Observed Signal
The Pioneer 10/11 probes showed a persistent Doppler drift:
ḟ ≈ +6 × 10⁻⁹ Hz/s at f ≈ 2.29 GHz
⇒ α = ḟ / f ≈ 2.6 × 10⁻¹⁸ s⁻¹
⇒ α = ḟ / f ≈ 2.6 × 10⁻¹⁸ s⁻¹
This is equivalent to an apparent sunward acceleration of
aₚ ≈ (8.74 ± 1.33) × 10⁻¹⁰ m/s²
Integration over 30 years
The time-scale interpretation gives:
Δt ≈ ½ α T² ≈ 1–3 s (over 30 years)
Thus the anomaly is not only a force-like effect, but can be equivalently viewed as a tiny drift in the underlying phase-time.
Mainstream vs. Dephaze Interpretation
| Aspect | Mainstream (PRL 2012) | Dephaze Interpretation |
|---|---|---|
| Cause of aₚ | Thermal recoil from RTG & antenna reflections | Equivalent time-scale drift (α = ḟ/f) |
| Mathematical link | aₚ(t) | α(t) = 2aₚ/c |
| Long-term effect | Secular acceleration (decreasing with Pu-238 decay) | Cumulative Δt ≈ seconds / decades |
Falsifiable Prediction
Dephaze makes a concrete, testable prediction:
- After subtracting the thermal model, residual Doppler data should contain step-like offsets.
- These should correlate with Δcosδ (geometry of Earth–probe line of sight).
- Expected amplitude: 0.1–1 mm/s equivalent ΔV.
- If absent → Dephaze falsified. If present → new physical layer revealed.
Conclusion
The Pioneer anomaly is both:
- A thermal recoil effect (dynamic, mainstream consensus).
- An equivalent time-scale drift (chronometric, Dephaze view).
The two are not contradictory, but complementary. The open question is whether residual Δcosδ-correlated steps exist — a falsifiable test that can deepen our understanding of spacetime structure.