Electron-assisted fusion
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Electric charge can be calculated through Gauss law by integrating electric field over closed surface - what has also topological analogue if interpreting spatial curvature of field as electric field.
In similar way they experimentally get Coulomb-like interaction in liquid crystals: https://www.nature.com/articles/s41598-017-16200-z
Temporal change fits better magnetic field, e.g. in Faber's model: https://inspirehep.net/files/f…21cb8020c10f84ca4fdf0ff68
This way he get Coulomb potential if calculating energy of pairs of charges in various distances ... with slight deformation for very small distances - as in running coupling effect.
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Electric charge can be calculated through Gauss law by integrating electric field over closed surface
Unluckily this does not work for the near field of electron/proton. It's perfect for the far field or a large set of charges. It's does not fit particles charges. Also the Coulomb law breaks down for the e/p near field (just gives you 3-4 digits out of 10). So for basic physics you must find an other approach.
This is one reason why the standard model is a total fail. Charge is not a point!
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Indeed electron being perfect point makes no sense - e.g. would have infinite energy of electric field, wouldn't have running coupling effect (as experiment and Faber have).
Here are gathered experimental arguments for size of electron: https://physics.stackexchange.…ries-for-size-of-electron
And so what I and Faber emphasize is regularization - deformation of this field to prevent infinite energy, what can be easily realized using Higgs-like potential: preferring e.g. unitary vectors, but also allowing to deform them to prevent infinity, discontinuity.
See e.g. https://arxiv.org/abs/2108.07896
or just top above:
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And so what I and Faber emphasize is regularization - deformation of this field to prevent infinite energy, what can be easily realized using Higgs-like potential:
In math you can do all you like. But in physics a potential needs a physical generator. There is none for Higgs.
I would no longer waste my time with the standard model math as obviously the solutions for fields using a 3:1 metric are fringe physics. There are no physical generators for 3D fields! The only allowed actions in physics are 1:1 and 2:1
what leads to 1/r and 1/r2 force fields. The unification with 1/r fields in 3D is not possible! So only a magnetic "field" (flux) solution will help.
I did it in SO(4) 6D! what works pretty well and introduces the needed golden ratio flux quantization.
The approach you did follow is similar to what Kransohovelet did try on the sub-matter = instanton level.
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Higgs potential e.g. (|n|2 - 1)^2, quite popular in physics, here just means nontrivial vacuum - e.g. "director field" in liquid crystals, leading to electromagnetism as Goldstone bosons ... potential allows to deform to finite energy to prevent infinite energy singularities.
The 1/r2 (Coulomb) force is proportional to field curvature around topological charges e.g. hedgehog configuration - hence we interpret curvature as electric field, in Gauss law getting charge quantization as topological.
Here they experimentally get even stronger 1/r force in liquid crystals: https://pubs.rsc.org/en/conten…m/c9sm01710k#!divAbstract
Biaxial nematic has SO(3) vacuum in 3D space ... which naturally extends to SO(4) in 4D spacetime - adding 4th axis which tiny perturbations are governed by second set of Maxwell equations - popular GEM approximation of general relativity ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism )
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The 1/r2 (Coulomb) force is proportional to field curvature around topological charges
Sorry: 1/r2 Only in the far field not around e/p!
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Indeed in physics and our models we have asymptotically 1/r2 Coulomb force for topological/electric charges.
For very low distances it is deformed - so called running coupling ( https://en.wikipedia.org/wiki/…constant#Running_coupling ) seen experimentally and in our models - see distance energy dependence diagram in #742 above.
Update: Prepared slides with lots of materials about this resemblance between liquid crystal topological defects and particle physics:
Good talk about topological defects in liquid crystals, their similarity with particles:
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This is what a solid made of electrons looks like
Physicists have imaged elusive ‘Wigner crystals’ for the first time.
This is what a solid made of electrons looks likePhysicists have imaged elusive ‘Wigner crystals’ for the first time.www.nature.com -
This is STM image of hexagonal lattice of graphene, here on right side is STM image for semiconductor instead (source: http://www.phy.bme.hu/~zarand/LokalizacioWeb/Yazdani.pdf ) comparing with standard random walk in defected lattice and MERW ( https://en.wikipedia.org/wiki/Maximal_entropy_random_walk ) having the same stationary density as QM - we can see Anderson localization:
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This has nothing to do with a Wigner crystal. Graphene is hexagonal and has long range connected pi-orbitals already seen in Benzol. So if you use Graphene as a condenser then an electron can only stay in one place - in the center of the hexagon. So the grid constant is given by Graphene and not by any Wigner physics...
