Solitons and Complete QED Lagrangian

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sat Mar 28, 2020 11:07 am

We can continue this discussion here.

Jarek wrote:Higgs-like potential as above regularizes charges to finite energy without any artificial cutoffs (also leading to charge quantization due to minimum having nontrivial topology) - as in diagram above: electromagnetism deforms into other interactions in particles to prevent infinities.


I believe the following is the complete QED Lagrangian for a free charged fermion or close to it that includes gravitational torsion.



Where .

The second term on the RHS is the charge interacting with the field it creates. The last term on the RHS is the torsion term and it is basically the intrinsic spin interacting with itself and has the gravitational coupling but that can be shown related to Planck length. There is no external potential necessary like in Faber's soliton model. The Lagrangian can be solved for length factors for a static situation and two positive solutions are obtained. One near the classical radius and one near Planck length. Of course the one near the classical radius has been excluded by experiment but Compton wavelength can be extracted from it. So we can see that including gravitational torsion provides a natural cutoff and no external potential is necessary.

However..., one still wonders how this can be kept together as a particle. So I am wondering if there might be a soliton solution for the above Lagrangian?
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Sun Mar 29, 2020 12:00 am

There is hidden electron's spin in Lagrangian you have written - Faber's model ( https://iopscience.iop.org/article/10.1 ... 1/1/012022 ) is just electric charge: repair Maxwell's equations to add charge quantization (Gauss theorem giving only integer charges) and regularization (of electric field to finite energy).
It is just a base for the real complete model (to be found), can be realized with just a vector field:
Jarek wrote:Faber model can be realized with just a vector field, with Higgs-like potential preferring unitary vectors e.g. V(u) = (|u|-1)^2.
Defining its curvature as dual F tensor with electric and magnetic field, Gauss-Bonnet theorem works as Gauss law, additionally having built in charge quantization - as topological charges.
We get finite energy of charge thanks to potential allowing to get to u=0 in the center of singularity - deforming EM into other interactions to prevent infinity.

Here is analogous in 2D, getting 1/r interaction:
Image

The question is how to interpret this vector field - you can use spacetime for that, but I prefer to see it as just a field in spacetime.


Its regularization leads to finite size effects: that electron is not a perfect point - they observe "running coupling" in simulations ( https://en.wikipedia.org/wiki/Coupling_ ... andau_pole ) - that Coulomb interaction deforms for charges being very close.
Here is energy of the field of Faber's charge-anticharge configuration in various distances:
Image

Returning to spin/magnetic dipole moment, this is one of places we disagree with Faber - he says that spin is just a dynamical response, I believe it is a real tiny magnet - what is required to get observed e.g. Larmor precession or spin echo.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sun Mar 29, 2020 12:33 pm

Actually, Faber is probably right about the external potential. It's the interaction with the quantum vacuum that keeps it together as a particle. Actually, "wavicle" is probably more correct.

Yes, I agree about the magnetic moment. There is a "current" flow within the wavicle.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Sun Mar 29, 2020 12:55 pm

In soliton particle view the perfect situation would be having just a single field:
- field being in minimum of potential (e.g. unitary vectors for Higgs potential) is called 'vacuum state' - its dynamics should recreate what's happening far from particles: electromagnetism ... + QM + gravity,
- it gets out of this potential minimum only if enforced, e.g. forming topological charge, which would have infinite energy without leaving this minimum - other interactions (weak/strong) are kind of deformation of EM by using Higgs' potential to prevent infinity. Ideally, the space of such solitons should correspond to entire particles menagerie.

Investing e.g. 2 x 511keV energy in above vacuum, we should be able to create electron+positron pair:

Image

but this is a continuous process, so it can be started (and soon cancelled) with much lower energy - interpreted as virtual pair creation.

1D pair annihilation, running it backward we get pair creation:
Image
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sun Mar 29, 2020 5:58 pm

FrediFizzx wrote:Actually, Faber is probably right about the external potential. It's the interaction with the quantum vacuum that keeps it together as a particle. Actually, "wavicle" is probably more correct.

Yes, I agree about the magnetic moment. There is a "current" flow within the wavicle.
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So I think what we may have here for an electron, is an object near the size of Planck length representing the charge circulating about near the Compton wavelength (zitterbewegung). That gives the magnetic moment.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sun Mar 29, 2020 7:59 pm

FrediFizzx wrote:
FrediFizzx wrote:Actually, Faber is probably right about the external potential. It's the interaction with the quantum vacuum that keeps it together as a particle. Actually, "wavicle" is probably more correct.

