Status: CANONICAL Paper: 01 — Radial Scaling Gauge for Maxwell Fields
SSZ defines a radial scaling factor:
s(r) = 1 + Ξ(r) = 1/D(r)
This factor transforms the radial coordinate to a "physical" (segmented) coordinate:
dρ = s(r) · dr
where ρ is the physical (segmented) radial distance and r is the coordinate distance.
In the presence of segmentation, electromagnetic fields are scaled:
E'(r) = s(r) · E(r)
B'(r) = s(r) · B(r)
This means fields are stronger in regions of higher segmentation.
The scaling factor acts as an effective refractive index:
n_eff(r) = s(r) = 1 + Ξ(r)
This is the key connection between segmentation and light propagation:
- Light travels slower (in coordinate terms) through highly segmented regions
- The Shapiro delay arises naturally from this effective index
- No new physics is needed — just the geometric consequence of segmentation
The modified Maxwell equations in segmented spacetime:
∇ · (s² E) = 0
∇ × (s² B) = μ₀ε₀ s² ∂E/∂t
The transformed wave equation in 1D:
(1/s) ∂/∂r [(1/s) ∂E/∂r] - (1/c²) ∂²E/∂t² = 0
CRITICAL: When transforming dρ = s(r)·dr, the second-derivative operator includes an extra s·s' term. Missing this term is a technical error, not physics (see Paper 01, Section 4).
| Location | s(r) | n_eff | Effect |
|---|---|---|---|
| r → ∞ | 1 | 1 | No scaling |
| Sun surface | 1.000001 | 1.000001 | Tiny |
| NS surface | 1.3–1.5 | 1.3–1.5 | Measurable |
| r = r_s | 1.802 | 1.802 | Strong scaling |
- 45/45 tests PASS (2025-12-28)
- GPS, Pound-Rebka, S2 star validated
- 13 astronomical objects consistent
- PPN correction (1+γ) for Shapiro/Lensing confirmed
| Test | Repository |
|---|---|
| test_radial_scaling.py | frequency-curvature-validation |
| All 45 tests | maxwell (FINAL_TEST_REPORT_2025-12-28.md) |
© 2025–2026 Carmen N. Wrede, Lino P. Casu