Introduction

Why is the Alpha-Particle such an important construct for the RQM? Because it bridges the world between:

• the macroscopic additive world where nucleons stack up together to form graspable 3D matter
• the world of quantized resonances

Any theory which can not give a graspable explanation to why the alpha-particle is as it is, risks to fail. I did not find a established theory which could explain it reasonably enough. When you see the success on how the RQM needs and proposes and explains its constituents you will see what the author meant.

From Proton to the Alpha Particle

This section demonstrates a proof of concept for the natural-optimization approach used in the creation of alpha-like particles within the RQM framework.

Guiding question:
Are generic particles with a distance-locking character able to form stable clusters on their own?

Answer:
Yes. They assemble into remarkably robust and symmetric configurations.

The Alpha–Quark Dilemma

Deep-inelastic electron scattering revealed three hard, point-like substructures inside protons and neutrons, which led directly to the quark model.
In contrast, the alpha particle shows no such features: its scattering pattern is perfectly smooth, fully symmetric, and displays no hints of internal point-like constituents.
No experiment has ever resolved quarks inside an alpha particle; its internal structure remains empirically opaque and is fully compatible with collective, emergent or alternative structural descriptions.

Requirements

Before contrasting RQM with standard quantum physics, we briefly summarize the structural demands an alpha particle must fulfill.

RQM Requirements

• It must expose two independent, center-symmetric electron-resonance channels, allowing paired electrons to rotate freely around it.
• Its shell must appear neutral and symmetric with respect to electron-span resonances and scattering.
• It must generate resonance potentials enabling binding to nearby alpha-particles.
• It must also generate resonance potentials enabling binding to proton- or neutron-like objects.
• Its inertia (rotonal energy) must be almost exactly four times that of a single proton or neutron, and twice us much that of a deuterium core
• Its geometry must constitute the energetically optimal configuration; no even more stable arrangements may exist.

In short: the alpha shell must be geometrically fixed within the atomic core, while its electron-span couplings remain fully symmetric and freely rotatable.

Standard and Quantum Physics Requirements

• Strong binding and saturation: a compact, deeply bound four-nucleon configuration.
• Spin-0, isospin-0 ground state: all angular momenta cancel, leaving no preferred orientation.
• Spherical charge and density distribution.
• Pauli compatibility: all nucleons occupy the lowest s-shell (as in He-4).
• Contained Coulomb repulsion: proton–proton repulsion must be dominated by the strong force.
• Energetic isolation: no lower-energy rearrangement must exist.

Remarkably, these requirement sets align almost perfectly.
The difference is conceptual:
Quantum physics summarizes what is observed; RQM proposes why it must take precisely this form.

And the remaining question for the RQM theory is this:

• Event though an alpha, a deuterium, a proton and neutron are completely different nuclear elements why shall they have masses/inertia/rotonal-energy in integer multiples?
• What gives these particles their main inertia (mass)?

Requirements Summary

Can two electron-like particles exist inside an alpha-shell without revealing their axial alignment?
Yes.
A perfectly symmetric spin-0 sphere exposes no stable dipole or orientation markers.
The alignment axis of internal charges becomes un-measurable, and the external observer sees only a smooth, isotropic shell.

Conclusion:
Two electron-like particles can indeed reside within an alpha-particle sphere without detectable orientation.

Construction Overview

The RQM framework starts by identifying the first spatially extended, rotation-based building block in three dimensions.
This fundamental unit is no longer assumed to be a single rotation, but a multi-channel rotational entity capable of generating stable resonance patterns in space.

To reflect this, we introduce two key actors:

1. Gridon: the elementary resonance carrier with one or more internal resonance channels.
2. Gridlet: the distance-locking interaction between two Gridons, a single resonance channel forming the basic connective tissue of structured matter.

Together they form the seed of all higher-order constructs such as emergent nucleon-like clusters and alpha-type shells.

1. The Gridon (formerly “Trion”)

A Gridon is an elementary Roton-based object defined by:

• its position and velocity in 3D space
• multiple internal rotation channels, each with:
  • its own axis and chirality (orientation relative to motion)
  • its own rotational impulse

We no longer require that a Gridon has exactly three channels; its channel count is a structural degree of freedom determined by the local resonance environment.
This change disentangles the Gridon concept from older “tri-rotational” (Trion) assumptions and makes it more universal.

What a Gridon does

A Gridon can establish resonance-based couplings along its rotational axes whenever another Gridon presents a compatible rotational phase and axis alignment.
Once a channel locks into resonance, the two Gridons act as a combined oscillatory unit (spring-like), suppressing further rotonal propagation along that axis.

Two coupling types arise naturally:

1. Anti-parallel coupling (strong entanglement)

• axes aligned but with opposite chirality
• creates a tightly bound, energetically saturated link
• stabilizes small-scale rotating structures (e.g. within nucleon-like clusters or tight Quon–Quon pairing)

2. Parallel coupling (weak entanglement)

• axes aligned with the same chirality
• forms a distance-locking constraint rather than a deep bond
• stabilizes geometric configurations by enforcing resonant separation lengths (multiples of a characteristic lambda)

These rules originate from the Roton-level interaction principles defined earlier in the model.

2. The Gridlet

A Gridlet is the interaction channel between two Gridons: a resonant distance-locking constraint that defines the geometry of a cluster.

Gridlets:

• act like elastic spacers whose equilibrium length depends on resonance ratios
• carry a tunable restoring force
• determine the shape and stiffness of higher-order structures

This is the RQM analogue to the gluon role in QCD, but conceptually simpler and purely geometric:
Gridlets do not “mediate” forces; they are the forces, encoded as resonant geometric constraints.

