Rotonal Definition of the Electron-Field

(A) Introduction

We will dive into the electromagnetic field today, or rather start with the electrical field.

We will see:

• The coulomb potential arises from the uniformly rotating directional distribution of the Rotonal Wave-Tube
• The force onto a single electron/roton emerges from the integral of all rotational axes directions of the environmental electrons
• The electric (field) lines in typical diagrams show in which direction the rotation axis of the roton/electron is dragged (initially causing precession)
• The density of the lines (1 line per Electron if you like) tells how strong this precession force is.
• The magnetic (field) lines tell you in which direction (and how strongly) the electrons-body will be accelerated as a result, based an the applied forces by the electrical field.

Figure – Lines show the direction of the force applied to the axis of the roton (tilt). This corresponds to the Electrical-Field.

Figure – Lines show the direction the electron will take depending on its spatial inertia and delay. This corresponds to the magnetic field.

Therefore both fields are globally interchangeable and one can be derived from the other via differentiation (differential over time). This might not hold on small distances/scales though, as (1) the ratio of the inertia compared to the field forces changes, and (2) the field lines might get curved more strongly.

SUMMARY: This setup corresponds to the equations which are setup by Maxwell.

Further consideration: The willingness/resistance of a roton-axis to change its direction might not be linear and depend on the strength and angle of the force (or integral of the forces). If the angle changes too fast, the roton might not be able to follow and will instead fall with its axis into the opposite direction. Which will change the electron into a virtual positron (which does not exist, it just has the opposite direction) and might leave the setup.

Prediction: Fast changing overall electromagnetic field angles might swap electrons into “virtual positrons”.

Question: Such a “virtual positron” might only be observable though, if the field change was only applied to a small spatial range or with a sharp cut. Such that the “virtual positrons” can interact with electrons in a way that these changes are observable. How could this be measured? A loss in overall field strength?

Prediction: A virtual positron might attract one other electron and potentially annihilate (depending on energy density pressure and proton/electron energy difference). The 3 rotonal rings of each electron might overlap and two of them responsible for the attraction will annihilate. Now 4 single rings remain. The result will be: One remaining electron (3), 1 Neutrino (remaining wobbling ring) and some Photons from the 2 roton ring annihilation. We expect 2-4 photons of high energy but lower frequency then usual, I’ll tell you later why: The two combined Rotons instantly have the wrong frequency for their existing oscillation path so they will fly away.

Folks are you as eager as I am now to find out if this is the right prediction Check: TODO

Further points of interest:

• When electrons/rotons get aligned in rows or parallel with parallel axes, they will tend to keep their distances and build spatially distributed entangled chains with some stronger lock-in resonant distances. This explains how and why electrons travel uniformly through metal and latices - without getting disturbed by the surrounding atoms.
• Metals get heaten up if too many electrons want to pass caused by strong fields. This can either happen because they are faster, denser packed along the entanglement chains, or more parallel entanglement chains are created. The electrons bump into the atom.

Prediction: There will be special interlocking of electrons traveling in parallel. Measurements: How could this be measured?

Question: What does the Interlocking distance tell us? It will give evidence for the electrons main rotation frequency.

Lets see how this can be mapped to the Standard Physics interpretation and calculations.

Inverse-Square law from rotating directed emission

Rotonal Entanglement force (co-axial)

To describe the electric field we have two simple rules:

When Rotons are aligned co-axially, this leads to a distance independent constant attraction force of:

Figure – Attraction force between two electrons

Figure – Spatial Lock-In force between two electrons

The attractive force in co-axial direction is given by this trivial (distance independent) constant equation: $$ F_e = k_e e^2. k_e = fixed constant. $$

Where: $k_e$ is a simple constant in $N/C^2$ which tells how strong the force is depending on the electrical potentials (similar to a linear coulomb-constant).

Where will we get at?

Coulomb potential With an arbitrary rotation of the source roton, we will get a coulomb potential $1/r^2$ force. With an arbitrary rotation of the sink roton, we will get a coulomb potential $1/r^2$ force. With the integral over all rotational forces from other electrons, we will again end up at the coulomb potential $1/r^2$ force.

