Clifford Algebra and Maxwell-Dirac theory.

In the 2017 Celani et al paper on Occam's razor for the electron, it seems that they start out in section 3 with a simplified infinitely thin ring charge. Perhaps this is because it is a very good approximation of what is actually happening, and it is instructive. But they don't say this.

In section 3.5 they upgrade it to a torus with big radius r_e and small radius r_0. This was solved approximately by Bergman and Wesley 1990. I don't think it works in an exact sense because the outer part of the ring is moving faster than the inner part of the ring.

Is there a favored, exact Zitterbewegung geometry?

In 2010, Richard Wayte solved the classical electron problem (massless, charge moving at c, EM fields having electron mass energy, static charge and static currents to have zero radiation) with general relativity equations. Probably some of you are aware of this one, I've seen a similar picture of it posted recently in the ICCF22 thread juxtaposed with condensed plasmoid pictures.

https://www.researchgate.net/p…6_A_MODEL_OF_THE_ELECTRON

Are there other solutions or is Wayte's model the gold standard at this point?

Well, a few minutes before my post this was posted to facebook by MFMP:

Quote from Wyttenbach

The four potential is a time dependent potential as Maxwell equations contain time derivatives...

The trouble with Maxwell's equations is that they aren't really Maxwell's equations - Heaviside "improved" them. Nevertheless you can glean something from them. See for example Faraday’s law, ∇ × E = − ∂B/∂t. It doesn't mean what some people think it means. The curl of E is the time rate of change of B. Because E is the spatial derivative of four-potential, and B is the time derivative. I've used a canoe analogy to try explain this.

See the Wikipedia electromagnetic radiation article and note this: “the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first order in time”. The orthogonal sinusoidal electric and magnetic waves in the depictions are misleading. The electric wave is the spatial derivative of the electromagnetic wave, whilst the magnetic wave is the time derivative. For an analogy, imagine you’re in a canoe at sea. Imagine something like an oceanic swell wave or tsunami comes at you. Let’s say it’s a 10m high sinusoidal hump of water without a trough. As the wave approaches, your canoe tilts upward.

The degree of tilt denotes E, whilst the rate of change of tilt denotes B. When you’re momentarily at the top of the wave, your canoe is horizontal and has momentarily stopped tilting, so E and B are zero. Then as you go down the other side, the situation is reversed.

I don't think Maxwell's equations tell you much about the electron. However I think Maxwell's 1871 paper Remarks on the Mathematical Classification of Physical Quantities does. He drew this picture:

The convergence is what's typical drawn to depict an electric field. The curl is what's typically drawn to depict a magnetic field. You have to combine them to depict an electromagnetic field. Here's my version of the above:

And here's a picture that's akin to the strip depiction in post 58:

Quote from Arun Luthra

In section 3.5 they upgrade it to a torus with big radius r_e and small radius r_0. This was solved approximately by Bergman and Wesley 1990. I don't think it works in an exact sense because the outer part of the ring is moving faster than the inner part of the ring.

Is there a favored, exact Zitterbewegung geometry?

I think the favoured geometry is spherical because the electron has no measurable electric dipole. You start with a ring, then you upgrade it to a torus. Then you "inflate" the torus to a horn torus, then you inflate it further to a spindle-sphere torus:

Then it starts to look something like a typical electron depiction:

Note however that it has no surface. The electron's field is what it is, and it doesn't stop abruptly.

Quote from Arun Luthra

In 2010, Richard Wayte solved the classical electron problem (massless, charge moving at c, EM fields having electron mass energy, static charge and static currents to have zero radiation) with general relativity equations. Probably some of you are aware of this one, I've seen a similar picture of it posted recently in the ICCF22 thread juxtaposed with condensed plasmoid pictures.

https://www.researchgate.net/p…6_A_MODEL_OF_THE_ELECTRON

Are there other solutions or is Wayte's model the gold standard at this point?

I don't think I've ever seen Wayte's paper before. I read it and thought it was partly correct. The first paper I read about this was written by John Williamson and Martin van der Mark in 1991. They had trouble getting it published, so it didn't see the light of day until 1997. It's called Is the electron a photon with toroidal topology? Also see Qiu-Hong Hu’s 2005 paper The nature of the electron:

The electron seems to be a special photon with a locked in wave. If I transport the proton inner force equation to the electron frame, then the result is that the electron magnetic mass is not bound to a radius. That's also what experiments tell.

Only a more fundamental approach than current physics uses could solve that issue.

Within the framework we use the electron cannot be fully explained as it is partly defined by an axiom called charge! As said from a logical point of view it is nonsense to find a model based on one axiom to finally explain the axiom.

Nevertheless, within the improved SO(4) framework we can give the electron the known structure it has, based on the electron g-factor, what helps to solve some old problems.

Structure & logic is the basis of all theory (math). It looks like many people in the field missed that class.

Sorry for posting nonsence, I did a new update of the paper on google docs.

