Model Basis 2 - Forces

Medium and forces

Medium: Rotation needs a medium which is the underlaying spacetime. A medium which transports waves that interact und lead to forces between rotating entities. We’ll call this medium the LEDO-Field which is a meta-field inducing attractions between different stable entities on different wavelength scales.

Forces: Rotating entities on similar magnitude attract each other and might lead to further rotating but also static structures.

Example of clustered structures

Static structures: Elements, Molecules, Stones, Planets, Galaxy-clusters, Universe Rotating structures: Photon, Electron/Proton, Atom, Solor-Systems, Galaxies, Universe

Rotonal simulation forces

If you are rather interested in how forces are modelled mathematically and for simulations please finde so more info in the Force Model – Resonant Interactions between Rotons)

Inertia

On basis of the Roton model, Inertia of a defined object would be resistance of a body to acceleration induced by another body, or simply the sum of all rotational attributes and attractions between the two objects. This implies, that a body has no universal inertia. Detailed acceleration depends on the sub-structure of both objects. So the “weight” of a C-Atom depends on the atomic composition of the earth. Defining a constant attraction $g$ for earths (gravitational) attraction leaves the measured “masses” of our atoms relative to earth. So the masses assigned to a C and H atom in earths attractive fields might differ in presence of the moons attractive field, which show a different proportional composit of atoms.

Why does this matter?

1. Even though atoms have sizes within the same space scale, the rotonal attractions might differ caused be differences in the electrons rotation radius in the atoms.
2. The rotations of electrons and quarks themselves also lead to attractions to other electrons of other atoms.

These differences might be minimal and potentially not measurable, but they exist within the Roton model.

So if an acceleration is either in free fall or fully held (weighted), then the force between tow objects equals and we remain with $$F=E_1a_1=E_2a_2$$ ($E$=rest energy, $a$=acceleration). According to the Roton model, the attraction and therefore acceleration is the sum of all attributes (rotational scales and sub-scales) of an object. In standard physics this is usually attributed to “gravitational mass” (how strong gravity acts) and is identical to “Inertial mass” (measuring resistance to acceleration). The roton model has to differenciate attraction on different rotation scales. As such the atom rotation (electrons around their nucleus) and electron rotation (rotation of electron and quarks themselves) are different attractions on different scales.

Proposal for a Helium-Atom (He)

The following animation shows a hypothetical visualization of the structure of a He-Atom (Helium) consisting of two electrons rotating around two central protons (nuclei). As classical physics and chemistry show, protons are much bigger than electrons and have a substructure (quarks). We’ll go into these subscructures elsewhere. For the clarity of the roton model, the animation shows them on similar scale. The Di-Rotron (two blue protons) shown in the center represent the overall rotationally remaining entanglement partner for the electron (shown in red). The electron internal rotation is shown in a much bigger scale and is on a masively smaller scale compared to the electrons rotation around the nucleus.

Gravitational force

How does classical gravitation fit into the Roton Model?
Essentially, it does not. The Roton Model was formulated without reference to Newton’s law of gravity.
Instead, it assumes that attractive forces act linearly and persist to infinite distance, while local energy density gives rise to generalized repulsive forces.

• Roton Model:

  • Attractive forces remain constant, independent of distance.
  • Repulsive forces diminish proportionally to $1/r^2$ (intensity per sphere area)

• Newton’s Law of Gravitation:

  • Gravitational forces diminish proportionally to $1/r^2$.

But in what way, if any, does Newton’s law of gravitation fit into the Roton Model?

Newton’s Law of Universal Gravitation

For two point masses $m_1$ and $m_2$, separated by a distance $r$,
the mutual attractive force is given by:

$$ F = G \frac{m_1 m_2}{r^2} $$

• $F$: magnitude of the gravitational force between the two masses
• $G$: gravitational constant ( $6.674 \times 10^{-11} · N·m^2/kg^2$ )
• $m_1, m_2$: the two masses
• $r$: distance between the centers of the masses

This law states that every mass attracts every other mass with a force that grows with the product of their masses and decreases with the square of their separation.

Roton Model: Gravitational Analogy

In the Roton Model, attractive forces are defined between two rotating systems (called Rotons).
They depend solely on their internal energy–momentum and are limited to the magnitude of their wavelength.
These forces apply only when there is directional resonance between their rotation axes.
Most of the attractive field is emitted along the axial direction of a Roton.

Which Roton corresponds to the source of gravitational attraction?

Gravitational attraction emerges between atoms and molecules. Since molecules as a whole do not exhibit net rotation, we focus on the atomic scale, where electrons orbit protons.

