What is an Atom?

An atom is a remarkable example of how stable oscillating instances can form resonances with other stable instances.
Resonances arise between rotating electrons and their counterparts. The more resonances they find, the stronger their mutual bond becomes, and the closer the electrons arrange themselves around each other.

Resonant Structure

The atomic structure will show that the planar, rotating singular entities we have considered so far now adapt into new configurations.
In these configurations, additional resonances appear that exist only within a combined network of resonant entities.

For now, let us fill up the electron orbitals of an atom while ignoring the nucleus and treating it merely as the central anchor for each electron’s bonding.

Stepwise Filling of Orbitals

  • 1–2 electrons
    Simple — let both rotate in a single plane around the center.

  • 3–4 electrons
    Now we have two Rotons (each consisting of 2 electrons). Let them rotate co-axially, which produces the strongest attraction.
    Assign their shells (orbitals) suitable distances so that their oscillations can resonate — their angular velocities being harmonic multiples.
    For e.g. the beryllium atom with 4 electrons, this corresponds to radius 1 for the inner shell and radius 4 for the outer one. Simple Atoms

  • 5–10 electrons
    When we add two more electrons, they will seek positions that maximize the number of possible resonances.
    They can couple to both existing shells, so the new electrons will oscillate with two resonance components — one corresponding to $\omega_1$ (inner resonance) and one to $\omega_2$ (outer resonance).

    Although they likely occupy the second shell (as electrons 3 and 4 do), their motion may combine a radius of shell 2 in the x-direction with a radius of shell 1 in the y-direction. More precisely, an electron can rotate in the second shell while simultaneously precessing with the magnitude characteristic of the inner shell.

    This hybrid resonance pattern can be visualized in several equivalent ways, which we will explore in the following chapters.

Goal

The goal is to demonstrate how a simple and intuitive model can explain the fundamental structure and properties of atoms.

Visualization of resonance coupling via precession:

Resonance Relations

The harmonic coupling between the first two shells (1s, 2s) can be expressed as: $\frac{r_2}{r_1} = 4 \qquad \text{and} \qquad \omega_2 = \frac{\omega_1}{4}$

These ratios define the stable resonance condition for the first two shells and set the basis for higher-order orbital configurations.

*The smallest harmonic ratio $\\omega_2 / \\omega_1 = 1/4$ is chosen in the examples, because it represents the simplest **phase-locked resonance**, where four inner oscillations complete exactly one outer rotation. In contrast, the quantum-mechanical Bohr model predicts $\\omega_2 / \\omega_1 = 1/8$, though the radius ratio $r_2 / r_1 = 4$ remains consistent in both frameworks.*

This slower 1/8 relation allows the outer electron to sweep through all resonance phases of the inner oscillation. It allows even a single electron to dynamically reach all spatial extensions of the 2p orbital — consistent with experimental observations of orbital field coverage and electron density distributions. The resonance coupling model (RCM) will take up the 1/8 relation later on.

Rotonal Olavian Atom Model

We introduce the “Resonance Coupling Atom Model (RCM)” or in short “Olavian Atom Model” describing the existence and properties of atoms within the periodic system of atoms.

This is a proposal, how atoms and their structure and bonding might be explained on basis of the Quantum-Roton-Model in a much more intuitive way.

Optimization

The universe is a constant wobbling of stable resonances approaching an energetically optimal placing in space. More levels of rations and resonances result in more attraction and a better energy distribution. So optimal states are reached by random background noise or external energy/influences disturbing the current minima.

A simple atom model can initially only describe a part of what is an optimal placement of Electrons, Protons and Neutrons - until other more optimal resonances are found. This even holds for the same atom which might favor different structures in different situations and environments (single atom, excitation, molecules).


Atom structure TRY 1

Let’s start with a FIRST TRY (not ground state) to give you a glimpse on how a more optimal placing solution can be found. These are some original notes on this topic - FIRST TRY (not accurate):

Initial try - attention: this is not the optimal ground state of an atom:

This illustration shows protons and electrons (neutrons are omitted for now) and how they build electron-pairs via entanglement (long distance co-axial rotation). The valence-electrons (sketched in magenta) do not have a sparing electron partner and therefore can not reach a nearer location to the center. The attraction is never-the-less created to the proton. So there are pairs of entangled electron-proton pairs and electron-proton-proton-electron double-pairs.

Important note: After first discarding these atom structures very soon, I realized, that many or similar variants of the shown atom structures actually do exist - but they are not the energetically optimal solutions (ground state) so they will decay into more stable configurations. But as they do exist, I allow myself to show them at this place, as intermediate excited versions of the base atom states. Intermediate states in the transition to finding the most energetically optimal configuration (best energy density, closest to the nucleus).

This can be visualized more closely in the following figures showing three atoms.

  • Helium atom He with order number 2 (2 electrons, 2 protons)
  • Berilium atom Be with order number 4 (4 electrons, 4 protons)
  • Carbon atom C with order number 6 (6 electrons, 6 protons)
Helium (2) Berilium (4) - UNSTABLE Excited $\text{Be}^* : 1s^0 ; 2s^4$ ($1s^0 ; 2s^2 2p^2$) ($\text{Be} : 1s^2 ; 2s^2$) Stable Carbon (6) - UNSTABLE Excited $\text{C}^* : 1s^0 , 2s^2 , 2p^4$
$- - >$

These figures basically show a proposal, where electron-pairs rotate in separate parallel planes (co-planar). This leads to attractive forces between these rotations which binds the electron-pairs closer to each other. BUT the planes will eventually align into one plane caused by their attractions. So this might not be a stable final solution. The electron spins are co-axial pointing into the center of the atom. This seems to result in the most optimal attraction. We are not going into discussion of nucleus structure here, but further calculations show, that the shown Carbon Roton-Structure does not result in the energetically most optimal configuration. Therefore the shown model of the Carbon-Atom is discarded as the ground state atom. We might most likely need go to structures with rotations of different radii.

