Something is rotten in the state of QED

[Joy Christian]

Faber has repaired lacks of standard electromagnetism - of charge quantization (that Gauss law can only give integer charges) and charge having finite energy (point charge has infinite). There indeed remains some freedom of interpretation.
Do you? Claiming to have a model of nature, start with showing that it properly handle the best known interaction: electromagnetism.

Your mistake --- as Fred has been trying to explain to you but you wouldn't listen --- is to think that electromagnetism can be "repaired" in isolation from gravitational torsion. It cannot be.

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[Jarek]

Not true.
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:


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.

[FrediFizzx]

Faber has repaired lacks of standard electromagnetism - of charge quantization (that Gauss law can only give integer charges) and charge having finite energy (point charge has infinite). There indeed remains some freedom of interpretation.
Do you? Claiming to have a model of nature, start with showing that it properly handle the best known interaction: electromagnetism.

Your mistake --- as Fred has been trying to explain to you but you wouldn't listen --- is to think that electromagnetism can be "repaired" in isolation from gravitational torsion. It cannot be.

***

Oh, I understand what he means by "repaired" now. Yeah, no problem with that since gravitational torsion provides a natural cutoff in the complete QED Lagrangian and counter balances the EM energy. Well, I think we have hijacked John's thread enough. Probably should start a new thread about this.
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[Jarek]

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.

[Jarek]

Just got email from Oliver with improved version: https://arxiv.org/pdf/2110.02078

The renormalization quotes are great:
Feynman: “It is whether or not the theory gives predictions that agree
with experiment. It is not a question of whether a theory
is philosophically delightful, or easy to understand, or per-
fectly reasonable from the point of view of common sense.
The theory of quantum electrodynamics describes Nature
as absurd from the point of view of common sense. And
it agrees fully with experiment. So I hope you can accept
Nature as She is: absurd. I’m going to have fun telling
you about this absurdity, because I find it delightful. Please
don’t turn yourself off because you can’t believe Nature is
so strange.”

Dirac: “I must say that I
am very dissatisfied with the situation because this so-called
’good theory’ does involve neglecting infinities which ap-
pear in its equations, ignoring them in an arbitrary way.
This is just not sensible mathematics. Sensible mathematics
involves disregarding a quantity when it is small – not ne-
glecting it just because it is infinitely great and you do not
want it!. ”

[FrediFizzx]

We solved the problem with QED and electrodynamics in general.

https://www.mdpi.com/2218-1997/6/8/112
"On the Role of Einstein–Cartan Gravity in Fundamental Particle Physics"

https://arxiv.org/abs/1903.10902
"Existence of Matter as a Proof of the Existence of Gravitational Torsion"

https://arxiv.org/abs/2103.04468
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[Jarek]

The problem of subtracting infinity by hand in renormalization?
I have briefly looked but don't see the solution there - could you elaborate?

QED is Feynman ensemble of fields - which already have the infinite energy problem e.g. for electric field around electron, hence its ensemble still has infinite energy.
We need to regularize this field to finite energy - we do it by using Higgs potential allowing field to deform to avoid this infinity like in diagram above.
How would you like to do it?

[FrediFizzx]

The problem of subtracting infinity by hand in renormalization?
I have briefly looked but don't see the solution there - could you elaborate? ...

Eq. (25)

First term is the electrostatic term, second term is spin-torsion term of which the electrostatic term cancels it out leaving the rest mass-energy. The radius is close to Planck length.
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[Jarek]

So what is energy density distribution around electron?
Here is Faber's from https://iopscience.iop.org/article/10.1 ... 012022/pdf - the red line is from electric field, which normally would go to infinity, but here is regularized by activating Higgs-like potential:


Integrating standard electric field energy density from 1.4 femtometers, we get 511keV mass of electron.
Not to exceed mass of electron, we need deformation in femtometer distance, not of Planck length.

[FrediFizzx]

@jarek I don't know what the numbers on the LHS of the plot mean.
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[Jarek]

This is Fig. 2 from https://iopscience.iop.org/article/10.1 ... 012022/pdf
r0 = 2.21 fm chosen to integrate to total 511keV electron's mass, which can be released as energy in annihilation, vertical axis is energy density.

The red plot is asymptotically energy of electric field \propto r^-4 multiplied by sphere area, so asymptotically it should be ~r^-2.

Such radius energy dependence would integrate to infinity for r->0
Instead we can see it goes down to zero - what happens due to activation of Higgs-like potential (blue, also requiring green).

Intuitively, we activate other interactions (weak, strong) to prevent infinite energy singularities like in center of charge - indeed these weak/strong interactions only appear in the particles (are short-range).

[FrediFizzx]

Well, you can see from our formula,

,

that there is a solution at the classical electron radius also. That is because at that radius the spin-torsion term becomes essentially zero.

So, in effect, an electron has two "sizes". One near Planck length at meters and one at the classical radius both giving .
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[Jarek]

I see one radius in your formula, while we need rho(r) dependence - so what is mean energy density in given distance from electron? (like in plot from Faber)

Asymptotically rho(r)~1/r^2 from electric field, but it integrates to infinity, while cannot exceed 511keV.

[FrediFizzx]

I see one radius in your formula, while we need rho(r) dependence - so what is mean energy density in given distance from electron? (like in plot from Faber)

Asymptotically rho(r)~1/r^2 from electric field, but it integrates to infinity, while cannot exceed 511keV.

As I was saying the spin-torsion term is essentially zero at the classical radius.



So, we in fact have two "sizes" to deal with. I will calculate the rest later.
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[Jarek]

The question is single function: rho(r) - mean energy density in distance r from electron.
Asymptotically it should only contain energy of EM field, but needs to be deformed in fm-scale not to exceed 511keV mass.

[FrediFizzx]

The question is single function: rho(r) - mean energy density in distance r from electron.
Asymptotically it should only contain energy of EM field, but needs to be deformed in fm-scale not to exceed 511keV mass.

We don't need to do the energy density. Our formula says that the energy of the coulomb field is the rest mass-energy of the electron at the classical electron radius. And that the energy of an electron is entirely electromagnetic.
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[FrediFizzx]

What is more is that it's the same at the meter radius. The energy of the coulomb field is the rest mass-energy of the electron.
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[Jarek]

Electric field of electron has concrete energy density, asymptotically rho(r) ~ 1/r^2.
But it integrates to infinity, not to exceed 511keV electron mass, you need to ingrate from at least r0 ~ 1.4fm.
So there is big question of behavior of rho(r) in fm-scale: 10^-15m.
Integrating from 10^-34m, you get ~10^19 times too large energy.

[FrediFizzx]

Electric field of electron has concrete energy density, asymptotically rho(r) ~ 1/r^2.
But it integrates to infinity, not to exceed 511keV electron mass, you need to ingrate from at least r0 ~ 1.4fm.
So there is big question of behavior of rho(r) in fm-scale: 10^-15m.
Integrating from 10^-34m, you get ~10^19 times too large energy.

No you don't get too large of energy. Electric coulomb field is still equal to . I don't have to integrate anything. I already have the answers that I want.
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[Jarek]

To get total energy you have to integrate energy density. Integrating energy density of electric field from distance lower than 1.4fm one exceeds mc^2 of electron - nonsense.
That's the big charge regularization problem, officially still unresolved, requiring deformation of standard EM energy density.
https://physics.stackexchange.com/quest ... int-charge