New finding is that If you take an sort of even distribution of a EM soup with mostly high frequence stuff or related to small length scales

and then note that an EM field cand be used as a source term and produce an EM field that in turn produces a source term etc, if we consider this process

and consider themagnitude of the new source terms as a constant to the old one and then add all those field together you get my [f]. With this

I think I understand wuite well where QED is comming from. PLease read my linked google doc piece, Im starting to really get it now.

Quote from Wyttenbach

The electron seems to be a special photon with a locked in wave. If I transport the proton inner force equation to the electron frame, then the result is that the electron magnetic mass is not bound to a radius. That's also what experiments tell.

Only a more fundamental approach than current physics uses could solve that issue.

Within the framework we use the electron cannot be fully explained as it is partly defined by an axiom called charge! As said from a logical point of view it is nonsense to find a model based on one axiom to finally explain the axiom.

Nevertheless, within the improved SO(4) framework we can give the electron the known structure it has, based on the electron g-factor, what helps to solve some old problems.

Structure & logic is the basis of all theory (math). It looks like many people in the field missed that class.

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The problem is that current physics claims that photons don't interact with photons, when they do. It's called gamma-gamma pair production, it's been demonstrated at SLAC, see gamma rays create matter just by plowing into laser light. That concerns the Breit-Wheeler process which dates from 1932. But quantum electrodynamics will tell you this:

“From classical electrodynamics we know that EM waves pass through each other without any interference. From Quantum Electro Dynamics (QED) we know that photons cannot couple directly to each other, since they don’t carry charge, but they can interact through higher order processes: a photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion/anti-fermion pair, to either of which the other photon can couple”.

It's garbage. So is the notion that creation and annihilation operators cause the gamma photons pop out of existence whilst the electron and the positron pop into existence. Again, remember what Schrödinger said on page 26 of quantization as a problem of proper values, part II: "let us think of a wave group of the nature described above, which in some way gets into a small closed ‘path’, whose dimensions are of the order of the wave length”. The gamma photons interact and change direction, that's all. From an open path to a closed path. Then each is turned into a standing wave with a standing field, to which we apply the name "charge". The electron g factor is 2.002319. It's twice what it should be in classical mechanics because the wave is wrapped round twice in a spin 1/2 "trivial knot" configuration. The wavelength of a 511 keV photon is 2.426 x 10^-12 metres. Divide this by 2π and what you get is 3.86 x 10^-13 metres:

Many people in the field took the class, but then they decided to ignore it, because Schrödinger was their rival. So was Charles Galton Darwin, who wrote a 1927 paper on the vector-wave electron. They also ignored the Born-Infeld model in the 1930s. That featured a unitarian standpoint, which assumes only one physical entity, the electromagnetic field, wherein “matter particles are considered as singularities of the field”.

GNUFDL image by AllenMcC, see Wikipedia commons and the Wikipedia vector field article

Looks like we have to go way back in time to unravel these mysteries obscured by QM. What about Phat photons of Pharis Williams is this another QM phudge?

Quote from JohnDuffield

“From classical electrodynamics we know that EM waves pass through each other without any interference. From Quantum Electro Dynamics (QED) we know that photons cannot couple directly to each other, since they don’t carry charge, but they can interact through higher order processes: a photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion/anti-fermion pair, to either of which the other photon can couple”.

This is OK for free space. But in solid matter some photons travel on SO(4) orbits and simply do interact as Schrödiger thought.

Quote from Alan Smith

Theoretical Feasibility of Cold Fusion According to the BSM -Supergravitation Unified Theory

Stoyan Sarg Sargoytchev York University, Toronto, Canada *

Stoyan Sargs model (I did look at it about 2 years ago) is a good heuristic approach but not able to give or calculate anything new.

As the exact gravity formula in SO(4) shows: Gravity is only based on the electro weak and electro strong force thus cannot be used to explain nuclear structure. Mills faced the same problem with a much more elaborate gravity based approach that finally paved the way to SO(4) physics. But also Mills did not/find understand the link to the strong force. But his so called "sec" factor (missing force factor) derived from the neutron is only off by 74eV (of neutron mass!!) from the true strong force factor. This did in fact help to find the correct factor.

Maybe I'm missing something, but I don't see how gravity (or supergravity) can contribute an appreciable force at the proton-neutron infinitesmally small mass level. One can't apply the same principles at the beginning of this derivation as apply to cosmological dimensions, and arbitrarily ascribe E = Gm1m2/r3 ie r distance cubed rather than squared without giving any reason for it. If we just replace G with B, a supermagnetic field constant then it all makes sense since it is magnetic fields B which vary with the cube of distance!

Could call it the BSM-Supermagnetic Unified Theory which if we recalculate the model accordingly probably ends up with something approaching SO(4). Otherwise its good to know the theoretical basis for Santilli's magnegas ideas (para-H2 configuration) and I suppose why R.Mills has been using Gd (in the hope of fusion reactions expelling alpha particles as theoretically described here). If we dig deep enough I'm sure we'll find out the rationale behind BLP's experiments, there are undoubtedly kernels of truth to be found amongst the somewhat wacky methodology/unfounded claims/dodgy verifications no doubt trying to keep investors satisfied - while the rest of the scientific community has been tearing it all to shreds. So we should still keep an open mind and not throw the baby out with the bathwater, as they say.