The atom models shown above do actually exist in the Bohr-Atom model as excited states:

What happens in physically in excited atoms (Bohr Model)

Neutral ground-state beryllium has configuration: $\text{Be: } 1s^2 ; 2s^2$ If both 1s electrons are excited into the 2s shell, the configuration becomes: $\text{Be}^* : 1s^0 ; 2s^4$

That means all four electrons occupy the same principal shell (n = 2) — an energetically unstable state that quickly decays back to $1s^2 2s^2$.

Ground-state carbon: $\text{C: } 1s^2 , 2s^2 , 2p^2$ Excited configuration (promote both 1s → 2s or 2p): $\text{C}^* : 1s^0 , 2s^2 , 2p^4$ (with sub-shells actually $1s^0 ; 2s^2 2p^2$)

In an excited carbon atom, both core electrons transition into the second resonance shell. All six Rotons now oscillate at the same harmonic domain ($\omega_2$), forming three mutually orthogonal orbital planes corresponding to the 2s and 2p families. The result is a spherical resonance lattice of six interacting oscillators — maximally coherent but energetically unstable, as the inner coupling $\omega_1$ vanishes. When the system decays, two Rotons collapse back into the $\omega_1$ domain, re-establishing the inner stabilizing core of the atom.

What is missing in our model?

(A) Radial resonances (varying radii)

This model misses the fact, that rotations of different sizes still might have resonances. If the frequencies of two rotations have a common integer divider, they might create resonant attractions. The distances and speeds of the rotating electrons need to match these condition in respect to their attractive forces.

These resonances might apply, when the LEDO-waves build full multiples in respect to their frequency and rotation-phases within a plane. If we calculate the distances between these rotation-shells, we quite easily end up with the standard physics boor-atom model shell structure. You can find the calculations for the resonant placements further down. Here is the resulting formula: $r_n = \frac{r_1}{n^2} .$ The shell radii correlate to the inverse square of the resonance index.

How nice: From our own considerations, we have derived the shell distances of the standard boor atom model in physics.
Resonance Distance of 2 shells 3 resonant shells (+ sub-shells) Integer multiple phases Multiples in circumferences

This illustrations show:

  • 1: The shell distances calculated with rotation resonances where the frequencies share common integer multiples.
  • 2: More main-shells. Some sub-shells. Some calculations for further partially harmonic Sub-Shells are also shown. This concept is not used further on though.
  • 3: A symbolic visualization of integer multiples in rotations.
  • 4: Symbolic resonances shown with N-point figures.

With this in mind, we have to place the electrons on orbitals which show this additional resonances in case of “co-axial” rotations.

Shell Hypothesis: While entering the world of multi shell electron orbits, the orbits will share an integer multiple of their frequencies.

(B) Bi-Resonant coupling

After having entered the world of different rotation radii (3-4 electrons) any further atoms might want to synchronize with any of the present electron rotations to reach an energetically more optimal state.

Bi-Resonance Hypothesis: Electron rotation-paths will try to have a resonant frequency with as much other electrons as possible (mostly with 2 other shell main-radii). We now open the atom model into the 3 different spatial directions.

Basically we expect, that a new shell will first contain a 2-electron Roton main shell (1s, 2s, …) before the harmonic sub-shells are filled (2p, 3p, …). Otherwise there would be no resonance.


Atom structure TRY 2

The following illustration shows a more optimized and more detailed possibly energetically better possibility for rotational electron positions. In addition we take up the idea of multiple parallel planes with similar rotation radii but bi-resonant coupling (to multiple $_omage$). These plains have a main rotation (the biggest) and some precession in the other spatial directions. This makes sense as parallel rotating planes attract each other so the electrons are attracted towards the second plane resulting in some oscillation around the main plane.

This model only shows the first 2 main resonance shells, potential sub-orbitals are not shown (energy level).

Examples:

  • H: A single Electron rotating around the central nucleus (nucleus is not shown).
  • Li 3: Two electrons in the first inner shell and one single electron on the second outer shell. Up to for electrons can share the same rotation plane, keeping the co-axial entanglement with the protons.
  • C 6: This atom with 6 electrons starts to get interesting. Now the inner two electrons build a further perfect rotation partner for the further outer electrons in X-Axis.
  • O 8: Now this gives a very nice view onto a similar additional electron-pair with rotations in Y-Axis (*extension)
  • (Ne 10): Not shown (adding the Z-Axis)

( *extension): experiments show that x,y,z are first filled with 1 atom. This might therefore result in better resonant attractions

We are currently looking at 3 Levels of electron placement:

  • 2 at innermost shell (1s), in blue
  • 2 in the second shell (2s), in red
  • 2, 4 or 6 in the third shell (2p), in green most likely slightly closer to the center than 2s, caused by more rotation resonances.

