Model Basis 1 - Rotations in the LEDO Field

Origin of temporaly stable particles

Rotation: The world we perceive is based on small entities that orbit themselves and thus form stable structures over time like photons (Sonon). Multiple rotating Sonons create stable structures in space and time forming the basis for matter like electrons or protons.

Universe: The whole universe consists of rotating objects (Rotons), which create forces between themselves - in a layered structure of rotations of different magnitudes like: photon, electron, atom, solar systems, galaxies, universe.

LEDO-Field = Lambda Energy Density Oscillation (LEDO)

Abstract

The Lambda Energy Density Oscillation (LEDO) Field is a wavelength-resolved field of local energy density, carrying not just scalar amplitude but the spectral composition and gradients of overlapping oscillations.

Definition

Lambda Energy Density Oscillation (LEDO) designates a field concept in which local energy density is not confined to a single harmonic mode but unfolds as a superposed spectrum of wavelength-resolved oscillations. Individual modulations flow, interweave, and resonate, embedding not only a scalar value but also information about the frequency composition and gradient at each point in space.

Here, Lambda explicitly denotes wavelength awareness: the field carries a spectral decomposition akin to a local Fourier content, such that different frequency components remain distinguishable even while overlapping. This enables instant, scale-dependent and direction-dependent interactions — local energy density contributes to a total value and gradient, while the spectral separation allows wavelength-specific coupling and resonance to occur across arbitrary distances.

Locally this simply contributes to a total energy density value and gradient. The frequency separation and its awareness allows for wavelength individual interactions over arbitrary distances. Such rotating modulations lead to resonances in other locations of the LEDO-Field infering de-localized oscillations.

Discussion - difference to a scalar or vector field

Through rotational modulations, the LEDO field can thus sustain nonlocal resonances: oscillatory patterns at one site induce correlated responses elsewhere, rendering the field an inherently wavelength-sensitive, frequency-structured medium of energy oscillation.

Scalar Field vs. LEDO Field

Differences:

• Scalar field: total value $\rho(x,t)$ only. Overlapping gradient can be calculated via sourrounding.
• Local FFT: $\tilde{\rho}(x,\omega)$ reveals frequency content, but loses spatially resolved detail.
• LEDO field: retains $\rho_\lambda(x,t)$ and $\nabla \rho_\lambda(x,t)$, making the field spectrally aware and capable of wavelength-specific interactions.

In short:

LEDO = frequency spectrum aware, resonant oscillation of local energy density

Please find below a few visualizations for the discussed topic.

Peak Visualization 3D visualization of a single scalar field with overlapping waves of different frequencies

Rotons of different magnitude This is a 2D cut from an overlapped modulation of superposed LEDO-Field. Static Rotons. Colors indicate difference in roton-magnitude. Intensity shows the gradient of the field.

Gradient visualization LEDO-Field 2D cut of radial Roton oszilation paths - superposition alongsite the rotational plane. Static Rotons. Color indicates the graident direction, intensity indicate the gratient value

For axial oszillation paths see further down.

Motivation

• In conventional physics, oscillation is often represented as a simple sinusoidal function in time or space.
• Complex systems (quantum states, coupled fields, condensed matter, or cosmological structures) rarely follow such simple oscillations.
• LEDO emphasizes interference, resonance, and overlay of multiple oscillations, producing a more lifelike, “musical” structure of energy density dynamics.

Characteristics

• Lambda or Layered: denotes the frequency aware, de-interwoven character of the oscillations (not a single pure tone).
• Energy Density: refers to the local field value of energy per unit volume, in general a fundamental scalar quantity. LEDO allows lfor ocal frequancy depenand gradients.
• Oscillation: periodic or quasi-periodic modulations of single or potentially multiple overtone/harmonic frequencies.

Base field fluctuations and caracteristics

The LEDO field carries waves emerging from stable rotating structures (like photons and matter) and spreads out into different spacial directions. These waves might lead to resonances between different stable objects. Being the source for all forces between stable entities. The base waves in the LEDO field do not manifest themselves directly, unless we add another stable rotating entity with a given frequency (time aspect) at a given location. If unmanifested, the LEDO field simply appears as a background noise leading to small fluctuating forces to the manifesting entities.

Please also see the chapter on Quantization and vacuum fluctuations).

So in other words, the LEDO-Field mostly corresponds to the concept of “vacuum fluctuations” in standard physics.