I know, but relativistic or near speed of light particles eg neutrons or muons have to be slowed down so they have time to interact with other particles eg protons or deuterons to induce fusion reactions. Also supergravity theory has been confused with DST (deformed space-time) in the literature, I really don't think AE ever intended this cosmological - scale theory to be applied to the atom. And beware mathematical tricks to try and include gravity into the Standard or not-so-Standard Models of nuclear physics (usually occurring on the first page of most derivations under assumptions). I think theoretical physics needs a good kick up the backside to resolve all four forces into a coherent theory which would account for LENR phenomena too and give us a working hypothesis. Some hope!

Quote from Dr Richard

Looks like we have to go way back in time to unravel these mysteries obscured by QM. What about Phat photons of Pharis Williams is this another QM phudge?

I read this: "A new theoretical development based upon Weyl’s gauge field theory predicts that photon energies are quantized with the energy given by N²hν. Such quantization of photon energy changes the character of the photon from the Einstein photon that does not have a quantum number. Photon energy that includes a quantum number means that for a given energy the frequency may have more than one value". That isn't like any photon I've ever heard about. IMHO the E=hν is there because the dimensiontality of action h can be expressed as energy x time or momentum x distance. I thought action h applies to all photons because they all have the same amplitude of 3.86 x 10^-13 metres. Which is why you can only make an electron with a wavelength of 2.426 x 10^-12 metres. I think of it as something like plucking a guitar with a constant pluck regardless of where your fingers are on the frets. There are no electrons with a mass of 4, 9, 16, 25... times the mass of an ordinary electron. By the way the mass of a body is a measure of its energy-content. Because a wave in a closed path opposes change-in-motion just as a wave in an open path opposes it. See https://arxiv.org/abs/1508.06478 by Martin van der Mark and Gert (not the Nobel) 't Hooft.

Electromagnetic spectrum image thanks to NASA

Quote from Dr Richard

...I think theoretical physics needs a good kick up the backside to resolve all four forces into a coherent theory which would account for LENR phenomena too and give us a working hypothesis. Some hope!

I like to think that I know how they work. Perhaps you'd like to start a new thread on that?

.

The thin ring solution (or better, the ring made of a helix) is stable electrostatically. The ratio of the torus radii needs to be the inverse of the fine structure constant. I don't think spindle toruses or any sphere shaped torii work. unless they have been proved to be static/force-free and stable.

Strictly speaking, it seems charge and current don't even need to be defined, except for convenience purposes in describing measurements and correspondence to the Maxwell equation. There ought to be some principle from a string theory analog or some other theory that fixes the compton wavelength to a huge multiple of the planck length.

Fun fact: the Zitterbewegung solution is similar/analagous (but different) from the stellarator hot plasma confinement geometry, for good reason.

Quote from Wyttenbach

This is OK for free space. But in solid matter some photons travel on SO(4) orbits and simply do interact as Schrödiger thought.

The photons definitely interact. It isn't called gamma-gamma pair production for nothing. As for whether they really travel on SO(4) orbits I don't know. But this picture from the Wikipedia article on rotations in 4 dimensional Euclidean space is similar to depictions of spin ½:

CC By SA image by RokerHRO, see Wikipedia commons

The caption says this: "A 4D Clifford torus stereographically projected into 3D looks like a torus, and a double rotation can be seen as in helical path on that torus. For a rotation whose two rotation angles form a rational number, the paths will eventually reconnect, while for an irrational ratio they will not. An isoclinic rotation will form a Villarceau circle on the torus, while a simple rotation will form a circle parallel or perpendicular to the central axis".

JohnDuffield

Nice attempt to not decorrelate mathematical toughts from your geometric projections, the great Einstein knew how to do it too.

You said:

For a rotation whose two rotation angles form a rational number, the paths will eventually reconnect, while for an irrational ratio they will not.

I think this concept of finite objects is related to our small life duration.

Are they atoms or galaxies really finite if you consider longer of time ?

Both your objects seem to be very alone in the middle of our large empty space ?

you should make geometric attempts in order to "link" them to our empty space.

Our physics seems to consider only two kinetically interacting objects in an inert vacuum, maybe we should try to link these 3 pseudo entities to improve our understanding? object A+object B+ object void C ?

For a rotation whose two rotation angles form a rational number, the paths will eventually reconnect, while for an irrational ratio they will not.

Quote from JohnDuffield

The photons definitely interact. It isn't called gamma-gamma pair production for nothing. As for whether they really travel on SO(4) orbits I don't know. But this picture from the Wikipedia article on rotations in 4 dimensional Euclidean space is similar to depictions of spin ½:

CC By SA image by RokerHRO, see Wikipedia commons

The caption says this: "A 4D Clifford torus stereographically projected into 3D looks like a torus, and a double rotation can be seen as in helical path on that torus. For a rotation whose two rotation angles form a rational number, the paths will eventually reconnect, while for an irrational ratio they will not. An isoclinic rotation will form a Villarceau circle on the torus, while a simple rotation will form a circle parallel or perpendicular to the central axis".

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