theory) ... but what I need for ellipsoid field is something more complicated :
- vectors are undirected - 'without arrowheads' ( /{1,-1}),
- not single direction, but we have such whole undirected reper (making e.g. that simplest charge-like sigularity has to be simultaneously spin-like singularity)
Maybe you could suggest some papers of analogues for such topologically more sophisticated fields?

Last edited: Feb 16, 2011
18. ### quadraphonicsBloodthirsty BarbarianValued Senior Member

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I am not a string theorist, but from what I know of solitons they require that said field exists in the context of a medium with specific properties (nonlinearity, dispersivity). So I don't see how you could have electrons be solitons in an electric field unless you're happy for electrons not to exist in, for example, a vacuum. Which is to say that you're raising more questions than you're answering with this line, specifically the question of where the pervasive, universal medium with the appropriate nonlinearities is coming from. The aether?

Meanwhile, I have myself actually created actual electric field solitons in lab experiments. They were emphatically not electrons.

19. ### Jarek DudaRegistered Senior Member

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quadraphonics, ellispoid field has nothing to do with string theory - just oppositely: it's something extremely simple - there is ellipsoid in each point of 4D spacetime - that's really all.
Mathematically it's exactly like stress–energy tensor, but with specific, Higgs-like potential (with topologically nontrivial minimum): there is tensor field - real symmetric matrix in each point, which prefers some set of eigenvalues (eigenvector represents ellipsoid axis of radius being corresponding eigenvalue).
Yes, this model is nonlinear - because potential prefer some shape of ellipsoid - set of eigenvalues.
This field far from particles becomes EM field and simultaneously it describes particle behavior - it's kind of combination of electromagnetic field and wavefunction.
In this simple single filed, there appears topologically nontrivial situations - solitons - having mass, EM properties etc. - and their family surprisingly well qualitatively correspond to our particle menagerie. (I'm going to sleep now)

20. ### chingluValued Senior Member

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"In this simple single filed, there appears topologically nontrivial situations".

21. ### Jarek DudaRegistered Senior Member

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Yes, chinglu - you needed only to look at some link I gave ...
Ok - if it's too complicated to look at 21-30 page of presentation of 4-5 section of paper, let me take some basic description here...

Let's start with ellipse field - there is an ellipse in each point of 2D plane, which prefer some shape (2 radii) because of potential.
Mathematically - there is tensor field - real symmetric matrix in each point, which prefers some set of eigenalues being constants of the model (its eigenvectors represent ellipse axis of radius being corresponding eigenvalue).
Now here are two simplest topologically nontrivial situations for such field:

looking at loops around such points, 'phase' make some mulitiplicity not of full rotations like we would expect for vector field, but thanks of ellipse symmetry - some multiplicity of 1/2 rotations - singularities from picture have index/spin +1/2, -1/2.
On such loop, there are achieved all possible angles of ellipse axis - while looking at smaller and smaller loops down to a single point, we see that in some moment these entities have to loose directionality - in this case ellipses have to deform into circle (two eigenvalues equalize).
This enforced by topology deformation means that we get out of potential minimum - soliton chooses minimal energy for this topology, which is nonzero - it has rest energy (mass), which can be released as nontopological excitation (photons) while annihilation with antisoliton.
This mass creation mechanism is based on that potential minimum is topologically nontrivial (circle) - exactly as in Higgs potential: Mexican hat ((|z|^2-1)^2) - if on a circle the field achieves all values from the energy minimum (|z|=1), inside this circle it has to get out of the minimum, giving soliton mass.
Such solitons create/are strong deformations of the field - standard energy density of such field increase with its variousness - taking opposite solitons closer (the same further) make the field less various - give them attraction(repelling) force - it can be see using this demonstration.

Ok, let's go from ellipse field used e.g. by 'singular optics' as representing light polarization to 3D ellispoid field in 3D.
Now singularities as previously create 1D constructs - vortex line/spin curve.
We can make them in three ways - choose one axis along line and remaining two make singularitiy equalizing these 2 eigenvalues.
Now they have mass/energy density per length, which generally should be different in these 3 cases - let's call them electron/muon/tau spin curves correspondingly. By synchronous rotation 90deg of axes along such line, they theoretically can transform one into another.
Loops made of something like this are extremely light (comparing to further excitations), very weakly interacting and generally can transform one into another - we get 3 families of neutrinos.

Now if along such 1D construction, axes rotate toward/outward, we get charge-like singularity on it, transforming spin curve into opposite one, like on this picture:

in such more complicated singularity, now topologically all three axes have to equilibrate in the center, giving it much larger rest energy (mass) - we get three families of leptons.
Alternative view on such singularity is by looking at axis along curve - it's for example targeting the center while such singularity, so looking at perpendicular submanifold which is nearly sphere now, we have to align somehow remaining two axes there - hairy ball theorem says we cannot do it without singularity - or in other words: that electron has to have also spin.

Further excitations is making loop with additional twist along it, like in Mobius strip - in center of something like this appears really nasty topological singularity requiring much larger ellipsoid deformations and so giving these unstable meson-like structures larger mass.
Then there are knots - loop around curve of different type - now on inside curve phase make 1/2 rotation, while on the loop it makes full rotation - enforcing nasty deformations on their contact - we get even heavier constructions: baryon-like. Some integrated irregularity of inside curve could make such combination easier and so proton has smaller mass than neutron.
Now if we have two loops around one line, they generally repels each other, but the energetic income of having charge, make them get closer to share the charge - getting deuteron with centrally placed charge (like on this picture).
Further nucleons can also help holding their structure by creating/reconnecting loops - creating complicated interlacing structures like here:

While deep inelastic scattering, such mesons/baryons seem to be made of 2/3 regions.
Weak interaction here corresponds to spin curve structure, while strong to interaction between two such structures - they work only on specific for these constructions distances (asymptotic freedom).
Far from singularities, ellipsoids have fixed shape and so the only dynamics is through their rotations - it occurs that such spatial rotations can be described using Maxwell's equations - we get electromagnetism and situation around singularities gives them magnetic flux/charge.
To get full spacetime picture, we have to use 4D ellipsoids in 4D instead - fourth axis correspond to local time direction (central axis of light cones) and has energetically strongest tendency to align in one direction - in such case we would get pure EM as previously, but small rotations of this axis gives additionally second set of Maxwell's equations - Lorentz invariant gravity (called gravitomagnetism) - in this picture spacetime is flat and what is curved is space alone - submanifolds orthogonal to time axis.
...

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lol!

23. ### Jarek DudaRegistered Senior Member

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I'm mainly asking where to search for eventual differences with our physics - this extremely simple model (combining EM and QM) gives very concrete qualitative picture: particles, properties, decays, interactions ... finding a single essential qualitative discrapency could spare me horrible simulations ...