Further this only works if you charge the back side positively! So a net force holds the electron.
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This is Wigner crystal from plasma charged particles - also hexagonal
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This is Wigner crystal from plasma charged particles - also hexagonal
Plasma sheer wave can induce a quasi crystalline order. Also here its not a crystal - only a quasi crystal. A true crystal has a 3D structure = "is not flat". In plasma you have sheer forces that balance the repulsion. So it's a meta stable quasi crystalline = "grid like" state.
In a plasma you also cannot take a photo at t1 and t1+delta and get the same picture. This works for flat graphene. So for me such publications are pure science marketing by using big names...to get more funds...
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Quote
A true crystal has a 3D structure = "is not flat".
Wigner crystal of electrons inside graphene would also have 3D structure, but it remains flat because its carrier - i.e. graphene plane - is also flat.
QuoteIn plasma you have sheer forces that balance the repulsion. So it's a meta stable quasi crystalline = "grid like" state.
Well - this is just the way, in which Wigner crystal is defined. The electrons within such a crystal don't touch each other - instead of this, they're held in their metastable positions by repulsive electrostatic forces at distance, in similar way, like charged particles in plasma crystals.
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like charged particles in plasma crystals.
I don't like marketing with wrong terms. Crystals are called crystals because of certain features that are never present in fake termed crystals. May be this is the only way the English language can be used in research. English is an imprecise spongy language not suited for science. You cannot construct new terms and thus you falsely reuse old ones..
So correct is only. Wigner quasi crystals. Same in particle physics. Most of them are quasi-particles. Like Quarks.
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Fake-crystals = Quasicrystals. Pefectly acceptable term.
ETA
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.
Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the field of crystallography. In crystallography the quasicrystals were predicted in 1981 by a five-fold symmetry study of Alan Lindsay Mackay,[2]—that also brought in 1982, with the crystallographic Fourier transform of a Penrose tiling,[3] the possibility of identifying quasiperiodic order in a material through diffraction.
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Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of natural quasicrystals.
The matter is complex and as said the English language cannot deal with adding features to substantives. Classic quasi crystals are still solids. E.g. if you cool down glass at several 100C/second you get amorphous glass. But the above mentioned "Wigner crystals" one should exactly call "quasi - quasi crystals" as these are neither solid nor really periodic = have a 3D Brillouin element/ grid constant.
So the more English papers you read the less you understand because there is no strict terminology....
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To get a deeper understanding of the central here Coulomb force, turns out long-range interactions for (quantized) topological charges are experimentally recreated in liquid crystals, e.g.:
Coulomb: "Coulomb-like interaction in nematic emulsions induced by external torques exerted on the colloids" PRE
dipole-dipole: "Novel Colloidal Interactions in Anisotropic Fluids" Science
quadrupole-quadrupole: "Long-range forces and aggregation of colloid particles in a nematic liquid crystal” PRE
I have prepared simple calculation of such Coulomb (materials, sources: https://github.com/JarekDuda/l…crystals-particle-models/ ) - for two topological charges in various distances, calculate total energy of such configuration by integrating energy density, getting Coulomb effective potential - attraction/repulsion of charges from energy minimization:
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If you want to explain LENR, there is no chance to get 10^6 times energy amplification - the only way is that there is a help with crossing the barrier - like electron staying long enough between them: attracted by both nuclei.
Like initially static p - e - p system: Coulomb says it should collapse.p-p-p sistem is not bad.
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Fake-crystals = Quasicrystals. Pefectly acceptable term.
ETA
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.
Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the field of crystallography. In crystallography the quasicrystals were predicted in 1981 by a five-fold symmetry study of Alan Lindsay Mackay,[2]—that also brought in 1982, with the crystallographic Fourier transform of a Penrose tiling,[3] the possibility of identifying quasiperiodic order in a material through diffraction.
We must notice that the palladium-deuterium alloy is an “hidden quasicrystal” : the deuterium nuclei are randomly inserted in the palladium lattice. There is a short-range disorder, but a long-range order:
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