With this in mind we can think of the following extensions (spoiler):

Electrons Atom shell (s) bi-resonant sub-shells (p) Resonances Added e- Total filled Atom electrons Roton plains (*) Comment
2 He 1 (1s) 1-0-0 s*2 = 2 :1|
4 Be 2 (2s) 2-0-0 + 2 s*2 = 4 :1|1:
10 Ne 2 1 (+2p) 2-1-0 + 6 (2 per axis) s*2+p*6 = 10 :1|:2:3:2: p2 orbitals, sync s2 and s1
12 Mg 3 (3s) 3-0-0 + 2 s*2+p*6 = 12 :1|:2:3:2:|1:
18 Ar 3 2 (+3p) 3-2-0 + 6 s*2+p*6 = 18 :1|:2:3:2:|:2:3:2: p3 orbitals, sync s3 and s2
20 Ca 4 (4s) 4-0-0 + 2 s*2+p*6 = 20 :1|:2:3:2:|:2:3:2:|1:
… …
order ? … 4 2p + 3d (xy, xz, yz) 3-1-0 + 6 (2 per axis) Ca + 6 ? Ar+2/2/2/ |1: 2D sync of s3 with s1
order ? … 4 2p + 3d (xyz) 3-2-1 + 2 Ca + 6 + 2 ?? +|.010.|… 3D sync of s3 with s2 and s1
order ? … 4 2p + 3d (xyy) 3-2-2 + 2 Ca + 6 + 2 + 2 ?? +|.101.|… 3D sync of s3 with s2/s2
36 Kr 4 2p + 3d + 3p 4-3-0 + 6 (3p) Ca + 6 + 2 + 2 + 6 :1|:2:3:2:+:111:|:2:3:2: +2/2/2/|:2:3:2:|1: 2D sync of s4 with s3
… … … … … … … further combinatorics
(\*) *Resonance notation:* x-y-z where x,y,z are the shell numbers to which there is a resonance in the corresponding spatial direction (\*) *Roton Plain notation:* This n|m|o|p indicate the number of plains in the corresponding shell 1-4 (1|2|3|4). The notation ":1" is a single shell with 2 electrons. The notation ":x:z:y:" indicates the number of Rotons/planes in the corresponding spatial direction with a "." for each electron. So ":2:3:2:" is a shell with 1 middle Roton (2s) and 2 additional planes per spatial direction with one electron each and a total of 8 electrons.

Sub-Shell Rotation Type

What makes the rotations in the green shells special? They are rotations around at least 2 axis in space. Why is that? The issue with an electron rotation in a parallel plane to the s-planes is, that the electron has no entanglement to any proton if two electrons would rotate at that place. So the electron still has to couple to a proton and a potential other paired electron would need to be placed on the opposite side of the nucleus. So in the end, the electron in a 2p shell first rotates along the X-Axis as the two 1s electrons. And second it also rotates around the nucleus giving the overall rotation a rotating 2-cone structure.

Going into 3D. Now this same rotation could happen in the direction of the Y-Axis which is shown in the O-8 (oxygen) atom. The electrons can rotate without getting each other into their way. You might surely give a solution for filling two further 2p electrons into the Z-Axis cones.

Having a look at the standard physics atom model shows, that the shells and sub-shells we just introduced within the roton-model have standard names (1s, 2s, 2p). Even the number of electrons per shell give a perfect match: 2 electrons in single plane, 2 co-axial electrons in second resonance shell, $3*2$ electrons per spatial 3D direction.

When building molecules, the position of the 2p electron “Rotons” might partially be a little closer to the perimeter of the atom. So they will provide the most relevant valence electrons and will most likely do the bindings also with an odd number of electrons in the p-shells. So also in molecules the s-shells are most likely filled with the 2 electrons before the p shells. The s-shells are needed fully filled for providing the resonance layer. Or in other words the 1s/2s rotons will realign to resonate optimally with the 2p electrons. So 2p electrons might be slightly farther away from the center than the 2s electrons.

The Roton model would intuitively predicts though, that for single isolated atoms, a single (unpaired) valence electron (e.g. for the N-Atom or F-Atom) might rather be placed on the 2s shell. But this would mean, that enough 2p self-resonances would need to be present with no need for a full 2s resonance.

Will the s or p shell be first filled up in an atom? It will be the one, which gives the system more energy - and most likely draws parts closer to the center.

It is difficult to tell what “closer” means:

  • Most probable distance: 2p is closer to nucleus.
  • Average distance: 2s slithly smaller
  • Energy (binding strength): 2s (stronger nuclear penetration)

Result: This means, that the 2s shell is energetically better compared to the 2p shell and allows a “smaller” or rather more optimal atom structure. Even for isolated atoms. So the s-shell is always preferred to be filled up first.

Predictions:

Elliptic: The atoms H to Be have the electrons placed more in a planar way than the other atoms (with p-shells). Verification: This is the case, if e.g. a He atom can be placed (polarized) within a magnetic field, which is only possible if an electron is excited. The resulting spin-polarized helium has a precession (Larmor frequency). This confirms the slightly elliptic shape if it can be polarized.

Further atom shells

Now what’s the next extension? We now have an Ne Atom with full shells: $1s^2 2s^2 2p^4$

Ok, let’s add the next 2 rotating electrons one resonance layer further. As we add only 1 or 2 electrons they fit into a further plane quiet well. No need for cone-like wobbling shells. Next we can add the 3p (inner) double-cone electrons in their X, Y and Z rotation directions.

Atom with 3rd shell filled with electrons, example $1s^2 2s^2 2p^6 3s^2 3p^2$

I’m honestly really exited about this match. Perfectly intuitively explaining why electrons might arrange themselves this way. NOT because of their repulsive character (which they do not have anyway, at least not more than between other electrons and protons) - but because the rotations create a higher level of attraction. This results in a more compact and energetically optimal placing and rotating of the electrons. All experiments so far indicate that the N-Atom has 3 unpaired electrons in the p-shell.

Orientation variants of Electrons in an atom

The Roton model can give consistent explanations which stable positions and orientation electrons take within an atom. The most favorouble constellation is an opposite coaxial orientation of the electron rotation axis (spins) in which they reach an energetically optimal constellation.

Please find the full detailed descriptions here

Layering of electron orbitals (Ledoigtian atom shell model)

Basic considerations:

  • An optimal stable structure is reached, when electron rotations have a phase which aligns over time to a base phase.
  • Every electron-pair is identically attracted to the center with the same distance independent force. This is supported by an “Electron <-> 2 Proton <-> Electron” entanglement.
  • Every odd valence electron is attracted to the nucleus with a constant distance-independent force (Electron <-> Proton entanglement).

