Topological Solitons Of Ellipsoid Field, correspond to our particle menagerie

[Jarek Duda]

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 mesons/baryons, they automatically give particles masses (rest energy), allows for various number of them 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, for a TOE 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 equations became electromagnetism and gravity far from particles (vacuum state).
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 for example Berry, Dennis ( http://www.phy.bris.ac.uk/groups/theory/th...s_mr_thesis.pdf ).
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/Separati...lSingularities/
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.

All of it can be basically seen on pictures - they start on 21 page (after motivations for considering solitons) of this presentation:
http://docs.google.com/viewer?a=v&pid=expl...U3M%20jQ1&hl=en
It is described and derived in 4-5 sections of: http://arxiv.org/abs/0910.2724

I'm going to make simulations some day, but I would be grateful 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?

[Jarek Duda]

Ok, let me take some basic description here ... maybe it will help with discussion ...

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:

User posted image: <a target='_blank' href='https://dl.dropbox.com/u/12405967/fqm8.jpg'>User posted image</a>

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:

User posted image: <a target='_blank' href='https://dl.dropbox.com/u/12405967/lepton_resize.jpg'>User posted image</a>

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:

User posted image: <a target='_blank' href='https://dl.dropbox.com/u/12405967/fqm10.jpg'>User posted image</a>

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 corresponds 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.
...
Questions? Comments? Counterarguments?

[Moderator: Suspended 20 days for multiposting on multiple forums and being stupid. You have been warned about both in the past. http://sciforums.com/showthread.php?t=106395 Your grasp of experimental particle physics is over 50 years out-of-date and thus your grasp of theory is completely wrong-headed. Not suspending you at this time would only contribute to your delusions of competence.]

This post has been edited by rpenner on Feb 17 2011, 04:35 PM

[Jarek Duda]

rpenner, it's difficult to find someone for discussion about nonstandard topics, so one just have to try a few different forums ...
I've replied to your questions on the sciforum ( http://www.sciforums.com/showthread.php?t=106395&page=2 ) - the only reasonable ones I got on a forum ...

I wanted to add that there is conceptually very similar electron model developed for 20 years by prof. Manfried Faber from Vienna: http://arxiv.org/PS_cache/hep-th/pdf/9910/9910221v4.pdf
Instead of three axes of ellipsoids, he has only one - the field in vacuum is from 2D sphere, which is equator of 3D sphere, but getting out of the equator costs potential energy (instead of deforming in ellipsoid field).
Dynamics of directions in vacuum effectively becomes electromagnetism like - in his paper there is very throughout explanation of that (muuuuch better than in mine).

So having hedgehog field configuration for charge, to glue this field to the center, we have to get out of the equator to one of 2 poles of 3D sphere - choosing +- spin of electron and giving it rest energy (becoming also inertial energy thanks of Lorentz invariance).
So in ellipsoid field the two additional perpendicular axes give one additional degree of freedom - representing quantum phase required for wave nature - it rotates as soliton's internal clock. Professor invited me and we talk a lot - he doesn't like the internal clock concept and he would like to avoid it.
These additional axes also grows the family of solitons of this field - up to menagerie from our physics ...

[Jarek Duda]

If someone is interested in this model, I've just written an essay gathering my considerations:

http://dl.dropbox.com/u/12405967/elfld.pdf

For example nuclei are better explained there - this model seems to explain why neutron requires charge for stability and how charge is distributed in nucleon, nucleus...

I would gladly discuss about it.

[Jarek Duda]

Here is discussion on FQXi: http://fqxi.org/community/forum/topic/1416