Mathematical modelling (IGT)

More precicely:

** Forces in this field are mediated via “Energy densitiy gradients”. Their derivatives or modulations over time can be expressed as a local Tensor. ** The whole structure is a highly “iterative” process which might rather be investigated via simulation than via calculations of already solved formal equations. With this tensor we are asking not only “where does energy density rise?” but “how does that rising itself bend and twist in space?”.

So the modelling might make use of “Iterative Gradient Tensor” (IGT)

Image: Colors show amplitude

Possible Formal Expression

Let $$ \rho_E(\mathbf{r},t) = \sum_i A_i(\mathbf{r}) \cos(\omega_i t + \phi_i) $$ represent the local energy density as a superposition of modes.

Then LEDO can be understood as the effective oscillation pattern emerging from the collective superposition of such modes, i.e. the perceived rhythmic modulation rather than any single frequency.

Moddeling

Energy Density as a Field

We define the local energy density as a scalar field $$ \rho_E(\mathbf{r},t), $$ which assigns to each point in space and time the energy per unit volume.

Gradient of Energy Density

The gradient of this scalar field is a vector field: $$ \nabla \rho_E(\mathbf{r},t) = \left( \frac{\partial \rho_E}{\partial x},, \frac{\partial \rho_E}{\partial y},, \frac{\partial \rho_E}{\partial z} \right). $$

• Units: energy per volume per length.
• Interpretation: direction and magnitude of steepest increase in local energy density.

Image: Colors show gradient

Gradient Tensor (Hessian)

The derivatives of this gradient form a rank-2 tensor, i.e. the Hessian: $$ H_{ij} = \frac{\partial^2 \rho_E}{\partial x_i \partial x_j}. $$

• Encodes the curvature of the energy density field.
• Describes how the gradient itself changes in different spatial directions.
• Eigenvalues/eigenvectors of (H_{ij}) indicate principal directions of curvature (maxima, minima, saddle points).

Physical Significance

• Fluid dynamics analogy: velocity gradient and stress tensors describe shear/expansion; the Hessian plays a similar role for energy density fields.
• General relativity analogy: covariant derivatives of the stress-energy tensor (T_{\mu\nu}) encode conservation and curvature effects.
• Field theory: the Hessian of an energy functional governs stability, mass matrices, and dispersion relations.

Summary

• Gradient: vector field of energy density changes.
• Gradient tensor (Hessian): rank-2 tensor describing curvature of energy density.
• Physically meaningful as a tool to analyze inhomogeneities and local stability in energy distributions.

Image: This image shows a planar intersection of the LEDO waves within the rotation plane. We see different Rotons emitting radial waves into the LEDO-Field. Colors: Colors show overall gradient vector direction. Hue is the local gradient value.

Relation to Known Concepts

• Similar to Lissajous figures: LEDO describes not only the existence of multiple frequencies but their interplay.
• Extends beyond linear superposition by allowing resonant amplification or beating patterns (constructive/destructive).
• Bridges physics and metaphor: conveys that energy density oscillations may carry musical, rhythmic qualities.

Potential Applications

• Quantum models: describing interference of multiple oscillatory field contributions.
• Condensed matter: collective excitations (phonons, magnons) with nontrivial superposition.
• Cosmology: oscillations in primordial fields, dark energy modulation, or “beats” in large-scale structure formation.
• Roton-inspired models: LEDO captures the resonance-driven, non-pointlike nature of energy density oscillations.

Summary Statement

LEDO (Lambda Energy Density Oscillation) provides a metaphorically enriched yet mathematically precise concept for describing interwoven, resonant oscillations of local energy density, transcending simple harmonic motion and highlighting the emergent rhythmic character of complex systems.

Image: This image shows a perpendicular intersection of how Rotons of different sizes emmit waves in axial direction (perpendicular to the rotation plane) into the LEDO-Field. Colors: Colors show gradient vector direction. Hue is the gradient value.

The Rotonic Model: A Taxonomy of Rotational Entities

In a reality where spin is sacred and symmetry whispers across spacetime, we distinguish several classes of rotational entities. These objects, conceptual or real, emerge from the primordial rotational essence: the Roton. From there, configurations become more complex, layered, and deceptive in their simplicity.

“Where particles are poetry and spin is structure,
the Roton sings first, but the Gyrotron brings the echo across spacetime.”