Resulting orbital structure:

Oscillation Version:

We define: $x(t) = f_x(t), \quad y(t) = f_y(t), \quad z(t) = f_z(t)$ where each f_i is an independent 1D oscillation (e.g. sinusoidal, resonant, with its own frequency ωᵢ and phase φᵢ).

This means the total “state” is a product of three orthogonal oscillators: $\mathbf{r}(t) = (f_x(t), f_y(t), f_z(t))$

In total this gives the following path for a single point in space: $r(t) = A_x \cos(\omega_x t + \phi_x) + y(t) = A_y \cos(\omega_y t + \phi_y) + z(t) = A_z \cos(\omega_z t + \phi_z)$

With amplitude $A_n$, relative frequency $\omega_n$ and relative phase $\phi_n$ in each direction $n={x,y,z}$

To make it a closed resonant figure we need to align $\omega$ such that the frequencies are integer multiples. To make them continuous figures we also have to adjust the relative phases in some matching way.

This generates Lissajous figures that form 3D standing or rotating loops — and those are analogues of complex-valued eigenstates in quantum mechanics. Three independent oscillations (x,y,z) with adjustable frequency ratios and phase offsets are the direct geometric analogue of Schrödinger’s separable wavefunctions. Playing with phases and ratios gives you angular momentum, quantization, and orbital symmetry.

🧩 Oscillator parameters for orbital analogues

Orbital Resonant meaning Aₓ : Aᵧ : A_z ωₓ : ωᵧ : ω_z (φₓ , φᵧ , φ_z) Geometric / physical interpretation
s₁ fundamental radial mode (1s) 1 : 1 : 0 1 : 1 : 0 (0 , 0 , 0) All axes in phase → single circular loop; isotropic “breathing”
s₂ 2s with one radial node 4 : 4 : 4 2 : 2 : 2 (0 , 0 , π) Same frequencies but opposite global phase → inner + outer shells (node between)
p₂ 2p (one nodal plane) 4 : 4 : 0 1 : 1 : – (0 , π , –) One axis 180° out of phase with others → two opposite lobes separated by a plane
s₃ 3s (two radial nodes) 9 : 9 : 9 3 : 3 : 3 (0 , 0 , π) Triple-frequency breathing → three concentric shells
p₃ 3p (one major + one minor lobe) 9 : 9 : 0 3 : 3 : – (0 , π⁄3 , –) Higher frequency, partial phase offset → three-lobe p-like shape
d₃ 3d (quadrupole pattern) 9 : 9 : 9 2 : 1 : 3 (0 , π⁄2 , π) Unequal integer ratios produce four-lobe or cloverleaf geometry with nodal planes

Precession Version:

Rotonal Version:

Shell Radii Scaling in the Olavian Resonance Atom Model

Introduction

In the simplified Olavian Resonance Atom Model, electrons are particles on circular shells (at $r_n$) around a central nucleus.
Two guiding principles shape the shell structure:

  1. Constant central force: each electron experiences the same attractive force $F_0$ toward the nucleus, independent of its distance.
  2. Resonant phase synchrony: all orbital angular frequencies are integer multiples of a common base frequency $\Omega$, giving the atom a periodic stability and stable oszillations/resonances.

With these assumptions, the structure of the electron shells can be derived in a simple and elegant form.

Calculation

Please find the full detailed calculations here

Calculation Summary

Define the outermost shell (slowest rotation) with index $n=1$: $r_1 = \frac{F_0}{m \Omega^2}$

Then every other shell radius is given by the simple quadratic law: $r_n = \frac{r_1}{n^2} .$

This is the core result: the shell radii shrink inversely with the square of the resonance index $n$. This exactly correlates with Boors standart model of electron shells.

Step 4: Derived orbital properties

Velocity relation: $v_n = \sqrt{\frac{F_0 r_n}{m}} = \frac{v_1}{n}$

Orbital periods: $T_n = \frac{2\pi}{\omega_n} = \frac{T_1}{n}$

The kinetic energy on shell $n$ is: $K_n = \tfrac12 m v_n^2 = \frac{K_1}{n^2}$

Because all frequencies are multiples of $\Omega$, the global atomic state is exactly periodic with common recurrence time: $T_{\text{global}} = \frac{2\pi}{\Omega} = T_1$

Discussion
  • The model produces a $1/n^2$ law for shell radii, a simple resonance structure directly tied to the assumptions of constant central force and integer phase locking.
  • Inner shells rotate faster and carry higher angular frequency, while their kinetic energies diminish as $1/n^2$.
  • The entire atomic configuration re-aligns perfectly after the fundamental period $T_1$, ensuring stability of the resonant structure.
Conclusion

The Olavian Resonance Atom Model shows that even with a distance-independent central force, the imposition of integer phase synchrony is sufficient to generate a discrete shell structure. The natural outcome is a hierarchy of radii:

$$ r_n \propto \frac{1}{n^2} , $$

demonstrating how resonance principles can give rise to stable, quantized atomic configurations.

Size of atoms

Why do atoms have the size they have today? Because all others have, so they are in oscillatory resonance with each other which gives them the stability.

More precisely though, atoms receive their size based on the background fluctuations in the LEDO-field. Or on more standard terms by the cosmic microwave background (CMB).

Resonant origin of atomic scales

In this view, the cosmic microwave background (CMB) is not just a relic glow, but a continuous resonant field that defines the stable dimensions of matter.

When the primordial plasma cooled to about 3000 K, electrons and protons began forming the first bound atoms.
That temperature marks the threshold where the average photon energy dropped below the ionization energy of hydrogen — the moment when stable atomic structures became possible.