Yes, I agree about the magnetic moment. There is a "current" flow within the wavicle.
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So I think what we may have here for an electron, is an object near the size of Planck length representing the charge circulating about near the Compton wavelength (zitterbewegung). That gives the magnetic moment.
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I should add that a photon will always interact with the point-like charge that is near Planck length so no structure will ever be seen other than the magnetic moment. And electric dipole will effectively be zero.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Sun Mar 29, 2020 11:44 pm

Regarding de Broglie's clock/zitterbewegung, observed e.g. in https://link.springer.com/article/10.10 ... 008-9225-1 , indeed again Faber cannot get it in his model, hence says that it is only dynamical response ... but it doesn't make sense as we have SRT - Lorentz invariance here, getting time dilation of some static clock - as in the linked experiment.

This is indeed related with the spin/magnetic dipole disagreement, as we use field's curvature as dual F electromagnetic tensor - electric field corresponds to spatial-spatial curvature, magnetic to spatial-temporal, hence there should be a periodic process related with magnetic dipole of spin.

Another hypothesized possibility (can be both) is using spin precession as periodic process ... especially in Bohr-Sommerfeld quantization condition: https://link.springer.com/article/10.1007/BF00670821

I get constant magnetic dipole and hence hopefully the clock by expanding Faber's model by single vacuum degree of freedom ( https://fqxi.org/data/essay-contest-fil ... lfld_1.pdf ): the original gives electromagnetism, I interpret this additional (low energy) one as quantum phase - e.g. rotated by the clock.
Specifically, just recognize internal rotations of these vacuum unitary vectors (like pens pointing some direction but rotating internally):
- in vacuum we have reper of 3 distinguishable axes (like biaxial nematic in liquid crystals),
- hedgehog configuration can be made with one of 3 axes - we get asymptotically the same electric charge, but with different energy - we get 3 leptons,
- such hedgehog of one axis requires to align second axis on a sphere - what cannot be done due to the hairy ball theorem, requiring spin-like singularity,
- further we get baryon-like configurations requiring some small positive fractional electric charge - which needs to be compensated in neutron, hence it has higher mass than proton ...
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 8:31 am

So, it looks like we have two "sizes" for an electron. One for the magnetic moment about the Compton wavelength and one for charge near Planck length. I'm trying to figure out if one or the other has S^3 topology or perhaps both do. Or magnetic moment (spin) has S^3 and charge has S^7. Yeah, maybe that is the ticket.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 9:38 am

From 5 x 511keV energy in photons (EM radiation) we can create electron + positron.
Hence EM field of electron cannot have higher energy than 511keVs.
Electric field for perfect point charge has infinite energy, we would need to integrate from r ~ 1.4fm to get 511keV energy from electric field alone ... hence we need to deform electric field of perfect point charge in a few fm distance, also in these distances they see deformation of coupling constant in running coupling.

Compton wavelength is a few orders of magnitude larger: ~2400fm for electron.
It is distance related with the pilot wave: how far it will go with speed of light during one tick of ~10^21Hz de Broglie's clock propelling these waves.
In Couder's experiments it corresponds to Faraday wavelength - distance between maxima of standing waves e.g. in slid 8 of https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 10:27 am

Jarek wrote:From 5 x 511keV energy in photons (EM radiation) we can create electron + positron.
Hence EM field of electron cannot have higher energy than 511keVs.
Electric field for perfect point charge has infinite energy, we would need to integrate from r ~ 1.4fm to get 511keV energy from electric field alone ... hence we need to deform electric field of perfect point charge in a few fm distance, also in these distances they see deformation of coupling constant in running coupling.

Compton wavelength is a few orders of magnitude larger: ~2400fm for electron.
It is distance related with the pilot wave: how far it will go with speed of light during one tick of ~10^21Hz de Broglie's clock propelling these waves.
In Couder's experiments it corresponds to Faraday wavelength - distance between maxima of standing waves e.g. in slid 8 of https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf

I suspect you still don't understand the model with gravitational torsion. Torsion (spin) energy is negative and counter-balances the EM energy. The result is mc^2 where the "m" is rest mass. So it is possible to have charge at a "size" near Planck length without huge energy.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 10:33 am

I am sorry, but kinetic terms in Lagrangian have positive contribution to energy - field tends to reduce tension.
I don't believe in negative energy contributions of this type, introducing it would give e.g. spacetime tendency to bend itself, what makes no sense.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 10:39 am

Jarek wrote:I am sorry, but kinetic terms in Lagrangian have positive contribution to energy - field tends to reduce tension.
I don't believe in negative energy contributions of this type, introducing it would give e.g. spacetime tendency to bend itself, what makes no sense.

