Electron-assisted fusion

Quote from Wyttenbach

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.

That's what I understood.,.. the 4D bit I think

The further dimensions ...

Quote from Wyttenbach

5 rotations in 6D walk over the fully space with 5 independent axes.

are for further meditation...

but in the meantime

fishing is boring

I will make takoyaki..3D balls

for the congregation , Covid bans are off..3 water baptisms at Balmoral beach tomorrow

Quote from RobertBryant

That's what I understood.,.. the 4D bit I think

Please help me understand what is going on in Figure 1 of Wyttenbach's Researchgate paper (the one you posted earlier). What is your understanding of what is depicted there? And how does it relate to a Biot-Savart operator or a Clifford torus?

Quote from Bruce__H

Please help me understand what is going on in Figure 1 of Wyttenbach's Researchgate paper (the one you posted earlier). What is your understanding of what is depicted there? And how does it relate to a Biot-Savart operator or a Clifford torus?

I've taken a peek a while ago and got frightened away, but have avowed I'll try to understand the thing in time even if it takes learning some more math.

Probably someone has mentioned this before here, which is why it comes to mind : I envision the fourth dimension (time) becoming somehow spatialized at very small scales and in certain circumstance, so we get 4D space but at the expense of time. This might be why some particles like protons and electrons have staying power : they internally experience little or no time component. Similarly, I envision that a measly photon of light can travel millions of years between galaxies and survive intact because internally it is experiencing little or no time, a trade off for experiencing externally a whole lot of space.

On a lighter note, for your enjoyment here's a very metaphysical primer regarding the joys of (just) 3D geometry of the universe. Toroids and hyperboloids unite!

Quote from Bruce__H

Please help me understand what is going on in Figure 1 of Wyttenbach's Researchgate paper

In classic 3D space two magnetic moments settle down in a minimal force configuration. With two independent ring current only a 1D interaction happens from the field to the the other current. Either left or right depending on the orientation of the ring current field. In reality these loops are connected and in total form out 8 loops. After four 90 degree rotations the loop has the same orientation but runs on the backside of the Clifford torus.

The picture shows that the 1D connected loops all start to rotate in the same sense.

If you understand the full physics, then you will know that in fact only the magnetic flux rotates and charge(current) is static = stays in place. So this picture is the classic mirror of the reality.

All depends on what is your inertial frame.

We could also say nothing rotates in reality. It's only the flux that naturally follows the Clifford Torus orbit - that is a minimal Lagrangian surface. Here we see the total symmetry of all involved pictures. EM-flux:: charge ; EM-flux :: coupling mass mass :: mechanics laws.

Quote from Wyttenbach

After four 90 degree rotations the loop has the same orientation but runs on the backside of the Clifford torus.

Thanks Wyttenbach

After four 90 rotations in 3D space.. this doesn't happen?

No matter how skilful the Grand Chef Chinois is..

This is the 'wiggle room" that 4D creates..

Now I have to chop up those poor little 3D octopi..

Quote from Wyttenbach

In classic 3D space two magnetic moments settle down in a minimal force configuration.

Thanks for the reply. I completely understand this part.

Quote from Wyttenbach

With two independent ring current only a 1D interaction happens from the field to the the other current. Either left or right depending on the orientation of the ring current field.

In these two sentences are you still talking about the classic 3D situation? Or are you now talking about what happens in a 4D space when the 2 loops lie in completely orthogonal planes?

Quote from Wyttenbach

In classic 3D space two magnetic moments settle down in a minimal force configuration. With two independent ring current only a 1D interaction happens from the field to the the other current. Either left or right depending on the orientation of the ring current field. In reality these loops are connected and in total form out 8 loops. After four 90 degree rotations the loop has the same orientation but runs on the backside of the Clifford torus.

The picture shows that the 1D connected loops all start to rotate in the same sense.

If you understand the full physics, then you will know that in fact only the magnetic flux rotates and charge(current) is static = stays in place. So this picture is the classic mirror of the reality.

All depends on what is your inertial frame.

We could also say nothing rotates in reality. It's only the flux that naturally follows the Clifford Torus orbit - that is a minimal Lagrangian surface. Here we see the total symmetry of all involved pictures. EM-flux:: charge ; EM-flux :: coupling mass mass :: mechanics laws.

I am still failing to understand what is going on in Figure 1 of your ResearchGate paper. The diagram indicates that the 2 current loops shown lie in orthogonal planes (x,y and u,v) of a 4-dimensional space. Is that correct? How does the Biot-Savart law work in 4-dimensions where there is no standard cross product available?

Quote from Bruce__H

How does the Biot-Savart law work in 4-dimensions where there is no standard cross product available?

All basic action in physics (Momentum-Operator) goes from 2D->1D in total 3D. In higher D space this is a cyclic action. Start with the Parsely Paper Robert once linked for you!

The problem with Physics in > 3D is your brain/ visualization needs extra training!

Same for basic pyhsic rules:

What is the center of mass/action in 3D,t physics in SO(4) is the whole Clifford torus surface. This can be logically derived as the topological order just gets extended with each tangent space (3-->6) you add. Point --> circle --> ball (Sphere surface area) --> manifold.

This step is basic and difficult to grasp as you will find no paper/book that shows this.

Quote from Wyttenbach

All basic action in physics (Momentum-Operator) goes from 2D->1D in total 3D. In higher D space this is a cyclic action. Start with the Parsely Paper Robert once linked for you!

The problem with Physics in > 3D is your brain/ visualization needs extra training!

