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.