Since then, the universe has remained immersed in this CMB field.
Its radiation acts as a universal background resonance, fixing the characteristic energy scales at which electrons orbit, atoms remain stable, and electronic excitations begin.
In that sense, the sizes and energies of atoms today still reflect the equilibrium conditions established
at the epoch of photon–matter decoupling.

One more thought before we continue: The same could be told for the point in time, when the subsequent hydrogen and helium plasma expanded and started to form the first suns. Until then, no photon the size of a sun could emerge or pass through the universe. Only after the first suns formed and there started to exist “empty” space between the stars, then photons of that size could emerge. So we expect some CMB for that occasion in time too.

Distribution of electrons to shells

Animations

For a more fancy view this is an animation of a Berilium atom Be:

And an animation of a Carbon atom C:

The following is not taken into account in these visualizations:

  • Detailed Structure of the nucleus e.g. neutrons
  • Rotation speeds of the electrons in the different planes. The center-plane in the C-Atom might e.g. rotate slower than the other planes.

Model rules

The rotonal model intends to show how the universe might be built up with the exact same rules on every level of expansion of space. So the model does not give specific rules like: There are at most 2 or 3 co-planar planes in an atom. Why not? Because nature does not do that either. Nature simply follows the process of energy optimization which depends on the surrounding especially in the presence of other particles and atoms nearby. So a single isolated C-Atom might look completely different, than a C-Atom within a compound molecule with bonds. This is partially reflected in the following visualization. So a C-Atom which initially might come as a structure of 2 double-planes in 2 different axial orientations might change into a three planar system where the two electrons in the outer shell are not necessarily co-axially entangled anymore, but change into a energetically more optimal structure bonding with electrons of other atoms.

Further simulations might show, whether this model can show local optima which will build up the universe of atoms and molecules with these simple rules.

For further reading on the different attractive and repulsive forces you might be interested in this part: Rotonal Forces

LEDO 5 Force - Itterative Resonance Modelling

05 October 2025

Absolutely—let’s make this concise, structured, and simulation-ready.

Names & Abbreviations:

  • $F_AR$ — Axial Resonance Force “Coaxial resonance” between nearly collinear Rotons with similar spectral paramameters. Axial Distance-independent axial magnitude (in axial 1D direction).
  • $F_CR$ — Centric Resonance Force “Cocentric inward lockin force between nearly co-centric and co-axial Rotons with resonant frequency params. Centric force decays 2D linearly proportional to distance $~ 1/d$.
  • $F_PR$ — Planar Resonance Force “Coplanar/parallel resonance” when both axes are parallel and the separation lies in their common rotation plane; decays in 2D linearly proportional to distance $~ 1/d$.
  • $F_GR$ — General Resonant Attraction (“fallback” attractive term) Weak, omnidirectional resonance pull based on overall similarity; decays into 3D space proportional to the distances power of two $~ 1/d^2$.
  • $F_EDP$ — Energy-Density Pressure Repulsive pressure from the gradient of total field energy density (sum of all waves); independent of detailed similarity, scaled by the roton’s own energy. Individual pressure typically decays into 3D space with $~ 1/d^2$.
Considerations:

The $F_CR$ force is separated from the $F_AR$ force, because it is a lock-in force (inwards and outwards) to the magnitude/radius of the rotation (or to their subparticles that is). It specifically applies, when the angular velocities are coherent (multiples of each other) and therefore have a common resonance frequency.

⸻

Clean definitions (with compact formulas)

Let $i \neq j$. Notation: • Positions $\mathbf{x}i, separation \mathbf{r}{ij}=\mathbf{x}i-\mathbf{x}j, r{ij}=|\mathbf{r}{ij}|, \hat{\mathbf{r}}_{ji}=(\mathbf{x}_j-\mathbf{x}i)/r{ij}$. • Axes $\mathbf{t}_i,\mathbf{t}j (unit)$, axis parallelism $c{ij}=\mathbf{t}i!\cdot!\mathbf{t}j$. • Planarity factor (separation lies in the plane ⟂ to the axes): $\Pi{ij}=\big(1-(\mathbf{t}i!\cdot!\hat{\mathbf{r}}{ij})^2\big)\big(1-(\mathbf{t}j!\cdot!\hat{\mathbf{r}}{ij})^2\big)$. • Chirality match (spin orientation, clockwise vs counterclockwise): $\chi{ij}=\operatorname{sign}(\boldsymbol{\Omega}i!\cdot!\mathbf{t}i);\operatorname{sign}(\boldsymbol{\Omega}j!\cdot!\mathbf{t}j)\in{-1,+1}$. • Spectral similarity (radius/frequency match; tune widths $\sigma_a$,$\sigma\omega$): $Q{ij}=\exp!\Big(-\frac{(a_i-a_j)^2}{2\sigma_a^2}-\frac{(\omega_i-\omega_j)^2}{2\sigma\omega^2}\Big)$. • Soft core $r_0>0$ to avoid singularities; $\bar a{ij}=\tfrac12(a_i+a_j)$.

  1. F_AL — Axial Locking (distance-independent magnitude)

Active when axes are almost collinear and spectra match. \boxed{ \mathbf{F}^{\mathrm{AL}}{j\leftarrow i} = \kappa{!AL},Q_{ij},c_{ij}^{,p},\chi_{ij};\hat{\mathbf{r}}{ji} \quad \text{for } r{ij}\le R_{AL}\ \text{(or always, if you want truly distance-independent)} } • p\ge 1 sharpens preference for parallel axes (c_{ij}\to 1). • \chi_{ij} lets you flip sign for opposite spin sense (same chirality attracts; opposite repels), per your note.

