# Cross‑Module Integration — Electromagnetism  
### TriadicFrameworks /docs/theories/electromagnetism/cross_module.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 force laws.  
Light = **self‑consistent field propagation**.

This file defines how Electromagnetism integrates with other modules in
the TriadicFrameworks canon.

---

# 1. Integration with General Relativity (GR)

GR provides:

- geometric structure (metric, curvature)  
- spacetime propagation constraints  
- tensor calculus  

Electromagnetism provides:

- the field tensor **Fᵤᵥ**  
- invariants (FᵤᵥFᵘᵛ, Fᵤᵥ⋆Fᵘᵛ)  
- geometry‑compatible propagation  

**Integration:**  
EM becomes **geometry‑coupled** in R3.  
Propagation follows curvature; E/B unify into Fᵤᵥ.

---

# 2. Integration with Quantum Field Theory (QFT)

QFT provides:

- quantization rules  
- gauge symmetry (U(1))  
- particle excitations (photons)  

Electromagnetism provides:

- the classical field structure  
- the operator grammar  
- the coherence framework  

**Integration:**  
QED = **quantized EM field**.  
Classical EM is the **coherence‑limit** of QFT.

---

# 3. Integration with Quantum Mechanics (QM)

QM provides:

- wavefunctions  
- probability amplitudes  
- operator algebra  

Electromagnetism provides:

- potentials (Aᵤ)  
- gauge structure  
- field‑based interactions  

**Integration:**  
EM couples to QM through **minimal coupling** and **gauge invariance**.

---

# 4. Integration with Information Theory (IT)

Information Theory provides:

- distinctions  
- coherence metrics  
- structural invariants  

Electromagnetism provides:

- stable field invariants  
- divergence/curl consistency  
- propagation coherence  

**Integration:**  
Field invariants behave as **stable information structures**.

---

# 5. Integration with Thermodynamics

Thermodynamics provides:

- energy flow  
- stability surfaces  
- dissipation structure  

Electromagnetism provides:

- Poynting vector (energy flux)  
- field energy density  
- propagation stability  

**Integration:**  
Energy flow in EM is **thermodynamically constrained**.

---

# 6. Integration with FFT / Wave Analysis

FFT provides:

- spectral decomposition  
- frequency‑domain operators  
- propagation analysis  

Electromagnetism provides:

- wave equations  
- propagation operators  
- coherence constraints  

**Integration:**  
EM waves become **spectral coherence structures**.

---

# 7. Integration with Systems Physics

Systems Physics provides:

- network‑level dynamics  
- feedback loops  
- multi‑component interactions  

Electromagnetism provides:

- field‑mediated coupling  
- propagation channels  
- coherence constraints  

**Integration:**  
EM acts as a **field‑level interaction network**.

---

# 8. Integration with Circuits & Electronics

Circuits provide:

- lumped‑element models  
- current/voltage abstractions  

Electromagnetism provides:

- field‑level grounding  
- source operators (ρ, J)  
- propagation constraints  

**Integration:**  
Circuits are **R1 approximations** of EM.

---

# 9. Integration with Optics

Optics provides:

- ray models  
- wave models  
- interference/diffraction  

Electromagnetism provides:

- full wave equations  
- coherence structure  
- propagation operators  

**Integration:**  
Optics is **R2 EM** in the high‑frequency limit.

---

# 10. Integration with Plasma Physics

Plasma Physics provides:

- charged fluid models  
- collective behavior  
- instabilities  

Electromagnetism provides:

- field‑particle coupling  
- propagation constraints  
- coherence structure  

**Integration:**  
Plasmas are **EM‑coupled multi‑scale systems**.

---

# 11. Integration with Computational Physics

Computational Physics provides:

- numerical solvers  
- discretization schemes  
- simulation frameworks  

Electromagnetism provides:

- operator grammar  
- coherence constraints  
- propagation rules  

**Integration:**  
EM simulations must preserve **divergence/curl consistency**.

---

# Summary

Electromagnetism integrates with the canon by providing:

- the **Maxwell operator framework**  
- the **field‑tensor coherence model**  
- the **geometry‑coupled propagation system**  
- the **multi‑scale EM regime structure**  
- the **collapse classification system**  

Electromagnetism = **coherent field behavior**.  
Light = **self‑consistent field propagation**.  
Physics = **operator‑driven coherence systems**.