Magnetic field

Rotational distribution –> Coulomb

Now we start to rotate all electrons arbitrarily in all directions. As there is no natively favored direction in completely relative space. As parameters we have the width of the directional resonance-wave (given be $r_e$).

We consider a source A that emits a constant force $F_e$ along its internal axis $\hat{\mathbf{n}}_A$.
The emission acts unidirectionally along both opposite axial directions:

$$ +\hat{\mathbf{n}}_A \quad\text{and}\quad -\hat{\mathbf{n}}_A. $$

Both A (source) and B (receiver) have an interaction area given by a circular cross-section of radius $r_e$:

$$ A_e = \pi r_e^2. $$

Crucially:
The emitted “beam” is assumed to be cylindrical, i.e. of constant width $r_e$ independent of distance.

The axis $\hat{\mathbf{n}}_A$ rotates freely and uniformly over all directions.
The receiver B is at a fixed distance $r$ from A.

B experiences the full force $F_e$ only when A’s cylindrical emission axis passes within distance $r_e$ of B. Otherwise the force is zero.

1. Angular Window for a Cylindrical Beam

For the cylindrical beam to “hit” B, the beam axis must point in a direction that passes within a lateral distance $r_e$ of the point B.

At distance $r$, a small angular deviation $\delta\theta$ deflects the beam laterally by approximately:

$$ \text{offset}(r) \approx r , \delta\theta. $$

To stay within the interaction radius $r_e$, we require:

$$ r,\delta\theta \le r_e \quad\Rightarrow\quad \delta\theta \le \frac{r_e}{r}. $$

Thus, even for a perfectly cylindrical beam, the set of directions that hit B forms a small spherical cap on the unit direction sphere around A.

The solid angle of that cap is approximately:

$$ \Delta\Omega \approx \pi \left( \frac{r_e}{r} \right)^2 = \frac{\pi r_e^2}{r^2}. $$

Because emission occurs in both directions $\pm\hat{\mathbf{n}}_A$, the effective accessible solid angle is:

$$ \Delta\Omega_{\text{eff}} = 2,\Delta\Omega = 2,\frac{\pi r_e^2}{r^2}. $$

Since all orientations of $\hat{\mathbf{n}}_A$ are equally likely, the hit probability is:

$$ p_{\text{hit}} = \frac{\Delta\Omega_{\text{eff}}}{4\pi} = \frac{r_e^2}{2r^2}. $$

2. Time-Averaged Force on the Receiver

Whenever the beam axis lies within the correct angular window, the full force $F_e$ acts.
Otherwise: zero.

Thus the time-averaged force at distance $r$ is:

$$ \boxed{ \langle F(r)\rangle = F_e , p_{\text{hit}} = F_e \frac{r_e^2}{2r^2} } $$

The force therefore falls as $1/r^2$, even though the emitted beam itself does not expand.

The inverse-square behavior arises purely from angular geometry:
as distance increases, the set of orientations of A that intersect B shrinks as $1/r^2$.

3. Mapping to Coulomb’s Law

The Coulomb force between charges $\pm e$ is:

$$ F_{\mathrm{C}}(r) = k_e \frac{e^2}{r^2}. $$

To reproduce this with the directed-emission model, we identify:

$$ k_e e^2 \equiv \frac{F_e r_e^2}{2}. $$

Thus the emission strength $F_e$ must satisfy:

$$ \boxed{ F_e = \frac{2k_e e^2}{r_e^2} } $$

This choice makes the rotating, constant-width beam model numerically equivalent to the Coulomb force law.

Summary

A cylindrical beam of constant radius $r_e$, emitted along the axis of a rotating source A, produces at distance $r$ an average force that falls as $1/r^2$. The reason is geometric: the set of beam directions that pass within $r_e$ of B shrinks with the square of the distance. Consequently:

$$ \langle F(r)\rangle = \frac{F_e r_e^2}{2r^2}. $$

Setting

$$ \frac{F_e r_e^2}{2} = k_e e^2 $$

makes the model exactly equivalent to Coulomb’s law.
The inverse-square law therefore emerges from geometry and uniform directional rotation, without requiring any beam spreading.

(B) Interpretative Framework

The following model is an interpretation of electrical and magnetic phenomena in terms of Electron-Rotons—fundamental directed excitations carrying a charge quantum $e$.
The purpose is to construct, from simple directional-coupling rules, an emergent description of the Coulomb potential, magnetic ordering, and electromagnetic propagation.