Figure out what spin squared is. It is negative. And it is not bending of space. It is twisting of space. Big difference. The kinetic terms are zero for the "static" situation. Simply put..., elementary fermions are a defect of spacetime.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 10:55 am

Bending and twisting are both tensions of spacetime - should have positive energy contribution to prevent tension, otherwise spacetime would have tendency e.g. to twist itself.
Spin is magnetic dipole - tiny magnet. I don't know what spin square is.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 12:21 pm

Jarek wrote:Bending and twisting are both tensions of spacetime - should have positive energy contribution to prevent tension, otherwise spacetime would have tendency e.g. to twist itself.
Spin is magnetic dipole - tiny magnet. I don't know what spin square is.

Spin squared is spin interacting with itself and is easy to figure out. Just look at the EPR scenario where the result is -a.b. So for spin squared it would -a.a = -1. However, it is really . Now just add a factor that gives energy from angular momentum squared. It will be negative energy.

One might think that torsion should give positive energy but not so in the case of elementary fermions. It is somewhat established that gravitational torsion is negative energy. I will look up some references if you don't believe it.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 12:43 pm

I see particles as topological solitons.
They don't have the problem with self-interaction as they are just localized field configurations.
They interact with other particles through entire field, e.g. with increasing tension with distance for below minus-plus charge configuration, leading to their attraction reduce this tension:
Image

And I see spins in very similar way, don't feel a need for their self-interaction, "squared spin".

Also I don't believe in negative energy of twisting ... or using spacetime geometry to explain electromagnetism - as they are a few dozens of orders of magnitude away.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 1:36 pm

Jarek wrote: I see particles as topological solitons.


Sure, and electrons are stable solitons.

They don't have the problem with self-interaction as they are just localized field configurations.


Why do you think self-interaction is a problem? I see no problem with charge interacting with the field it creates. Same for intrinsic spin.

They interact with other particles through entire field, e.g. with increasing tension with distance for below minus-plus charge configuration, leading to their attraction reduce this tension:

And I see spins in very similar way, don't feel a need for their self-interaction, "squared spin".

Also I don't believe in negative energy of twisting ... or using spacetime geometry to explain electromagnetism - as they are a few dozens of orders of magnitude away.


Well, electromagnetism can be easily explained purely by charge in spacetime. Of course we don't know exactly the mechanism behind charge if there is one. Most likely S^7 topology. Gravitational torsion becomes very strong (high energy) at short distances. So not sure where you get "orders of magnitude away"?
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 1:46 pm

Electromagnetism is ~10^36 times stronger than gravity - these are completely different worlds.
Start with doing EM right (vector field is enough) ... much later add unimaginably tiny gravity correction, like bending photon trajectories by stars.

I believe in standard 4D spacetime, for S^7 topology you need 8 dimensions - I completely absolutely do not see a need nor possibility for dimensions above 4.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 2:10 pm

Jarek wrote:Electromagnetism is ~10^36 times stronger than gravity - these are completely different worlds.
Start with doing EM right (vector field is enough) ... much later add unimaginably tiny gravity correction, like bending photon trajectories by stars.

I believe in standard 4D spacetime, for S^7 topology you need 8 dimensions - I completely absolutely do not see a need nor possibility for dimensions above 4.

Gravity due to curvature and gravitational torsion are two separate things. Like dual to each other. One is weak with positive energy; the other is strong with negative energy. Why don't you understand that?

So you get charge from a vector field? I don't think so.

Joy perhaps solved that problem with S^7.
https://royalsocietypublishing.org/doi/ ... sos.180526
"Quantum correlations are weaved by the spinors of the Euclidean primitives"
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 2:23 pm

Why bending and twisting spacetime would have energy different by ~10^36 times ???????????????????????????????????? (one question marks per order)

So you get charge from a vector field? I don't think so.

It was Faber's idea ... as written many times ... Higgs potential e.g. V(u) = (|u|^2-1) enforces unitary vectors in vacuum (far from particle) ... curvature of this field is interpreted as EM field to get Gauss-Bonnet as Gauss law calculating topological charge - integer ... using standard EM Lagrangian for EM field defined this way, leads to Maxwell's equation with built in charge quantization, and charge regularization to finite energy due to Higgs' potential.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 4:11 pm

Twisted spacetime is called matter.
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