  1. F_PR — Planar Resonance (~1/d)

Requires axes parallel and separation lying in their plane. \boxed{ \mathbf{F}^{\mathrm{PR}}{j\leftarrow i} =\kappa{!PR},Q_{ij},c_{ij}^{,p},\Pi_{ij}; \frac{1}{\max(r_{ij},,\bar a_{ij})};\hat{\mathbf{r}}{ji}\times \chi{ij}^{(\text{optional})} } • \Pi_{ij} suppresses pull if the line of centers points along the axis (not coplanar). • Optional \chi_{ij} factor if you want PR to also depend on spin sense.

  1. F_GR — General Resonant Attraction (~1/d^2)

A weak, isotropic “baseline” attraction that only cares about being somewhat similar: \boxed{ \mathbf{F}^{\mathrm{GR}}{j\leftarrow i} = \kappa{!GR},\tilde Q_{ij},\frac{1}{(,r_{ij}+r_0,)^2};\hat{\mathbf{r}}{ji}, } • \tilde Q{ij} can be a looser similarity (e.g., only frequency), or even set to 1 for a pure background term.

  1. F_EDP — Energy-Density Pressure (repulsive, gradient of total energy density)

Define a local energy density field (no phases needed; use envelopes only): \epsilon(\mathbf{x})=\sum_{k} \underbrace{\alpha_k,A_k^2}_{\text{source energy}};G!\big(|\mathbf{x}-\mathbf{x}_k|;,a_k\big), with a smooth, radial kernel (e.g., Gaussian·soft-1/r^2): G(r;a)=\frac{e^{-r^2/(2a^2)}}{r^2+r_0^2}. The pressure P=\gamma,\epsilon. The roton at \mathbf{x}_j feels: \boxed{ \mathbf{F}^{\mathrm{EDP}}j = -,\nabla P\big|{\mathbf{x}j} = -,\gamma,\nabla \epsilon(\mathbf{x}j) = -,\gamma \sum{i\ne j} \alpha_i A_i^2,\nabla G(r{ij};a_i). } • This is repulsive from high-energy regions (pressure pushes down the gradient). • Scale it relative to the roton’s own energy if desired: \gamma\to \gamma,f(A_j) (e.g., f(A_j)=1+\beta A_j).

Gradient (closed form): \nabla G(r;a)=\Bigg(\frac{-r}{a^2(r^2+r_0^2)}-\frac{2r}{(r^2+r_0^2)^2}\Bigg) e^{-r^2/(2a^2)},\hat{\mathbf{r}}.

⸻

One unified force vs. three separate forces?

Mathematically, yes, you can embed F_AL, F_PR, and F_GR in a single anisotropic potential with angular kernels and different radial laws—think of a multipole-like expansion: \mathbf{F}{j\leftarrow i} = \sum{n} \kappa_n,\mathcal{A}n(\mathbf{t}i,\mathbf{t}j,\hat{\mathbf{r}}{ij},\chi{ij});\frac{1}{r{ij}^{,\nu_n}};\hat{\mathbf{r}}_{ji}, choosing \nu_n\in{0,1,2} to emulate AL (constant), PR (1/r), GR (1/r^2). But: • It’s harder to tune/interpret (angular kernels couple nonlinearly). • You’ll likely want different cutoffs and similarity widths for AL/PR/GR anyway. • For exploration and clarity, the three-term model is better. You can always collapse them later.

Recommendation: keep F_AL, F_PR, F_GR separate; leave F_EDP separate by design (it’s a field gradient, not pairwise).

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Final total force & torques (what you’d sum in code)

\boxed{ \mathbf{F}j =\sum{i\ne j}\Big(\mathbf{F}^{\mathrm{AL}}{j\leftarrow i} +\mathbf{F}^{\mathrm{PR}}{j\leftarrow i} +\mathbf{F}^{\mathrm{GR}}_{j\leftarrow i}\Big) +\mathbf{F}^{\mathrm{EDP}}_j. }

Alignment torque (optional, same idea as before): \boldsymbol{\tau}j = \lambda{\tau}\sum_{i\ne j}\Big[c_{ij}^{,p} ,(\mathbf{t}j\times \mathbf{t}i),\Theta{\text{AL/PR}}\Big] -\gamma\Omega,\boldsymbol{\Omega}j, with \Theta{\text{AL/PR}} picking which resonance channels (AL, PR) produce alignment.

⸻

Notes on parameter choices (good defaults) • Exponents: p=2 (stronger bias for parallel axes). • Radii/frequency widths: \sigma_a \sim 0.3,\mathrm{median}(a), \sigma_\omega \sim 0.2,\mathrm{median}(\omega). • Soft core: r_0 \sim 0.05,\min a. • Magnitudes: choose \kappa_{!AL} \gtrsim \kappa_{!PR} \gtrsim \kappa_{!GR} (AL strongest, GR weakest). • Pressure scale \gamma: dial until clusters don’t over-collapse.

Electron Orbital Calculations

25 September 2025

Shell Radii Scaling in the Olavian Resonance Atom Model

Introduction

In the Olavian Resonance Atom Model, electrons are particles on circular shells (at $r_n$) around a central nucleus.
Two guiding principles shape the shell structure:

  1. Constant central force: each electron experiences the same attractive force $F_0$ toward the nucleus, independent of its distance.
  2. Resonant phase synchrony: all orbital angular frequencies are integer multiples of a common base frequency $\Omega$, giving the atom a periodic stability and stable oszillations/resonances.

With these assumptions, the structure of the electron shells can be derived in a simple and elegant form.

Step 1: Dynamics under a constant central force

An electron of mass $m$ moving in a circle of radius $r$ must satisfy the centripetal balance:

$$ \frac{m v^2}{r} = F_0 . $$

From this follows the orbital speed:

$$ v(r) = \sqrt{\frac{F_0 r}{m}} , $$

the angular frequency:

$$ \omega(r) = \frac{v}{r} = \sqrt{\frac{F_0}{m r}} , $$

and the inverted relation:

$$ r(\omega) = \frac{F_0}{m \omega^2} . $$

Thus, the orbital radius is completely determined once the angular frequency is known.