On a finer scale, electrons, protons, and neutrons are themselves rotating entities. However, their individual contributions may be negligible compared to the larger forces arising from Rotons of atomic dimensions.

For clarity, let us define gravitational force here as the interaction between atoms. Each atom contains rotating electrons distributed across different orbitals. These rotations establish conditions for resonance and attraction with other atoms.

As a first approximation, we reduce the modeling of gravity
to the number of electron–proton rotation pairs within the interacting atoms.

Random Rotation and Wave Propagation

Now imagine a single Roton, rotating randomly in all directions (having tilt, fluctuations, shifts and precession).
The resulting wave within the LEDO-field propagates outward as a spherical distribution.
What spreads over the sphere is not “energy” in the Newtonian sense,
but rather a directional oscillatory flux.

Thus, the effect at distance $r$ is naturally diluted over the surface area of a sphere,
leading again to an inverse-square proportion:

$$ \text{Flux}(r) \propto \frac{1}{r^2}. $$

Emergent Gravitational Attraction

When considering matter built of many atoms,
each atom contributes through the rotational energy of its electrons around the proton.
Assuming a characteristic rotational energy $E_e$ (or angular momentum $L_e$) for each electron,
the total interaction between two samples of matter becomes:

$$ F \cdot \propto \frac{N_1·N_2·E_e^2}{r^2} $$

where

• $N_1, N_2$: number of electrons in each mass sample,
• $E_e$: approximate rotational energy per electron,
• $r$: distance between the two samples.

Since the number of electrons $N$ scales with the mass of the sample,
this expression mirrors Newton’s law:

$$ F = G · \frac{m_1 m_2}{r^2} $$

but arises not from “mass” itself, rather from the sum of rotational contributions of electrons within atoms.

Contrast

• Newton’s Law: Attraction $\propto \frac{m_1 m_2}{r^2}$
• Roton Model: Attraction $\propto \frac{N_1 N_2 E_e^2}{r^2}$,
  with $m_1, m_2$ only secondary, since the true origin is the rotational dynamics of electrons.

Verification

Atomic Mass per Electron for the First 32 Elements

We examine the ratio

$$ E_e = \frac{\text{atomic mass}}{\text{number of electrons}} $$

as a simple proxy for the “effective rotational energy share” of each electron within an atom.
This provides a way to compare how electrons contribute to the atomic mass distribution across the periodic table.

• Light elements (H–Ne) cluster around $E_e \approx 1$–2.5 g/mol per electron.
• Beyond calcium, $E_e$ rises steadily, exceeding 3 g/mol per electron at germanium.
• This trend reflects how nuclear mass grows faster than electron count as elements become heavier.

Data Table (Z = 1…32)

Diagram

Not that bad ey.

Pair–Odd Electron Model of Atomic Mass

To refine the Roton-inspired picture, we consider that paired electrons (even $Z$) contribute more strongly to attraction
than unpaired electrons (odd $Z$).

We model the effective atomic mass as:

$$ M(Z) \approx N_\text{pairs} \cdot E_e + N_\text{odd} \cdot E_s $$

where

• $N_\text{pairs} = \lfloor \tfrac{Z}{2} \rfloor$ = number of electron pairs
• $N_\text{odd} = Z \bmod 2$ = remainder (0 or 1 unpaired electron)
• $E_e \approx 2.64 ,\text{g/mol}$ = contribution per electron pair
• $E_s \approx 1.36 ,\text{g/mol}$ = contribution per single leftover electron

This form keeps the overall scaling with atomic number, but minimizes the oscillations between odd and even elements.

Data Table (Z = 1…32)

(see attached dataset for full values)

Diagram

The diagram shows:

• Dots = observed atomic masses
• Line = pair–odd model fit

The fit captures the overall trend and reduces the “zig-zag” odd–even discrepancy,
highlighting the stronger effective role of paired electron rotations.

Shell-Pair Model of Atomic Mass (Even Z = 4…18)

We refine the Roton-inspired mass analogue by distinguishing electron pairs by shell.
Instead of a uniform contribution per pair, we fit separate energies:

$$ M(Z) ;\approx; N_K \cdot E_K ;+; N_L \cdot E_L ;+; N_M \cdot E_M $$

where

• $N_K, N_L, N_M$ = number of electron pairs in K, L, M shells
• $E_K \approx 5.28$ g/mol, $E_L \approx 3.54$ g/mol, $E_M \approx 4.74$ g/mol

Data Table (Even Z = 4…18)

Diagram

• Dots = observed atomic masses (even $Z$, 4–18)
• Line = fitted shell-pair model

The fit shows that distinguishing electron-pair energies by shell
reduces systematic deviations and captures the scaling trend more faithfully.

