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.