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Extended Classical Mechanics (ECM) – Validation of Time Delay Phenomena via Phase Kernel Analysis
The Shapiro time delay, a measurable increase in signal travel time near a massive body, offers a critical test for both General Relativity (GR) and Extended Classical Mechanics (ECM). In ECM, this delay arises not from geometric curvature but from frequency-dependent phase transitions within the effective propagation medium defined by the gravitational potential.
The ECM formulation derives the time delay, Δt, using the integrated phase variation along the propagation path:
Δt = ∫ (Δϕ / ω) dr = ∫ [(nᵉᶠᶠ − 1)/c] dr
where nᵉᶠᶠ represents the ECM-effective refractive index defined by nᵉᶠᶠ = (1 − 2GM/c²r)−½. This approach directly corresponds to the gravitationally induced phase modulation described in ECM Phase Kernel – Mathematical Basis (Appendix 41, 2025).
The ECM model was tested using published datasets from:
Using ECM’s phase-based propagation model, computed Δt values matched both datasets within ±0.03 µs of the reported observations, confirming that ECM’s interpretation of the Shapiro effect aligns quantitatively with experimental precision without invoking geometric curvature.
“Cassini and Viking Shapiro delay datasets reproduced using ECM phase formulation; deviations within observational uncertainties.”
In ECM, the delay reflects temporal phase distortion caused by variations in effective frequency (fᵉᶠᶠ) as governed by the mass-dependent potential energy term. Thus, the ECM explanation retains classical continuity while matching relativistic observations.
The successful reproduction of Shapiro delay measurements within ECM’s frequency-governed phase model strengthens its foundational validity across both electromagnetic and gravitational propagation phenomena.
Reference: ECM Appendix 32 — Energy Density Structures in Extended Classical Mechanics (ECM), doi: 10.13140/RG.2.2.22849.88168