# Regimes — Electromagnetism  
### TriadicFrameworks /docs/theories/electromagnetism/regimes.md

Electromagnetism (EM) in TriadicFrameworks is a **field‑coherence
theory**, not a force‑centric mechanism and not a particle‑first
narrative.

EM = **coherent behavior of the electromagnetic field**.  
Maxwell operators = **structural constraints**, not “laws of force.”  
Light = **self‑consistent field propagation**.

This file defines how EM behaves across RTT regimes (R1 → R3).

---

# R1 — Classical Field Stability Regime  
### (Static + quasi‑static coherence)

R1 is the regime where EM fields are **stable, slowly varying, and
geometry‑compatible**.

Characteristics:

- ∇·E = ρ/ε₀ (divergence‑source relation stable)  
- ∇·B = 0 (magnetic coherence constraint)  
- ∇×E ≈ 0 (quasi‑static electric field)  
- ∇×B ≈ μ₀J (quasi‑static magnetic field)  
- fields respond smoothly to charge/current distributions  
- no wave propagation required  
- no relativistic coupling required  

R1 supports:

- electrostatics  
- magnetostatics  
- DC circuits  
- static field solvers  
- low‑frequency approximations  

Coherence in R1 = **divergence stability + curl stability**.

---

# R2 — Dynamic Field Propagation Regime  
### (Full Maxwell dynamics)

R2 introduces **time‑varying fields** and **self‑consistent propagation**.

Characteristics:

- ∂E/∂t and ∂B/∂t active  
- ∇×E = −∂B/∂t  
- ∇×B = μ₀J + μ₀ε₀∂E/∂t  
- wave equation emerges naturally  
- light = self‑coherent field propagation  
- no medium required (no ether metaphors)  
- geometry still classical (flat or weakly curved)  

R2 supports:

- electromagnetic waves  
- antennas  
- AC circuits  
- optics (classical)  
- radiation and propagation models  

Coherence in R2 = **dynamic divergence + dynamic curl + propagation
stability**.

---

# R3 — Geometry‑Coupled, Multi‑Scale Field Regime  
### (Relativistic + quantum‑compatible EM)

R3 is the highest EM regime: **geometry‑coupled, multi‑scale, and
quantization‑compatible**.

Characteristics:

- EM fields couple to curvature (GR‑compatible)  
- field tensors replace E/B decomposition  
- invariants (FᵤᵥFᵘᵛ, Fᵤᵥ⋆Fᵘᵛ) become coherence anchors  
- propagation respects spacetime geometry  
- EM integrates with QFT (QED)  
- multi‑scale behavior (classical ↔ quantum)  
- gauge structure explicit (U(1) symmetry)  

R3 supports:

- relativistic electrodynamics  
- curved‑spacetime EM  
- QED compatibility  
- high‑frequency, high‑energy propagation  
- multi‑scale field analysis  

Coherence in R3 = **tensor‑level invariance + geometric compatibility +
gauge stability**.

---

# Regime Transitions

### R1 → R2  
- time‑varying fields activate  
- curl operators become dynamic  
- wave propagation emerges  

### R2 → R3  
- geometry becomes active  
- field tensor replaces E/B split  
- gauge structure becomes explicit  

### R3 → R2  
- geometry weakens  
- tensor reduces to classical Maxwell form  

### R2 → R1  
- time‑variation suppressed  
- quasi‑static approximation valid  

Transitions must preserve:

- divergence consistency  
- curl consistency  
- source compatibility  
- geometric validity  
- field coherence  

---

# Collapse Modes (EM1 → EM5)

- **EM1:** divergence collapse (∇·E or ∇·B invalid)  
- **EM2:** curl collapse (∇×E or ∇×B invalid)  
- **EM3:** propagation collapse (unstable wave evolution)  
- **EM4:** source collapse (invalid charge/current configuration)  
- **EM5:** geometry collapse (field‑geometry mismatch)  

Collapse is structural, not force‑based.

---

# Summary

Electromagnetism across regimes:

- **R1:** classical field stability  
- **R2:** dynamic field propagation  
- **R3:** geometry‑coupled, multi‑scale EM  

Electromagnetism = **coherent field behavior**, not force.  
Maxwell operators = **structural constraints**, not particle rules.  
Light = **self‑consistent field propagation**.