Step 2: Resonance condition

For global phase stability, the angular frequencies are constrained to integer multiples of a base frequency:

$$ \omega_n = n , \Omega, \qquad n = 1,2,3,\dots $$

Substituting into the radius relation gives:

$$ r_n = \frac{F_0}{m (n \Omega)^2} . $$

Step 3: Relative scaling of radii

Define the outermost shell (slowest rotation) with index $n=1$:

$$ r_1 = \frac{F_0}{m \Omega^2} . $$

Then every other shell radius is given by the simple quadratic law:

$$ r_n = \frac{r_1}{n^2} . $$

This is the core result: the shell radii shrink inversely with the square of the resonance index $n$.

Step 4: Derived orbital properties

From the velocity relation:

$$ v_n = \sqrt{\frac{F_0 r_n}{m}} = \frac{v_1}{n} , $$

the angular frequencies follow directly:

$$ \omega_n = n , \Omega , $$

and the orbital periods:

$$ T_n = \frac{2\pi}{\omega_n} = \frac{T_1}{n} . $$

The kinetic energy on shell $n$ is:

$$ K_n = \tfrac12 m v_n^2 = \frac{K_1}{n^2} . $$

Because all frequencies are multiples of $\Omega$, the global atomic state is exactly periodic with common recurrence time:

$$ T_{\text{global}} = \frac{2\pi}{\Omega} = T_1 . $$

Step 5: Rotation allignments on separate planes

Initialy while building rotonal rotation planes in atoms 3 planes with electrons on different rotation radii where considered. This though showed up in the calculations to be in contradiction with a timely stable overall resonance. As a result we need to stik with electrons having identical rotation radii within the same plane. But they do not necessarily have to rotate around the nucleos. They might share a rotation axis in two separate planes for each spacial 3D direction. So the shell might contain 4, 8 or even 12 electrons on the same shell. The 12 electron shell might potentially only be reached though, if there are more atoms on the outer shells.

Why only 4 Electrons (2 planes) form a resonant shell

  • Each plane with 2 opposite electrons → invariant under a half-turn (π rotation) → a Z₂ symmetry.

  • Two planes → at most two angular frequencies.

    • Closure condition:
      $$ \frac{\omega_1}{\omega_2}=\frac{n_1}{n_2}\in\mathbb{Q} $$ ⇒ common repeat time $T_*=\frac{n_1\pi}{\omega_1}=\frac{n_2\pi}{\omega_2}$.
    • Feasible by tuning radii/forces or setting $\omega_1=\omega_2$.

  • Three planes (6 electrons):

    • Introduces a third independent frequency.
    • Closure would need all three ratios rational → over-constrained.
    • Generically gives quasi-periodic motion (no finite $T_*$).

Conclusion:
A stable, repeating shell arises only with 2 planes × 2 electrons each = 4 electrons.
With 3 planes, exact resonance is lost.

Discussion
  • The model produces a $1/n^2$ law for shell radii, a simple resonance structure directly tied to the assumptions of constant central force and integer phase locking.
  • Inner shells rotate faster and carry higher angular frequency, while their kinetic energies diminish as $1/n^2$.
  • The entire atomic configuration re-aligns perfectly after the fundamental period $T_1$, ensuring stability of the resonant structure.
Conclusion

The Olavian Resonance Atom Model shows that even with a distance-independent central force, the imposition of integer phase synchrony is sufficient to generate a discrete shell structure. The natural outcome is a hierarchy of radii:

$$ r_n \propto \frac{1}{n^2} , $$

demonstrating how resonance principles can give rise to stable, quantized atomic configurations.

Electron speeds per shell

Why did we start numbering the atom model shells from outer to inner shell? This is, because the speed of the electron on the outermost shell is the relatively stable value. The closer the electrons the faster they rotate.

He 1s

Why ist this? Well, remember that building molecules with valence-electrons implies, that the valence-Electrons need to have similar phases and speed. Similar radius and speed are prerequisit for the Valence-Electron coupling of Molecules. [Expectation: Isolated and Molecule-compound Atoms with valence electrons have different sizes.]

The Roton named electron

25 September 2025

Energy optimization in atoms

Why do protons and electrons build atoms? Imagine 2 stationary (central) protons and two electrons.

What happens:

  • As they are rotating, both electrons and protons attract each other (in nearly the same way).
  • The LEDO-Field “wind” blows them apart so the electrons adjust oposite each other stationary around the proton. Attraction equals repulsion.
  • Now the electrons start to move influenced by the LEDO-Field fluctiations. As they start rotating the build a roton. This way they get attracted closer to the protons.
  • Looking at a Helium-Atom with 4 rotating electrons in a plane you can see and understand from the Roton model, that there is some attraction between these two phase-synchoneous Rotons of different sizes (Factor <4).
  • Now what about the H-Atom? It seems that even a single electron manages to get closer to the proton by rotating around it.
  • Now it gets really interesting, because this implies, that even a “self-rotation” can induce a rotonal attraction to ones own rotation center.
  • A kind of self-resonance in the LEDO-Field.

Furthter consideration:

  • So why does the electron not fly away when rotating? Because it is attracted by the nucleus (rotonally). So as long as its speed does not increase a certain level, we are all fine.
  • The electrons around the protons try to find the optimal rotational states so they can come as close as possible to the center. Hereby increasing energy density.
  • Does an electron “want” something by itself? No. It simply fails to leave the influence of a stronger attraction, as soon as it gets occasionally caught by it. The electron basically falls into the pod of higher attraction and denser energie while still beeing held back by the wave pressure in the LEDO-Field wind.
  • The universe is a constant way of optimizing itself. With more or less success. Every fluctuation here and there drags another ompimal state out of the optimom bumbing around
  • Maximizing energy density is minimizing local entropy and maximizing global Entropy. Both are limitted to the scale at which we look at the system so rather a “Ignorance measure of indistinguishability”
  • An electron has an entropy of 0 because it has only one state - but wait it has a spin? So minimizing entropy is minimizing the ignorance of indistinguishability.
  • Entropy is the quantitative measure of your blindness to hidden distinctions in the system.

