Four spatial dimensions seems to me to be a stumbling block to accepting SO(4) physics.
Sorry SO(4) has 6 Dimensions. At least this you should be able to remember...
We here deal with sub -De Broglie radius dimensions that we only can indirectly measure as all measuremnt must be made with particles too.
At some level, yes.
Good. That would be more understanding than I have then!
I could ask specific questions about the figure but perhaps it would be better if you could tell me a bit about the essence of what is showing. I don't find the printed explanation that goes with the figure very easy to read.
I don't find the printed explanation that goes with the figure very easy to read.
The 4 colour SO(4) picture is easier to understand than...3 color in QCD.. for me..
"
Quantum Chromodynamics is based on the gauge group SU(3), the Special Unitary group in 3
(complex) dimensions, whose elements are the set of unitary 3 × 3 matrices with determinant
one. Since there are 9 linearly independent unitary complex matrices3
, one of which has determinant −1, there are a total of 8 independent directions in this matrix space, corresponding to eight different generators as compared with the single one of QED. In the context of QCD,
we normally represent this group using the so-called fundamental, or defining, representation,
in which the generators of SU(3) appear as a set of eight traceless and hermitean matrices, to
which we return below. We shall refer to indices enumerating the rows and columns of these
matrices (from 1 to 3) as fundamental indices, and we use the letters i, j, k, . . . , to denote
them. We refer to indices enumerating the generators (from 1 to 8), as adjoint indices
, and
we use the first letters of the alphabet (a, b, c, . . . ) to denote them. These matrices can operate both on each other (representing combinations of successive gauge transformations) and on a set of 3-vectors, the latter of which represent quarks in colour space; the quarks are triplets under SU(3). The matrices can be thought of as representing gluons in colour space (or, more precisely, the gauge transformations carried out by gluons), hence there are eight different
gluons; the gluons are octets under SU(3)...
https://arxiv.org/pdf/1207.2389.pdf
I could ask specific questions about the figure but perhaps it would be better if you could tell me a bit about the essence of what is showing. I don't find the printed explanation that goes with the figure very easy to read.
This would I suspect be like trying to explain the colour purple to a blind man.
On reflection here's something a bit simpler. Most people can get their head around it, but it is generally a source of contention as to its validity as an argument.
A sphere is spinning along one axis, it can then be made to spin along a second axis, which is orthogonal to the first one. One or both od these axes can be made to precess, which adds a third form of motion, finally propel the sphere through space. You have added a fourth movement. All accomplished in 3-space.
This is not an explantion of SO4, just a way of saying that even simple motions may be very complex and the effect upon any particular point on the surface hard to visualise
This is not an explantion of SO4,
This is not an explanation either.. I'm practicing rotations with my light saber .. rotational moves.. some kind of kinaesthetic sensual experience..the eternity spin. from Hank's ashram/
in the anthropomorphic atom course
tried to do it with fingers and thumbs but this is more thrill..
Sorry SO(4) has 6 Dimensions. At least this you should be able to remember...
SO(4) has 6 degrees of freedom. I understand that. But SO(4) is the algebra of rigid rotations in 4-space ... which is how it seems to come up in your theory. You seem to posit 4 spatial dimensions through which circulating current flows and this, at first glance, seems to me to be a problem. I would like to see an account of how the 3 tangible spatial dimensions of ordinary physical experience arise from the original 4 dimensions.
On reflection here's something a bit simpler. Most people can get their head around it, but it is generally a source of contention as to its validity as an argument.
A sphere is spinning along one axis, it can then be made to spin along a second axis, which is orthogonal to the first one. One or both od these axes can be made to precess, which adds a third form of motion, finally propel the sphere through space. You have added a fourth movement. All accomplished in 3-space.
This is not an explantion of SO4, just a way of saying that even simple motions may be very complex and the effect upon any particular point on the surface hard to visualise
I agree with all this. I just don't see the role it plays in Wyttenbach's theories or, to be more specific, in understanding Figure 1 of Wyttenbach's Researchgate paper (i.e., the figure that RobertBryant posted earlieron this thread).
I understand the rudiments of rigid rotations in 4-dimensional space and I understand that the algebra for these rotations is the SO(4) group. I understand that double rotations are possible in 4D (but not in 3D) and that if you take an arbitrary vector extending from the centre of rotation and subject it to all possible double rotations its tip will trace out a Clifford torus (much as a 3D vector subjected to all possible 3D rotations traces out a 2-shere). But now I struggle trying to relate Wyttenbach's physical picture with all of this. I had hoped that the scheme shown in the figure in Wyttenbach's paper might be a way to think about this connection. But I just don't understand what is going on there. .
I agree with all this. I just don't see the role it plays in Wyttenbach's theories or, to be more specific, in understanding Figure 1 of Wyttenbach's Researchgate paper (i.e., the figure that RobertBryant posted earlieron this thread).
Well, take a deep breath and take up fishing instead.
Bruce__H , I know it’s hard to get around. I still struggle to visualize it and have devoted a fair amount of time. The real important issue here, at the bottom line, is that this model allows to make a series of calculations about particles masses. These calculations achieve a much greater level of accuracy than the SM does, with respect to the experimentally measured values, and that’s what should stand out at the end.
But SO(4) is the algebra of rigid rotations in 4-space ...
