Skip to content
This repository was archived by the owner on Jul 7, 2026. It is now read-only.

Latest commit

 

History

History
97 lines (67 loc) · 2.18 KB

File metadata and controls

97 lines (67 loc) · 2.18 KB

Radial Scaling Gauge

Status: CANONICAL Paper: 01 — Radial Scaling Gauge for Maxwell Fields


The Scaling Factor

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.


Electromagnetic Field Scaling

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.


Effective Refractive Index

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

Maxwell Equations with Scaling

The modified Maxwell equations in segmented spacetime:

∇ · (s² E) = 0
∇ × (s² B) = μ₀ε₀ s² ∂E/∂t

Wave Equation

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).


Key Values

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

Validation

  • 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

Tests

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