Distribution and Orientation of Electron-Rotons within Atoms

Introduction

This chapter focuses on how the Rotonal model might explain the basic Atomic structures. We will look at different constellations and how to build an energetically optimal stable state.

Let me give one important prelude:

  • The Quantum-Mechanics atom model assumes, that the orbitals (1s, 2s, 2p, 3s, 3p, 3d, 4s …) are the wavefunctions of an electron or the probability distribution of “where to find” an electron when you try to measure it.
  • Measuring changes/influences an atom though. So the resulting measurement will only show the reaction of the system to external influences.

To be really precise we’d need to say:

  • Atom orbitals are ONLY the resonances of the atom, which we are bumping with different photons of specific sizes/energies.
  • We do not actually “know” how the structure or probability distrubution of the electrons in an atom IS when it is left alone.

And having a look at the instable excitations into other orbitals, it seems there are other forms of “rotations” an electron can choose around a nucleus.

Roton types and orientations

As surely stated in other parts Rotons can come with several (maybe temporal) stable constellations.

Roton Coupling type Spin orientation Standard Term Resonance/Force Roton orientations Spin Locking
Co-Axial (Entangl.) Oposite Co-Axial Antiparallel spins Big Attractive o→ ←o ↦ ↤ strong
Co-Axial (Repulsi.) Concurrent Co-Axial Parallel spins Big (Repulsive) o→ ←o ↦ ↤ strong
Parallel Up/Up or Down/Down Parallel Medium ↑↑, ↓↓ medium
Anti-Parallel Up/Down or Down/Up Antiparallel Medium ↑↓, ↓↑ medium
Unaligned Arbitrary, unaligned Misaligned, skew ? Small (Gravitation) ↑↗︎→↘︎ none

This definitions/values come from interpretation of the observations with field directions and forces between two magnets of different orientations.

Rotonal combinations in atoms

H-Atom:

  • The Electron and the Proton build an (uneven) rotonal coaxial connection. They build an entanglement, so their rotation axis are kept synchronous.
  • Depending on external influences

He-Atom:

  • The two electrons (an electron-pair) take oposite sides to each other with oposite coaxial orientations.
  • In combination with the electron<->proton coupling this further increases attraction between electrons and leads to more optimal energetic positions.
  • External influences can lift electrons to higher energy levels (distance to nucleus). If a single electron is lifted (excited), they loose the entanglement.
  • Electrons on different energy levels (shells) loose their entanglement and coaxial orientation, as they will take different rotation speeds (1/n^2 distances)
  • They might tend to align themselves linearly (parallel, antiparallel) to still optimize for energy-density.
  • Once both electrons reach the higher energy level, they might remain in this intermediate parallel/antiparallel state for a while.
  • If this temporal stability is somehow disturbed (e.g. temperature?) the electrons will first find an unaligned orientation until the LEDO-Field base fluctuations lead the electrons into locked coaxial orientations.
  • Once reaching coaxial orientation again, they will drop back to the base level with the highest energy density.
He Groundstate $1s^2$ He Excited parallel / triplet He excited coaxial / singlet

This is how the Roton model would explain behavior and stability of exitation of electrons to upper shells.

Verification with the standard atom model

Helium: Electron Spin Orientations (1s and 2s)
Ground state: 1s²
  • Both electrons in the 1s orbital
  • Must have opposite spins (Pauli exclusion principle)
  • Spin singlet (S = 0):

1s: ↑↓

Excited states: 1s¹ 2s¹
  • One electron in 1s, one in 2s

Case 1: Antiparallel spins (singlet)
1s: ↑, 2s: ↓

  • Allowed
  • Lower in energy

Case 2: Parallel spins (triplet)
1s: ↑, 2s: ↑

  • Allowed
  • Higher in energy, often metastable
  • Transition to ground state is spin-forbidden
Forbidden configuration
  • Two electrons in the same orbital with identical spin
  • Example: 1s: ↑↑
  • Not allowed (violates Pauli exclusion principle)
Summary Table
Configuration Spins State Allowed? Comment
1s² ↑↓ Singlet ✅ Yes Ground state, stable
1s² ↑↑ or ↓↓ — ❌ No Forbidden by Pauli principle
1s¹ 2s¹ ↑↓ or ↓↑ Singlet ✅ Yes Excited state, lower energy, short-lived
1s¹ 2s¹ ↑↑ or ↓↓ Triplet ✅ Yes Excited state, higher energy, metastable
1s¹ 2p¹ ↑↓ or ↓↑ Singlet ✅ Yes Excited, short-lived
1s¹ 2p¹ ↑↑ or ↓↓ Triplet ✅ Yes Excited, metastable, important in spectroscopy

Assessment of the Roton Model

The Roton model provides a compelling framework to explain why specific positional constellations of electrons are energetically more favorable than others, and why certain arrangements naturally stabilize. Rather than declaring that a configuration is “forbidden,” the model demonstrates that it is simply less favorable compared to the energetically preferred alternatives. In this way, stability emerges as a natural consequence of energetic optimization, not as an imposed rule. The Roton model thus offers not only a consistent explanation, but also an intuitive picture of why electrons arrange themselves in these particular ways.

Take this phrase from Standart Physics: “Two electrons in the same orbital with identical spin are forbidden” Why is this?