I looked a the paper by Parsley. It is still in 3D (in a 3-sphere embedded in 4-space). They need to do this because the Boit-Savart operator they use takes vector fields to vector fields via a cross product and there is no cross product defined in 4D. The intent of the paper is to explore what happens to the Biot-Savart operator in a curved space (hence the embedding in a 4D space) but the action of the operator still takes 2D->1D. So I don't see how that paper talks about the Biot-Savart law in 4D or anything being cyclic

I think the problem is there is no 4D physics 1001 course

available online yet..

unlike wonton folding 16 ways

It took me awhile to figure out how to get 16 steps to return to 1111..

first I got 4 steps

next I got 8 steps twice

then I looked back how to get 16 steps..

RobertBryant

Could you please explain to me what is going on in the figure you posted ... the one taken from Wyttenbach's paper? I don't understand what is being depicted.

Quote from Bruce__H

The intent of the paper is to explore what happens to the Biot-Savart operator in a curved space (hence the embedding in a 4D space) but the action of the operator still takes 2D->1D.

As I said: Basic math field operators must always be 2:1. But the important fact is to notice that each added dimension ads left/right transport of the field. If you add more dimensions you can only go on by "right->right->" or left-> left->" all along new great circles you define with each added dimension (3--> 6). What you finally get is an infinite (time less) flux along the 4 great circles, because the Biot Savart force and then rotation speed in the equilibrium end up in the static Lorenz action.

The final picture is a 2D (1 added rotation) flux tube that produces the self induced charge mutually enwinded by a 4 rotation flux layer.

You obviously cannot use classic field math to describe the final static situation given e.g. by an alpha particle. The alpha is the first full symmetric 4 rotation particle (always + 1 rotation for charge). The modelling shows that it is composed by 4 symmetric protons that seem to go on with their own rotations. What produces the 4-He quadrupole field. To make this a bit more complex we still have the external charge flux-tube that is responsible for a "potential mass".

The final problems - to find a perturbative model are:

- Lorenz interaction and Biot Savart effects could coexist. Do we need 4:1 or 5:1 Operators?

- We know from experiments that only 2 "synchronous" rotations can stimulate the strong force binding. Thus perturbations must be 2D rotations at least. So again we we have 2:4 actions in 6D what could be reduced.. to 1:2 eventually.

- The Golden ratio is the fixpoint operator for the mass forming waves so with 5 rotations you get 72 degrees also know as golden angle...But this gives no correlation so far. You cannot break it down to 5 plain (photon like) rotations.

It took 10 years to settle down a first consistent math description for GR. Mostly done by Grossmann not Einstein and many others (Hilbert) did help discussing.

We here still even miss the starting line for any discussion. But contrary to GR we have the exact experimental proof that the model reproduces nature. So it should take less time, at the end, to enhance it.

And last: Larger nuclei potentially need octonions to complete the structure equations...

I think the wobble is just the expansion we are stuck in. If we are in a 16

flustering math

that everything is expanding from the wobble, slowly pulling everything apart.

Quote from Wyttenbach

As I said: Basic math field operators must always be 2:1. But the important fact is to notice that each added dimension ads left/right transport of the field. If you add more dimensions you can only go on by "right->right->" or left-> left->" all along new great circles you define with each added dimension (3--> 6). What you finally get is an infinite (time less) flux along the 4 great circles, because the Biot Savart force and then rotation speed in the equilibrium end up in the static

Can you relate this all back to Figure 1 from you paper? You show 2 current loops there. They are said to be in orthogonal planes (x,y and u,v) and you show a magnetic field vector, B, for both. But how do you get a magnetic field vector from a current loop in 4 dimensions when the right hand rule doesn't apply?

Quote from Bruce__H

But how do you get a magnetic field vector from a current loop in 4 dimensions when the right hand rule doesn't apply?

Who says this? Just replace right by (Xi-1, Xi) --> Xi+1 of course circular.

Once more: This is not Euclidian 4D its 4 rotation space! Just a projection to 4D. You don't get 4 independent 4D rotations in 4D unless you restrict the rotations to 3D sub-structures, what is one possible solution you see with the 3D/4D mass. (See rotation matrix/Sequence)

Quote from Bruce__H

I don't understand what is being depicted.

you need to meditate Bruce.. start with 1111..

the silverspoon is not free

Quote from Wyttenbach

Who says this? Just replace right by (Xi-1, Xi) --> Xi+1 of course circular.

It seems as though you are saying that the usual 3D right-hand rule for taking 2 vectors and finding a 3rd one should be replaced by a rule that takes 2 vectors Xi-1 and Xi as inputs and then outputs a new vector in the direction of Xi+1 with the indicies going around in a circular fashion. Hence in 4-space we would have the following cross products ...

(X1, X2) -> X3

(X2, X3) -> X4

(X3, X4) -> X1

(X4, X1) -> X2

Is that right?

In a circle the current basically always flows in two directions. So the above is OK.

The rest is not straight forward as you did see we cannot predict which direction the flux will turn. This is somehow given by the total energy/trajectory length that fits the CT and the charge induced 5th rotation orbit. The complete rotation matrix for the 3D/4D flux shows that we can have 2,3,5 wave coupling points. (3D/4D means 3 rotations of a 3D mass in 4D space)

This is further complicated by the fact that excess flux flowing outside of the CT changes its shape to a 9:8 torus ratio. This is why the proton (a 3D/4D particle) has 1/9 excess mass hence you can break it. For larger nuclei this gets even more complex with the torus 7:4 ration being active too.

As said: The model is a starting point and very complex but fits. To get the first two gamma lines of 12-C it took more than 3 years. As long as only one person works on SO(4) physics, its progress and understanding will grow slowly and in my case it will follow my LENR work. What sometimes delays the publishing due to other interests.