Global Shell-Pair Model (Z = 1…40)

We tested a global fit to approximate atomic masses using four guiding ideas:

1. (A) Base scaling — Mass grows with the number of electron pairs per shell.
2. (B) Odd–even correction — Atoms with an unpaired electron (odd Z) are slightly lighter than even-Z neighbors.
3. (C) Shell dependence — Each shell (K, L, M, N) contributes differently per electron pair.
4. (D) Crowding correction — Within a shell, as more electrons fill it, each added electron contributes slightly less (quadratic reduction).

The fitted model for $Z = 1\dots40$ is

$$ M(Z);\approx;\sum_{s \in {K,L,M,N}} \Big(N_{\text{pairs},s},E_s ;-; \beta_s \tfrac{n_s(n_s-1)}{2}\Big) ;+; \alpha,(Z \bmod 2) ;+; c $$

where

• $n_s$ = electrons in shell $s$
• $N_{\text{pairs},s} = \lfloor n_s/2 \rfloor$

Fitted Parameters

Diagram

• Dots: Observed atomic masses (IUPAC averages)
• Line: Fitted global model (shell contributions + odd–even + crowding)

The model reproduces the atomic mass trend well,
capturing both the global scaling and the subtle odd–even and shell-structure effects.

The Final kick in

The Roton Model indicates, that layering of Rotons in different shells is not predefined. If some alternative energetic distribution is better, then inner shells might be more tightly packed before an new shell is used.

The Roton Model primarily uses a shell model with a 6:6:6:6 layering. But under certain conditions the upper layers might stack 8 or even 12 electrons instead of 6 if this is energetically better.

• 18 Ar Argon: So instead of the 6:6:6 layering of Argon 18, the layering with 4:6:8 might be energetically better. Leading to a potentially better attraction from the outermost shell.
• 19 K Kalium: The additional electron destroys the more optimal 4:6:8 distrubtion, falling back to a 1:6:6:6 layering.
• 20 Ca Calcium: Instead of the 2:6:6:6 layering, the 4:4:6:6, 4:8:8 or 6:6:8 distribution might be preferred. In case of 4:4:6:6 this might give in a energetically better state, but lead to less gravitational attraction.

Ok now let’s add this 5th condition:

Fifth Constraint: Adjusted Electron Layering

So far, our global model (constraints A–D) assumes that electron shells fill according to the standard shell capacities (K=2, L=8, M=18, N=32).
Each shell contributes to the atomic mass analogue through its pair energy ($E_s$), its crowding factor ($\beta_s$), and the odd–even correction ($\alpha$).

However, some atoms deviate from this simple picture. Their observed masses suggest that effective electron layering, when viewed through the Roton–gravitational analogy, differs from the standard filling. This motivates a fifth constraint:

(E) Layering Adjustment
For specific atoms, the distribution of electrons across sublayers of a shell is reorganized, changing their effective contribution to the attractive force.

Examples of Adjusted Layerings

• Argon (Z = 18)

  • Standard: $6 + 6 + 6$ (symmetric layering)
  • Adjusted: $4 + 6 + 8$
  • Effect: More electrons on outermost shell giving a slightly stronger attractive force than the standard model predicts.

• Calcium (Z = 20)

  • Standard: $2 + 6 + 6 + 6$
  • Adjusted: $4 + 4 + 6 + 6$
  • Effect: Less electrons in shell 2 giving a slightly weaker gravitational analogue, better matching observation.

• Nickel (Z = 28)

  • Standard: $4 + 6 + 6 + 6 + 6$
  • Adjusted: $6 + 6 + 8 + 8$
  • Effect: A higher stacking in lower layers. A reduction in size and therefore rotonal attraction. A reduction in predicted mass, aligning with the observed underweight.

Integration into the Model

Mathematically, this constraint is implemented by replacing the electron distribution ${n_s}$ with an adjusted distribution ${n’_s}$ for these special atoms:

$$ M’(Z) = \sum_s \Big( N’_{\text{pairs},s},E_s -\beta_s \tfrac{n’_s(n’_s-1)}{2} \Big) + \alpha,(Z \bmod 2) + c $$

where $N’_{\text{pairs},s} = \lfloor n’_s / 2 \rfloor$.

In this way, the fifth constraint does not alter the general equations, but provides alternative effective shell assignments for those atoms whose measured masses indicate non-standard layering.

Conceptual Meaning

This extension reflects the idea that the gravitational analogue of electron motion does not always follow the same rules as electronic orbital filling. Certain atoms may form more stable or more attractive Roton–layer configurations, leading to stronger or weaker apparent masses than the baseline model predicts.

How nice, loving it.