Status: CANONICAL — ALWAYS FOLLOW
| Observable | Type | Method | Formula |
|---|---|---|---|
| Time dilation | Timelike (clock) | Ξ | D = 1/(1+Ξ) |
| Gravitational redshift | Timelike (clock) | Ξ | z = Ξ(r) |
| Frequency shift | Timelike (clock) | Ξ | ν_obs = ν_emit × D |
| GPS correction | Timelike (clock) | Ξ | ΔD × t |
| Pound-Rebka | Timelike (clock) | Ξ | Δν/ν = ΔΞ |
| Lensing deflection | Null (light) | PPN | α = (1+γ)r_s/b = 2r_s/b |
| Shapiro delay | Null (light) | PPN | Δt = (1+γ)(r_s/c)ln(...) |
| VLBI delay | Null (light) | PPN | (1+γ) factor |
| Perihelion precession | Timelike (orbit) | PPN | Δω = 6πGM/[a(1-e²)c²] |
| Frame dragging | Timelike (orbit) | PPN | Standard Lense-Thirring |
| Geodetic precession | Timelike (orbit) | PPN | Standard PPN |
Using the wrong method produces the wrong answer:
| Observable | Wrong method (Ξ-only) | Right method | Error |
|---|---|---|---|
| Lensing | α = r_s/b | α = 2r_s/b | 50% too low |
| Shapiro | Δt_Ξ | 2×Δt_Ξ | 50% too low |
| Time dilation | D_PPN (overcounted) | D_Ξ | Overcounted |
The factor-2 discrepancy is NOT a bug — it's the difference between g_tt-only (Ξ) and g_tt+g_rr (PPN).
β = 1 (exact in SSZ)
γ = 1 (exact in SSZ)
Confirmed: Cassini (2003): γ = 1.000021 ± 0.000023
1. Identify the observable
2. Classify: Does it involve LIGHT PATH or CLOCK/ORBIT?
→ Light path (null geodesic) → PPN with (1+γ)
→ Clock comparison (static) → Ξ directly
→ Orbital dynamics → PPN (β,γ) machinery
3. Determine regime (r/r_s)
4. Select correct Ξ formula for that regime
5. Calculate
© 2025–2026 Carmen N. Wrede, Lino P. Casu