Solitons and Complete QED Lagrangian

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

Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 5:53 pm

I'm afraid that only by you.

Spacetime is unimaginably rigid - there is needed enormous energy to bend it in nonngelible way e.g. in black hole or wormhole.
We can imagine super-rigid sheet of steel - we nearly cannot bend it ... but you say we can easily twist it???? (even it wants to twist itself in negative energy fairytale)
Using topological charge, each e.g. electron is full twist of this super-rigid sheet of steel????
How/why????
There are 36 orders of magnitude difference ... it is extremely difficult to explain large differences within one object/field.
Seesaw mechanism ( https://en.wikipedia.org/wiki/Seesaw_mechanism ) for neutrino mass is able to get ~10^17 times difference - this is a promising direction (and related to mine), but completely differeent than your guess.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 6:13 pm

Jarek wrote:I'm afraid that only by you.

Spacetime is unimaginably rigid - there is needed enormous energy to bend it in nonngelible way e.g. in black hole or wormhole.
We can imagine super-rigid sheet of steel - we nearly cannot bend it ... but you say we can easily twist it???? (even it wants to twist itself in negative energy fairytale)
Using topological charge, each e.g. electron is full twist of this super-rigid sheet of steel????
How/why????
There are 36 orders of magnitude difference ... it is extremely difficult to explain large differences within one object/field.
Seesaw mechanism ( https://en.wikipedia.org/wiki/Seesaw_mechanism ) for neutrino mass is able to get ~10^17 times difference - this is a promising direction (and related to mine), but completely differeent than your guess.

Did I say it was easy to twist spacetime? I don't think so. I would imagine the twisting happened way back at the big bang when particles were created. Is that enough energy for you? What happens with torsion is that the "loop" doesn't close. So it is a defect of spacetime called matter. And I can guess what is coming next from you.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 6:16 pm

But particles are still created, e.g. 2 x 511keV photons -> electron + positron.

The difficulty of such process is defined by this energy ... for bending of spacetime in black hole you need ~2x mass of sun in 10^33 g, times Avogadro number, time GeV per nucleon energy ... ~60 orders of magnitude more ...
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Mar 31, 2020 8:05 pm

Jarek wrote:But particles are still created, e.g. 2 x 511keV photons -> electron + positron.

The difficulty of such process is defined by this energy ... for bending of spacetime in black hole you need ~2x mass of sun in 10^33 g, times Avogadro number, time GeV per nucleon energy ... ~60 orders of magnitude more ...

Yep, I was right on target with what you were going to bring up next. Most likely due to the nature of the quantum vacuum. Particles are already twisted spacetime but perfectly nulled out so it looks like nothing is there. That pair production process has to be done in a strong magnetic field. And one of the photons has to be very off mass shell. It could have any energy.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Tue Mar 31, 2020 11:04 pm

I understand that a few dozens of orders of magnitude of disagreement is not an issue for you.

So what do you get for that?
The most basic interaction is electromagnetism, preferably with charge quantization and finite energy of charge - do you get it?
Another basic thing is pair creation from energy only - what for you is something exotic.
Both above naturally appear in just a vector field with proper Lagrangian.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Wed Apr 01, 2020 9:09 am

Jarek wrote:I understand that a few dozens of orders of magnitude of disagreement is not an issue for you.

So what do you get for that?
The most basic interaction is electromagnetism, preferably with charge quantization and finite energy of charge - do you get it?
Another basic thing is pair creation from energy only - what for you is something exotic.
Both above naturally appear in just a vector field with proper Lagrangian.

You are just making up this "few dozens of orders of magnitude of disagreement". It doesn't exist for gravitational torsion.

No doubt an electron is some kind of stable soliton. Can you derive the QED Lagrangian from your model including the part that gives finite energy of charge?
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Thu Apr 02, 2020 8:37 am

I suppose the easiest thing to do is add the external potential to the complete QED Lagrangian. I'm going to work on that to see what comes of it. I wonder if the length parameter of the potential matches up with the other length parameters. I suppose it would but which one? Or maybe two external potentials is required?
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sat Apr 04, 2020 10:54 am

So Jarek believes that the charge of an electron doesn't interact with the field it creates. What is the field (Coulomb field) that the charge creates? It simply has to be a polarization of the quantum vacuum and for sure the charge of the electron is interacting with it in order to create it. However, Jarek believes that electron-positron pairs can be created from the quantum vacuum by two photons and for sure that has been experimentally demonstrated with one of the photons way off mass shell in a strong magnetic field. Basically, it is another example of polarization of the quantum vacuum. So there can be no doubt about self-interaction.

Now, how about self-interaction of the spin field? For sure the electron's spin is also causing some alignment of the spins of the polarized particles in the quantum vacuum. So again, we have spin interacting with the field it creates. QED.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Wed Apr 15, 2020 11:15 pm

I had enough of this talk as were running in circles, with you ignoring a few dozens of orders of magnitude disagreement - that to really influence spacetime, no matter bending or twisting, you need black hole-scale of energy, not of electron.
FrediFizzx wrote:So Jarek believes that the charge of an electron doesn't interact with the field it creates.

While it is more complicated, basically indeed electron does not interact with own electric field - which is going to infinity in the center of electron, would need infinite force - nonsense.
In soliton particle models, we have only field governed by some Lagrangian - that should be the entire theory ... and we define its local (topologically nontrivial) configurations as particles.
Here at the top there are a few different topological charges, e.g. fluxons in superconductor would look like this, especially if being able to combine.
Saying that they interact with own field makes no sense, rather they just are their own fields.
At the bottom is example of interaction of minus-plus charge pair, the further they are the stronger tension of field - what translates into attraction of such solitons:
Image

Vacuum polarization here denotes its possibility to start such pair creation as continuous process, and quickly go back - just field's deformation toward pair creation.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Thu Apr 16, 2020 8:28 am

Jarek, can you derive the QED Lagrangian from your model including the part that gives finite energy of charge? Or can you extract the Dirac equation from the model?
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Thu Apr 16, 2020 11:50 pm

One more time, Faber's model is only repairing two fundamental lacks of Maxwell's equations:
- of charge quantization: such that Gauss law can only give integer charge,
- of charge regularization - preventing infinite energy of charge ... also explaining running coupling: modification of Coulomb interaction for very short distances.

To practically work with e.g. scattering of solitons, we need to consider ensembles of scenarios - Feynman diagrams in perturbative QFT, but I haven't worked on that.
Perturbative QFT is very general "algebra on particles", like standard algebra allowing to say that "apple + apple = 2 apples" without any understanding what "apple" is ... here we would like to ask what particle is, not assume but derive also e.g. charge quantization ... answer questions like "what is (e.g. EM) field configuration of a given Feynman diagram?"
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Fri Apr 17, 2020 9:33 am

Ok, if repairing Maxwell's equations that should translate over to QED. What would be different with the QED Lagrangian to accomplish those repairs?
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Sat Apr 18, 2020 1:01 am

Answer to this question you can also find in my first response in this thread:
Jarek wrote: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:

No, QED is built on Dirac equation - which uses spin, while Faber's model has no spin ... the big question is how to add it - I have my candidate, but 3D topological solitons are tough mathematically.
QED is different perspective - which assumes e.g. quantization, ignores field configuration question ... sweep many infinities under the rag.
In soliton models we would like to fill these lacks, e.g. derive quantization, remove infinites ... such that such final model is effectively described by perturbative QFT of the standard model.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sat Apr 18, 2020 8:03 am

Jarek wrote:Answer to this question you can also find in my first response in this thread:
Jarek wrote: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:

No, QED is built on Dirac equation - which uses spin, while Faber's model has no spin ... the big question is how to add it - I have my candidate, but 3D topological solitons are tough mathematically.
QED is different perspective - which assumes e.g. quantization, ignores field configuration question ... sweep many infinities under the rag.
In soliton models we would like to fill these lacks, e.g. derive quantization, remove infinites ... such that such final model is effectively described by perturbative QFT of the standard model.

Ok, you just don't know. You could have just said that. But there would have to be some kind of modification to the QED Lagrangian to accomplish "regularization (of electric field to finite energy)". We have that modification with the gravitational torsion term. But I am interested in what the modification from the soliton solution might be if you can figure it out. Any clues at all?
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Sat Apr 18, 2020 11:43 pm

No, twisting spacetime might be worth to consider for energy scales of Kerr's black holes, but not for single electrons.

Yes, I have my candidate for adding spin to Faber's model - which can be realized with vector field, I am additionally recognizing intrinsic rotations of these vectors: exactly as going from uniaxial to biaxial nematics. I interpret this additional vacuum's degree of freedom as quantum phase: rotated by de Broglie's clock of particle, leading to pilot waves. This way we get field of 3 orthogonal axes: we can perform hedgehog configuration with one of them: getting three leptons of the same charge, but different mass. Performing hedgehog with one axis, trying to align the second one, we cannot do it due to the hairy ball theorem - requiring additional spin-like singularity for charged particles...
But there is huge freedom for choosing Lagrangian for such model, testing them needs tough 3D nonlinear simulations - this task has overwhelmed me.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sun Apr 19, 2020 8:50 am

Jarek wrote:No, twisting spacetime might be worth to consider for energy scales of Kerr's black holes, but not for single electrons.

Yes, I have my candidate for adding spin to Faber's model - which can be realized with vector field, I am additionally recognizing intrinsic rotations of these vectors: exactly as going from uniaxial to biaxial nematics. I interpret this additional vacuum's degree of freedom as quantum phase: rotated by de Broglie's clock of particle, leading to pilot waves. This way we get field of 3 orthogonal axes: we can perform hedgehog configuration with one of them: getting three leptons of the same charge, but different mass. Performing hedgehog with one axis, trying to align the second one, we cannot do it due to the hairy ball theorem - requiring additional spin-like singularity for charged particles...
But there is huge freedom for choosing Lagrangian for such model, testing them needs tough 3D nonlinear simulations - this task has overwhelmed me.

Well, you ae suffering under the same misconception about gravitational torsion as many others so you are not alone. It has held up progress since 1971. But we will deal with that later.

The QED Lagrangian is the master equation for electrodynamics so eventually you will have to show some kind of modification to it to accomplish the regularization. Just start with that instead of trying to "choose" a different Lagrangian. Of course you will find in the textbooks the modification for re-normalization but I am talking about something other than that.
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Sun Apr 19, 2020 9:07 am

Schwarzschild radius of electron is ~10^-57m : https://en.wikipedia.org/wiki/Black_hole_electron
In contrast, not to exceed 511keVs energy with its electric field alone, we would need to integrate it from ~1.4 * 10^-15m radius (instead of zero).

So for bending spacetime there is ~10^42 times difference for radius ...
How much lower energy is required for twisting? If a trillion times lower, then there only left ~10^30 times difference ...

Regarding QED, so what electric field electron has in it?
If E ~ 1/r^2 then it would have infinite energy - nonsense.
Trying to respond such question with perturbative QFT seems extremely tough (not using perfect point particles), in soliton model perspective it is a bit more tangible, but still quite tough.
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Sun Apr 19, 2020 9:31 am

Jarek wrote:Schwarzschild radius of electron is ~10^-57m : https://en.wikipedia.org/wiki/Black_hole_electron
In contrast, not to exceed 511keVs energy with its electric field alone, we would need to integrate it from ~1.4 * 10^-15m radius (instead of zero).

So for bending spacetime there is ~10^42 times difference for radius ...
How much lower energy is required for twisting? If a trillion times lower, then there only left ~10^30 times difference ...

Regarding QED, so what electric field electron has in it?
If E ~ 1/r^2 then it would have infinite energy - nonsense.
Trying to respond such question with perturbative QFT seems extremely tough (not using perfect point particles), in soliton model perspective it is a bit more tangible, but still quite tough.

Sure, all that is well known but I'm trying to get to something new. E ~ 1/r^2 is only infinite if you let "r" go to zero. So what is it in the soliton model that keeps it from going to zero?
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Re: Solitons and Complete QED Lagrangian

Postby Jarek » Sun Apr 19, 2020 9:58 am

Field has to be defined everywhere, including for radius down to zero.
One more time, regularization is thanks to potential, like Higgs' below: V(u) = (|u|^2-1)^2.
This potential makes that field prefers |u|=1 unitary vectors - minimum of potential refereed as vacuum, its dynamics leads to EM in Faber's model, quantzation is thanks to having nontrivial topology.
However, maintaining |u|=1 to the center of singularity (e.g. hedgehog), energy of this field would be infinite due to noncontinuity - to prevent that, field activates potential, getting to u=0 in the center of singularity, as in vector field below.
So in vacuum we have electromagnetism, which deforms into other interactions (weak/strong) inside particles to prevent infinity - by activating Higgs' potential (getting out of its minimum).
Observed experimental consequence of this finite size is running coupling - that Coulomb interaction is deformed for very small distances.

Image
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Re: Solitons and Complete QED Lagrangian

Postby FrediFizzx » Tue Apr 21, 2020 10:09 am

Ok, what is the field energy with radius at zero?
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