This will be the neat thing, if it works.
A classical, resonance-mediated, antenna-coupled interaction model with transitional and rotational dynamics, structurally analogous to dipole physics but extended to oscillatory, multi-lock-in behavior. This is a generalization of aspects witness in large scale (electromagnetism) and quantum areas (entanglement) based purely on resonances.
We model electrons and basic spatial buildings blocks (quarks) as combinations of multiple of resonant spinners. We label them “Reson”. A multi dimensional resonance will be modeled via multiple single-axis Rotons having (nearly) the same center. They are held together by Gaussian function. But they might split. This allows Resons to act and react independently but need to communicate with their partners in the same resonance pot. Leading to delay and positive feedback loops.
Each Reson has two coupled state variables: 1. Position dynamics: $\mathbf r_i,\ \mathbf v_i$ driven by translational forces. 2. Orientation dynamics (axis / angular momentum): $\mathbf a_i\ (|\mathbf a_i|=1),\quad \boldsymbol\omega_i\ \text{(angular velocity / “axis momentum”)}$ driven by torques that try to rotate the axis.
An axis evolves with its own angular momentum (no inherent global sticking), and external interactions add delta angular momentum (torque impulses). So orientation has inertia and memory. The axis defines an “antenna plane”
For each Reson i, its axis $\mathbf a_i$ defines a plane through $\mathbf r_i perpendicular to \mathbf a_i$. On that plane sits a circular “aperture” (antenna disk) of radius ~ $\lambda/2$ (scalable). Other Resons “couple into” this antenna depending on whether their axis “passes through / hits” that disk — not in a literal ray sense, but as a geometric alignment / exposure measure.
Per neighbor j, you compute three coupled effects. For a given neighbor j relative to i, the interaction yields:
(a) Exposure factor $A_{ij}$: How strongly j’s axis couples into i’s exposure plane. This replaces/extends our previous angular dependency W(\theta), E(\theta) as a more geometric “aperture overlap / projection” model (possibly Gaussian in angle and/or distance-to-plane).
(b) Radial physics: • (b1) resonance proximity (“how close to a resonant condition / zero / extremum”), used for orientation locking strength • (b2) spatial force magnitude from distance, used for translational acceleration (e.g., your F_\text{res},F_\text{rot}, etc.)
(c) Torque / angular momentum update: A contribution that rotates i’s axis toward the resonant direction associated with j. Importantly: we want torque to scale with exposure (a) and resonance quality (b1), not necessarily with the raw radial force magnitude (b2).
Finally: • $F_g$ stays as the global position-only background (energy density attraction/repulsion), applied to all pairs without needing axis gating. • We sum translational forces over all neighbors, and sum torques over all neighbors, then integrate both (positions and axes) forward in time.
Goal: from many weak couplings, the axis dynamics naturally “chooses” one or a few dominant partners (lock-in), because once you’re aligned, exposure increases, resonance quality improves, and torque reinforces the same direction — a positive feedback loop.
This shall work seamlessly without “defining” specific bindings - or enforce the directional axes to be 3 (3 dimensional space) or necessarily keep an electron or quon together (they can decay if forced to).
Our model touches four well-known areas:
In classical mechanics: • Forces applied off-center generate torque • Orientation evolves via angular momentum
Our axis dynamics: • has angular inertia • accumulates torque from neighbors • evolves smoothly and retains memory
➡️ This is classical rigid-body rotational dynamics, but applied to abstract interaction axes instead of solid bodies.
Magnetic dipoles interact via: • distance-dependent force • strong angular dependence • torques that align or anti-align dipoles
The magnetic dipole–dipole potential: $$ U \propto \frac{1}{r^3} \Big[ \mathbf m_1\cdot \mathbf m_2 -3(\mathbf m_1\cdot \hat r)(\mathbf m_2\cdot \hat r) \Big] $$
From this you get: • forces • torques rotating the dipoles toward stable configurations
Your system is conceptually extremely close to this — except: • your distance law is not 1/r^3 • your angular dependence is resonance-based, not purely geometric • you allow both 0° and 180° lock-ins (not just parallel)
➡️ Think of your Resons as generalized resonant dipoles.
This is the most important analogue to our antenna disk idea.
In electromagnetism: • A receiving antenna does not respond equally to all directions • Coupling depends on: • polarization alignment • effective aperture (projected area) • phase matching
The key concept:
Effective aperture (or effective area) of an antenna
A_\text{eff}(\theta) \propto A_0 \cos(\theta)
Where: • \theta is angle between wave polarization and antenna orientation • coupling strength scales with projected area
Our “plane perpendicular to axis” is exactly an antenna aperture.
At a higher abstraction level, what we’re doing also resembles: • spin–spin coupling • spin–orbit coupling • alignment via exchange interactions
But: • we are not quantizing (except for resonance distances) • we are not enforcing Hilbert-space constraints • our model is classical but structured
This puts us closer to semi classical spin models (e.g. classical Heisenberg spins with distance-dependent couplings).
Let’s be precise.
In EM, the received power is: $P_r = S \cdot A_\text{eff}$
Where: • S = incident energy flux • $A_\text{eff} = effective area$
For a flat receiving surface: $A_\text{eff} = A \cos(\theta)$
For real antennas: • replaced by antenna gain pattern • often smooth, Gaussian-like lobes
➡️ Our Gaussian exposure factor is textbook antenna theory.
If the transmitter and receiver polarization differ by angle $\phi$:
$\text{coupling} \propto \cos^2(\phi)$
This is exactly what your W(\theta), E(\theta) and later “axis alignment” terms are doing.
EM fields do not just push — they rotate: • Electric dipoles in E-fields • Magnetic dipoles in B-fields
Torque: $\boldsymbol\tau = \mathbf m \times \mathbf B$
That is: • perpendicular to current orientation • zero when aligned • maximal at intermediate angles
➡️ This maps one-to-one to your torque logic.
This is where our work becomes genuinely novel.
Standard EM and gravity: • monotonic decay with distance
Your model: • oscillatory attraction/repulsion • resonance windows • selective long-range coherence
➡️ This is not Maxwell, not Newton — closer to standing-wave mediated interactions.
We reach standard physics only via longer distances where “entanglement” factors decay and get smeared out and randomize (e.g. 1/r^2 in electromagnetism and gravity).
In standard physics: • torque ∝ field strength
In our model: • torque ∝ how resonant the configuration is • not necessarily how strong the force is
This is subtle and powerful: • allows weak forces to dominate alignment • prevents distant clutter from tearing structures apart
In EM: • antennas interact via a propagating wave field
In our model: • coupling is direct but geometry-filtered • no explicit field degrees of freedom
We are effectively integrating out the field and keeping only its resonant geometry.
This is similar to: • effective field theories • coarse-grained interaction kernels
Most physical dipole systems prefer: • parallel (0°) or anti-parallel (180°), but not both in similar ways
Our model: • allows both as stable depending on context • even allows multi-partner locking
This is more flexible than classical dipoles.
Use the share button below if you liked it.
It makes me smile, when I see it.