This framework is not declared as final physical law but as a working hypothesis whose internal logic will be developed and later compared to observed electromagnetic behavior.

1. Electron-Roton: State Space and Basic Quantities

Each Electron-Roton is described by:

• Position
  $$ \mathbf{x} \in \mathbb{R}^3 $$

• Orientation / internal axis
  $$ \hat{\mathbf{n}} \in S^2,\quad |\hat{\mathbf{n}}| = 1 $$

• Charge vector
  $$ \mathbf{e} = e , \hat{\mathbf{n}} $$

• Rotational inertia
  $$ I $$

Interpretation:

• Low inertia $\rightarrow$ Roton rotates freely $\rightarrow$ behaves like a negative charge
• High inertia $\rightarrow$ Roton orientation is fixed by matter $\rightarrow$ behaves like a positive charge

Thus positive/negative charge is a directional inertia state, not a different particle.

2. Angular Participation and Effective Contribution

To derive the Coulomb potential from many electrons, we introduce the idea of angular participation.

Let $\theta$ be the angle between:

• electron direction $\hat{\mathbf{n}}$
• vector to the test point $\hat{\mathbf{r}}$

Effective contribution:

$$ P(\theta) = e , f(\theta) $$

where $f(\theta)$ is a smooth “participation function”:

• $f(0) = 1$ (full contribution)
• $f(\theta) \to 0$ for $\theta > \theta_c$ (beyond resonance cone)
• monotonic and smooth

Examples:

• $$ f(\theta) = \cos^2(\theta) $$
• $$ f(\theta) = e^{-\theta^2 / 2\sigma^2} $$

The exact form will later determine the precise Coulomb scaling.

3. Finite Spatial Range and the Electron Radius

At distances below the electron radius $r_e$, the force decreases smoothly to zero due to:

• saturation of coupling
• overlapping spatial extent of Rotons
• reduction of vector “participation”

We introduce a radial transition function $g(r)$:

• $g(r) = 1$ for $r \gg r_e$
• $g(r) \to 0$ for $r \to 0$

Example:

$$ g(r) = \begin{cases} 1, & r > r_e \ \frac{r}{r_e}, & r \le r_e \end{cases} $$

or a smoother polynomial form.

4. Fundamental Coupling Rules

4.1 Co-Axial Parallel (same direction)

Infinite-range distance-locking.

Coupling strength: $$ \alpha_{cx}^{(+)} $$

4.2 Co-Axial Anti-Parallel (opposite direction)

Quantized, distance-independent attraction: $$ \alpha_{cx}^{(-)} = e $$

Effective contribution is reduced by:

• $f(\theta)$
• $g(r)$

4.3 Parallel-Axis Resonance

$$ \alpha_{\parallel} $$
Defines magnetic structures and current filaments.

4.4 Angular Alignment Coupling

Rotons align toward the environment:

$$ \frac{d\hat{\mathbf{n}}}{dt} = \alpha_{ang} \left( \hat{\mathbf{n}}_{env} - \hat{\mathbf{n}} \right) $$

Limited by effective inertia: $$ \omega_{max} = \frac{1}{I_{eff}} $$

This introduces finite reaction times for field changes.

5. Building the Coulomb Potential from Many Electrons

The Coulomb potential emerges statistically from the integral over all electrons.

Each contributes:

$$ e , f(\theta) , g(r) $$

The full field at location $\mathbf{x}$ becomes:

$$ \mathbf{E}(\mathbf{x}) = \int \rho_e(\mathbf{x}’) , \alpha_{cx}^{(-)} , f(\theta) , g(r) , \hat{\mathbf{n}}(\mathbf{x}’) , d^3x' $$

Under assumptions of:

• uniform free-electron density
• isotropic distribution (far from matter)
• smooth participation functions

we obtain:

$$ |\mathbf{E}(r)| \propto \frac{1}{r^2} $$

Thus the Coulomb law is an emergent statistical average of Rotonal interactions.

6. Summary of Constants and Functions

7. Next Steps

We are ready to:

1. derive the static field equations,
2. define the Rotonal Gauss law,
3. derive Maxwell-like wave behavior.