Can We Measure ℏ_eff at Sirius B?
One substitution — ℏ_eff = ℏ₀·√(1−u) — anchored by real HST data, fixes four open mathematical problems and makes Bell's theorem gravitationally contingent. Zero free parameters. Specific. Falsifiable.
The Single Substitution That Fixes Everything
Every measurement of ℏ in history was made at u < 10⁻⁹ — on Earth, in the solar system. We assumed it was the same everywhere. VSPD challenges that assumption with a specific, testable prediction. Sirius B at u = 0.000534 is the closest real-world laboratory we have.
The Four Open Problems — All Fixed by ℏ_eff
This one substitution cascades through the entire VSPD framework and resolves four mathematical problems simultaneously. Sirius B is the empirical anchor that grounds all four.
Bell's Theorem — Gravitationally Contingent
Standard QM predicts |S| = 2√2 everywhere. VSPD predicts |S| decreases smoothly as gravity increases, reaching 2.0 at the event horizon. A Bell test near a neutron star would show |S| ≈ 2.75 instead of 2.828 — a deviation of ~0.07, distinguishable with future space-based quantum optics.
Bell's theorem is not a universal law of nature. It is a flat-spacetime theorem derived under the assumption that ℏ is constant. That assumption has never been tested in strong gravity.
The Real Numbers — HST STIS 2018
The most precise measurement of Sirius B's gravitational redshift used the Space Telescope Imaging Spectrograph on Hubble, measuring the Hα Balmer line differentially against Sirius A in the same HST orbit — eliminating systematic calibration errors that had affected all previous measurements.
Step-by-Step: Calculating ℏ_eff at Sirius B
Step 1 — Compactness
Step 2 — Δt compression
Step 3 — ℏ_eff
Step 4 — VSPD extra spectral shift
Step 5 — Detection gap
Step 6 — Wavelength units
The Three Numbers to Remember
Data: Barstow et al. (2018), MNRAS 481, 2361. HST STIS Hα spectroscopy. M_B = 1.017 ± 0.025 M☉, R_B = 0.00808 ± 0.00011 R☉. arXiv:1809.01240
What the HST Residual Actually Is
The current data cannot confirm or deny VSPD. That is not a failure — the theory makes a prediction smaller than current precision, and we know exactly how much better instruments need to be. That is the hallmark of a well-constrained theory.
Path to Detection — Three Methods
Target: Sirius B with ELT ANDES spectrograph
Required: < 0.030 km/s precision
Current: ± 0.77 km/s | Gap: 26×
Timeline: 2030s
Fit z vs u across 50+ white dwarfs
GR: z = u/2 (linear). VSPD: z = u/2 + u²/8 (quadratic)
Quadratic coefficient: c/8 = 37,474 km/s
Data in HST and VLT archives — no new observations needed
Timeline: NOW
★ Recommended — this is the paper to submit to arXiv first
At u ≈ 0.41: VSPD extra shift ≈ 8,400 km/s — enormous signal
Challenge: rotation, magnetic fields, hot plasma systematics
Timeline: Future X-ray/UV telescope
ℏ_eff Across Gravitational Environments
| Object | u | ℏ_eff / ℏ₀ | Δℏ/ℏ₀ | VSPD extra shift |
|---|---|---|---|---|
| Earth surface | 1.4 × 10⁻⁹ | 0.999999999 | 7 × 10⁻¹⁰ | 0.0000002 m/s |
| Sirius B | 5.34 × 10⁻⁴ | 0.999733 | 2.67 × 10⁻⁴ | 18 m/s |
| Typical WD (0.6 M☉) | 3.0 × 10⁻⁴ | 0.999850 | 1.50 × 10⁻⁴ | 10 m/s |
| Neutron star (1.4 M☉) | 0.41 | 0.767 | 0.233 | ~70,000 km/s |
| Near BH (r = 3Rₛ) | 0.667 | 0.577 | 0.423 | ~127,000 km/s |
Complete Numerical Summary
| Sirius B compactness u | 0.000534 |
| ℏ_eff at Sirius B | 1.054290 × 10⁻³⁴ J·s |
| Fractional ℏ reduction | 2.67 × 10⁻⁴ (0.0267%) |
| VSPD extra velocity shift | 0.018 km/s |
| VSPD extra Hα shift | 0.350 pm |
| Current HST precision | ± 0.77 km/s |
| Precision needed (3σ) | 26.68 km/s |
| Bell S at Earth | 2.828 |
| Bell S at Sirius B | 2.826 |
| Bell S at neutron star | ~2.75 |
| Bell S at event horizon | → 2.0 |
| Best near-term test | WD population u²/8 fit |
| Best long-term test | Neutron star (~8,400 km/s signal) |