4 rotations (of the Biot Savart Operator) are needed to get a self attractive current. This is what happens on the Clifford torus and delivers the strong force equation of attraction. But attraction can only happen between charge and EM flux so, in addition, you must place charge in radial distance to the Clifford torus - for simplicity just think its the 5th dimension (rotation).
Faraday's law for inducing charge is the existence of a bounded flux tube with a changing flux inside. The changing can easily be see . 5 rotations in 6D walk over the fully space with 5 independent axes. So always one dimension is carrying no vector. So a 6D symmetric 5 axes rotations generates a constantly changing flux at all places of the same size/frequency.
T5 rotations flux tube does self enclose the flux. This feature all the old folks did overlook.
The other thing people never did grasp. Charge can only be topological otherwise you could not use the QM formalism as classic charge is repulsive but topological charge is not.
The same thing we see in super conduction and the skin effect. Current in reality is spin wise transported magnetic flux. This is why the real measured electron flux in a conductor is of the size of 2-3mm/s
Sad this thread created by Jarek about Grizinsky deep theory below, was recovered by narrow-minded theorists 
Display MoreImagine zero velocity situation: two protons and electron in the middle between them ( p ---- e ---- p ).
The Coulomb force says that electron-proton attraction is four times stronger than proton-proton repulsion.
So this simple 3 body system should collapse – down to fusion into deuteron.
This trivial example suggests that electron could be very helpful in overcoming Coulomb barrier for LENR.
What is wrong with this picture? That it requires” classical” trajectory of electron, while we are expected to consider the quantum picture: with electron smeared into a probability density cloud – making such electron assisted fusion practically improbable.
So the main question here is: can we consider a trajectory of electron? For example averaging to the quantum probability distribution.
There are many arguments that we can, for example equivalent dBB interpretation: that inserting psi = rho * exp(iS) to Schrodinger equation, we get continuity equation for the density (rho) and “classical” Hamilton-Jacobi equation for action S, with h-order correction/perturbation: of interaction with the pilot wave.
Great intuition about this picture provides e.g. “classical-quantum” Couder experiments , getting for example interference: the corpuscle travels one paths, while its “pilot” wave travels multiple waves, influencing trajectory of the corpuscle (e.g.).External Content www.youtube.comContent embedded from external sources will not be displayed without your consent.Through the activation of external content, you agree that personal data may be transferred to third party platforms. We have provided more information on this in our privacy policy.
So imagine there is some (semi-classical) trajectory of electron’s corpuscle inside atoms, piloted by its wave, averaging to Schrodinger’s probability cloud.
What trajectories should we expect? The first answer is Sommerfeld-Bohr’s elliptic trajectories. However, the ground hydrogen has zero angular momentum: we should degenerate the ellipse into a line: a free-fall trajectory.
What is missing in Bohr-Sommerfeld is taking electron’s magnetic dipole moment into consideration – it is corrected in the free-fall atomic model of Gryzinski.
This correction, classical spin-orbit interaction, has large influence on the free-falling trajectories.There appear also backscattering trajectories: when electron turns 180 degrees – allowing it to jump a few times between two nuclei, screening the Coulomb repulsion. And so Gryzinski has a note in Nature about cold fusion in 1989.
Gryzinski's papers (~30 from Phys. Rev. type of journals, ~3000 total citations): https://scholar.google.pl/scholar?hl=en&q=gryzinski
Wikipedia article: http://en.wikipedia.org/wiki/Free-fall_atomic_model
Slides about free-fall atomic model: https://www.dropbox.com/s/38xidhztpe9zxsr/freefall2.pdf
Simple simulations in Mathematica: http://demonstrations.wolfram.com/KeplerProblemWithClassicalSpinOrbitInteraction/
What do you think about it?
update: simulations of atoms with electron's magnetic dipoles taken into consideration (classical spin-orbit interaction):
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update: gentle introduction to Maximal Entropy Random Walk - https://en.wikipedia.org/wiki/Maximal_Entropy_Random_Walk
2017 paper about its connection with QM: https://arxiv.org/pdf/0910.2724v2.pdf
showing why standard diffusion models are only approximation (of the Jaynes maximum uncertainty principle required by statistical physics models), and that doing diffusion right there is no longer disagreement with thermodynamical predictions of QM (Anderson localization):
Update: Gryzinski's 1991 CF paper "Theory of electron catalyzed fusion in Pd lattice": https://aip.scitation.org/doi/abs/10.1063/1.40688
One (top)/two(bottom) electron trajectories for molecular bonds from his book, top-left is the one which could allow for fusion: with electron traveling between two nuclei, screening their Coulomb repulsion. In the paper above he writes that Pd lattice helps stabilizing such trajectories:
Sad this thread created by Jarek about Grizinsky deep theory below, was recovered by narrow-minded theorists
Why sad? Why should be discuss about nonsense?
I built a lot of junk thinking it would help explain all this but understand why its better sometimes to just keep it to myself.
Farraday's birthday cake!
lol
History reminds us every day that those are the self-proclaimed messiahs who decide for all what is good and what is bad.
Why sad? Why should be discuss about nonsense?
History reminds us every day that those are the self-proclaimed messiahs who decide for all what is good and what is bad.
yup, its better to just point things out and let them decide for themselves
missing copper wire or is it just a dead bug
