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.
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 ...
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.
FrediFizzx wrote:So Jarek believes that the charge of an electron doesn't interact with the field it creates.
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:
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.
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.
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.
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