3. The Quon

When a stable network of Gridons and Gridlets forms a closed or semi-closed structure, some Gridons acquire a special dynamical role:

They begin to resonate within the grid, adjusting their internal rotation speed and radius to reinforce global stability.

Such dynamically self-tuning Gridons are called Quons.

Purpose of Quons

• They provide inertial feedback to the structure, carrying most of the rotational energy and thus dominating the effective inertia.
• They further contract alpha-like clusters to more compact, energetically optimal scales.
• They stabilize the cluster by tuning their rotation until the Gridlet distances sit at their optimal resonance lengths.
• When the structure is disturbed, the Gridlets absorb local perturbations, while Quon–Quon attraction helps relax the system back into an energy minimum.

Quons thus act as resonant stabilizers, ensuring that the cluster behaves as a coherent unit — much like nucleons in a nucleus acquire collective behavior, but here the mechanism is explicit and emergent.

When we move to the regime of nucleus–nucleus interaction, Quon–Quon resonances (Gridlets on the next hierarchy level) step in to form the inter-nuclear bonding.

4. Constructing Higher Structures

With Gridons (nodes), Gridlets (links), and Quons (resonant node dynamics), the model allows emergent formation of:

• proton-like rotational clusters
• neutron-like variants
• alpha-like shells
• extended lattice configurations

The resulting structures show:

• distance-locking
• collective inertia
• rotational symmetry
• saturation behavior

All this is achieved without requiring any sub-Gridon particles – aside from the separate electron-span attraction that couples the core to orbital electrons.

This provides a natural explanation of why certain clusters (such as the alpha particle) become uniquely stable in the observed universe.

Simulation

Simulation notes

The accompanying simulations serve as proof-of-concept and use:

• entanglement forces (anti-parallel and parallel Gridon couplings)
• a mild centering potential to prevent unbounded drift
• rotational damping and jitter to allow the system to relax into resonance
• optional long-range resonance fields (if enabled)

Despite the simplicity of these ingredients, the variability of simulation parameters and stabilizing structures opens a large configuration space.

The goal of the simulations is to identify parameter regimes and structural elements such that the system reliably forms stable clusters whose geometry mirrors the expected nuclear building blocks.

Energy Calculation

From a geometrical point of view, we seek a definition of energy that arises purely from structure. No masses, no forces, no fields introduced by hand. Only geometry, and relations between geometric primitives. The guiding idea is simple but demanding: energy shall be derivable from geometry alone, and it shall behave consistently across related figures.

The concrete task is to find a function
$$ e = f(E, K, F) $$ of the number of vertices $E$, edges $K$, and faces $F$ of a geometric figure, such that specific polyhedra carry energies in fixed ratios.

Our simulations have revealed and confirmed clear candidates for stable, geometrically oscillating grid structures in space. We now assign to these structures the experimentally known energy scale, expressed in units of $u$ (the proton mass), in order to anchor the purely geometrical model to physical measurements.

We impose the constraint $$ 4,e_{\text{tet}} = 2,e_{\text{oct}} = 1,e_{\text{ico}}, $$ where

• $e_{\text{tet}}$ is the energy of a tetrahedron,
• $e_{\text{oct}}$ the energy of an octahedron,
• $e_{\text{ico}}$ the energy of an icosahedron.

This relation expresses a conserved quantity: four tetrahedra, two octahedra, or one icosahedron represent the same total energy.

1. Motivation: Why derive energy from geometry?

If energy is to be a fundamental quantity, it should not depend on arbitrary external labels. Geometry offers a minimal language: counts of vertices, edges, and faces encode connectivity, symmetry, and constraint density.

In physical terms, geometry determines:

• how many directions interactions can propagate,
• how tightly a structure is constrained,
• how much internal coordination is required to maintain coherence.

These properties strongly resemble what we attribute to energy in dynamical systems. The working hypothesis is therefore:

Energy corresponds to the degree of geometrical coordination encoded in a structure.

We are not interested in size or scale, but in structural intensity.

2. Geometrical data of the relevant figures

We begin with the three regular Platonic solids involved:

All three have triangular faces. Consequently, $$ 2K = 3F $$ holds for all of them, and the Euler relation $$ E - K + F = 2 $$ is identical as well. These two invariants alone cannot distinguish their energetic character.

We therefore need a quantity that separates these figures structurally.

3. Identifying the relevant geometric invariant

There is no linear solution for these constraints in the form: $e=aE+bK+cF+d$ So we need to look for a non-linear differential of the variables K and E.

A natural candidate is the average vertex valence, defined as $$ v := \frac{2K}{E}. $$

This quantity measures how many edges meet at a vertex on average. It reflects how strongly each point of the structure is connected to its surroundings.

Evaluating $v$ for the three figures:

• Tetrahedron: $$ v = \frac{2 \cdot 6}{4} = 3 $$
• Octahedron: $$ v = \frac{2 \cdot 12}{6} = 4 $$
• Icosahedron: $$ v = \frac{2 \cdot 30}{12} = 5 $$

Thus, the figures form a clean integer sequence: $$ v = 3,;4,;5. $$

This already suggests a hierarchical ordering of structural complexity.

BUT: This equation gives no meaningfull simple solution. There exist an expenential solution which does not assicate with structrue though. There is a polynomial solution which purely relates to K/E which gives no additive aspects.

Take away

What are the implications:

• Energy of an isolated nucleus has a linear relation to the number of resonance channels.

• In all nuclei, the resonance channels therefore encode the same optimal energy per volume.

• The oscillatory part of the quon itself does not seam to be the main driver for inertia.

• Why is an electron not so heavy? Because it has a lot of uncoupled resonance channels, they are unbound and do not give much inertia to the main resonance channel.