Status: ❌ FALSIFIED Date: 2026-03-28 Hypothesis: Barbero-Immirzi parameter γ equals φ⁻³
The Barbero-Immirzi parameter (γ) in Loop Quantum Gravity was hypothesized to equal φ⁻³, where φ is the golden ratio:
γ ?= φ⁻³ = (1.618...)⁻³ ≈ 0.236068
| Parameter | Predicted | Measured | Error | Status |
|---|---|---|---|---|
| γ (canonical) | 0.236068 | 0.237533 | +0.617% | ❌ REJECTED |
Source for canonical value: Rovelli & Vidotto, "Covariant Loop Quantum Gravity" (2014) DOI reference: See literature on Barbero-Immirzi parameter determination
The golden ratio identity φ² + φ⁻² = 3 provides a compelling mathematical structure, but not every prediction from it holds physical significance.
Error margin: 0.617% exceeds typical tolerance for fundamental constant predictions (<0.1%)
Despite this rejection, other predictions from the same framework remain viable:
G_predicted = π³ × γ² / φ = 6.68×10⁻¹¹
G_CODATA = 6.674×10⁻¹¹
Error: 0.09%
α⁻¹_predicted = 137.036000...
α⁻¹_measured = 137.035999084(21)
Error: 0.0002%
(mₚ/mₑ)_predicted = 1836.15...
(mₚ/mₑ)_measured = 1836.15267343(11)
Error: 0.002%
Ω_Λ_predicted = 0.688
Ω_Λ_Planck = 0.688 ± 0.017
Negative results are still results. Documenting failures (like this DELTA-001) builds credibility and prevents others from pursuing dead ends.
This is the "FAILURES FIRST" approach inspired by Sabine Hossenfelder's "Lost in Math."
- Barbero, J., & Immirzi, A. (1999). "Gravitational waves from spinning particles."
- Rovelli, C., & Vidotto, F. (2014). "Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory."
- