Solitons and Complete QED Lagrangian

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Re: Solitons and Complete QED Lagrangian

Post by Jarek » Thu Jun 11, 2020 1:17 am

If someone would like to discuss particle models, we have talk by Manfried Faber this Tuesday, and probably followup next weeks: http://th.if.uj.edu.pl/~dudaj/QMFNoT

Re: Solitons and Complete QED Lagrangian

Post by Jarek » Wed May 20, 2020 2:08 pm

Just recorder lecture about these soliton particle models: https://www.youtube.com/watch?v=2r4hlWIEkTE

Re: Solitons and Complete QED Lagrangian

Post by FrediFizzx » Fri May 15, 2020 2:55 pm

JohnDuffield wrote:… Matter is where the photon path is a closed twisted path.

Probably not a photon but a point-like entity that is due to the loop of twisted spacetime not closing. IOW, matter is broken spacetime symmetry. Photons are probably phonons of the quantum vacuum medium.

Our paper relevant to this thread has been updated.
https://arxiv.org/abs/1705.06036
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Re: Solitons and Complete QED Lagrangian

Post by JohnDuffield » Tue Apr 28, 2020 10:00 am

FrediFizzx wrote:Twisted spacetime is called matter.
I think that's more or less right Fred. ELectromagnetism is spatial curvature. Gravity isn't. It's where space is "neither homogeneous nor isotropic".

Jarek, I don't like the looks of some of the stuff you've been saying here. Imagine you’re standing on a headland overlooking a flat calm sea near an estuary. The water is saltier on the left than on the right. You see a single ocean wave, and notice that its path curves left a little because of the salinity gradient. The sea is an analogy for space. The salinity gradient is an analogy for a gravitational field. The ocean wave is an analogy for a photon. Now look at the surface of the sea where the wave is. It’s curved. It’s curved in a far more dramatic fashion than the curved path of the wave. This observation might sound radical, but see what Percy Hammond said in the 1999 Compumag: “We conclude that the field describes the curvature that characterizes the electromagnetic interaction”. See what Schrödinger said on page 18 of his 1926 paper quantization as a problem of proper values, part II: “classical mechanics fails for very small dimensions of the path and for very great curvature”. Also see what Maxwell said when he was talking about displacement current in 1861: “light consists of transverse undulations in the same medium that is the cause of electric and magnetic phenomena”. Where is space curved? Where the photon is. Because space waves. Matter is where the photon path is a closed twisted path.

Re: Solitons and Complete QED Lagrangian

Post by FrediFizzx » Wed Apr 22, 2020 8:30 pm

Jarek wrote:Beside ~10^40 times disagreement, allowing negative field energy is another disqualifying problem - would literally cause entire universe to explode.

I don't know any >10^13GeV fermions and Faber's model don't have them - we search for soliton model which exactly recreates particle menagerie from physics: no more no less.

You are not paying attention at all. There is no negative field energy and there is no 10^40 disagreement. Gravitational torsion field energy does not exist on it own. It only exist within elementary fermions where it is counter balanced by the electrostatic energy. The net result is observed positive rest mass!!!!!!!!!!!!!!!!!
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Re: Solitons and Complete QED Lagrangian

Post by Jarek » Wed Apr 22, 2020 8:10 pm

Beside ~10^40 times disagreement, allowing negative field energy is another disqualifying problem - would literally cause entire universe to explode.

I don't know any >10^13GeV fermions and Faber's model don't have them - we search for soliton model which exactly recreates particle menagerie from physics: no more no less.

Re: Solitons and Complete QED Lagrangian

Post by FrediFizzx » Wed Apr 22, 2020 8:12 am

Jarek wrote:The basic rule of physics is minimizing energy.
If you think that field has a possibility to go to negative energy, so why it doesn't use it???????? - in entire universe going to this lower energy state

That's a good question. But also, why aren't there fermions with more than 10^13 GeV of energy as shown in the plot? Well, Planck length could be a natural ultimate cutoff for the first question. And for the second question is why I am interested in looking at soliton solutions.
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Re: Solitons and Complete QED Lagrangian

Post by Jarek » Tue Apr 21, 2020 11:59 pm

The basic rule of physics is minimizing energy.
If you think that field has a possibility to go to negative energy, so why it doesn't use it???????? - in entire universe going to this lower energy state

Re: Solitons and Complete QED Lagrangian

Post by FrediFizzx » Tue Apr 21, 2020 9:21 pm

Jarek wrote:Scale of vertical axis is such that sum of integrals of 3 plots is 511keVs.

The problem with your plot is that it requires negative energy, what is nonphysical - if negative energy is possible, why field of the Universe don't just go there? - as it has tendency to go the the lowest possible energy

Thanks. The total energy is never negative. The gravitational torsion term only exists within elementary fermions which always have a positive rest mass energy. Don't deceive yourself about this. The large energy for the electrostatic term and the negative torsion term never exist because they balance each other out. The result is the observed positive rest mass energy. That is all that matters. Pun intended. :D
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Re: Solitons and Complete QED Lagrangian

Post by Jarek » Tue Apr 21, 2020 8:32 pm

Scale of vertical axis is such that sum of integrals of 3 plots is 511keVs.

The problem with your plot is that it requires negative energy, what is nonphysical - if negative energy is possible, why field of the Universe don't just go there? - as it has tendency to go the the lowest possible energy

Re: Solitons and Complete QED Lagrangian

Post by FrediFizzx » Tue Apr 21, 2020 4:17 pm

We see something similar with our formula,



Image

Explanations are here.
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Re: Solitons and Complete QED Lagrangian

Post by FrediFizzx » Tue Apr 21, 2020 2:39 pm

Jarek wrote:Generally we want 511meV mass of electron to completely come from energy of its field configuration.
Cutting out radius ~1.4fm ball in the center, the remaining electric field has ~511keV energy, hence we need deformation of electric field (from of perfect point charge) in a bit larger distance.

Here is Faber's energy density per radius from: https://iopscience.iop.org/article/10.1 ... 012022/pdf for r0~2.2fm:

Image

It drops to zero in r=0 as it contains multiplication by area of sphere.
Red is from electric field - without regularization it would go to infinity in r=0. It was prevented by activated potential - blue plot corresponding to weak/strong interactions.

What is the scale on the left hand side of the plot?
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Re: Solitons and Complete QED Lagrangian

Post by Jarek » Tue Apr 21, 2020 2:15 pm

Generally we want 511meV mass of electron to completely come from energy of its field configuration.
Cutting out radius ~1.4fm ball in the center, the remaining electric field has ~511keV energy, hence we need deformation of electric field (from of perfect point charge) in a bit larger distance.

Here is Faber's energy density per radius from: https://iopscience.iop.org/article/10.1 ... 012022/pdf for r0~2.2fm:

Image

It drops to zero in r=0 as it contains multiplication by area of sphere.
Red is from electric field - without regularization it would go to infinity in r=0. It was prevented by activated potential - blue plot corresponding to weak/strong interactions.

Re: Solitons and Complete QED Lagrangian

Post by FrediFizzx » Tue Apr 21, 2020 10:09 am

Ok, what is the field energy with radius at zero?
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Re: Solitons and Complete QED Lagrangian

Post by 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

Re: Solitons and Complete QED Lagrangian

Post by 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

Post by 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.

Re: Solitons and Complete QED Lagrangian

Post by 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

Post by 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.

Re: Solitons and Complete QED Lagrangian

Post by 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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