# What Zitterbewegung is

• In my opinion, the weakness of your approach is that the formulas use the external vector potential, and not the potential generated by the electron.

The potentials in the Lagrangian formula are actually generated by the electron. Extra-dimensions are not necessarily wrongs but should be introduced only if there are no alternatives.

• But it seems to me that this is a selected value of the external potential, which is equal to the potential of an electron on a circle of a certain radius. The electron's own potential must be specified by a vector field in Minkowski space.

• But in such models, the mass of a particle can be equal to the length of a closed curve (node), which is formed by the flow current lines.

The mass can only be given as an equivalence relation between the total EM forces between the involved EM-flux masses. See SOP strong force equation.

The potentials in the Lagrangian formula are actually generated by the electron.

The EM (B) field geneated by the electron is a fiction as in reality it is the added EM flux mass corresponding to the increase in moment.

No moving charge can generate a B field that itself regenerates the E field. So there is no helical charge path. But factually the toroidal EM flux is helical (4D on CT without coupling)).

To understand this undergraduate logic is enough. Coil like B fields are internal only - almost only = if the helical path is infinite fine....what in reality is not given as we simply have a manifold that is = the field = flux. As the manifold is continuous and closed and single sided no net charge can be generated at all except you add one more rotation that leads to self enclosure of the flux manifold.

4 rotation produce + - + - = 0 net charge. 5 rotations + - + - + = 1 stable net charge.

So Bayak is right when he says that the external visibility of charge depends on the local structure of the field that e.g. for the electron is 2:1 ( (1x1)X(0.5x0.5) on CT) and the proton is 5:3.2.

Either you agree that we model flux as manifolds or we stay with the 100 years infantile physics starting with Einstein.

• for the electron is 2:1 ( (1x1)X(0.5x0.5) on CT) and the proton is 5:3.2.

Regarding CT orbits. The SO(4) tangent space to CT is 4D and provides 4 circle like rotations I denote as (1x1)X(1x1) = 4 orbits = 2 convex 2 concave or metric 1100 for one side and the same for the back side. Total 8 circle like rotations for a single helical path in a projection to 2D.

((1x1)X(1x1)) X (1x1)X(1x1) ) gives all CT paths (rotations) what I shortcut as (2x2)X(2x2) the rest (5th rotation) is an overlap with the electron structure (1x1)X(0.5x0.5) that generates the perturbative 3:2 rotations for charge (2) and magnetic moment (3).

4 - 3 rotations gives the magnetic moment path (1D visibility of charge) 4-2 gives the classic 2 rotation (S2) visibility of charge.

• Regarding CT orbits. The SO(4) tangent space to CT is 4D and provides 4 circle like rotations I denote as (1x1)X(1x1) = 4 orbits = 2 convex 2 concave or metric 1100 for one side and the same for the back side. Total 8 circle like rotations for a single helical path in a projection to 2D.

((1x1)X(1x1)) X (1x1)X(1x1) ) gives all CT paths (rotations) what I shortcut as (2x2)X(2x2) the rest (5th rotation) is an overlap with the electron structure (1x1)X(0.5x0.5) that generates the perturbative 3:2 rotations for charge (2) and magnetic moment (3).

4 - 3 rotations gives the magnetic moment path (1D visibility of charge) 4-2 gives the classic 2 rotation (S2) visibility of charge.

It looks like you are using your own (not generally accepted in mathematics) the language and therefore you are difficult to understand. For example, what are "convex and concave orbits"? Maybe these are Euclidean and hyperbolic turns?

• For example, what are "convex and concave orbits"?

On SO(4) you have 2 different types of curvature relative to S2/S3. So a world line on SO(4) partly looks concave on a projection to S2. Of course this is just in relation to the free space and also due to the single side nature of the manifold.

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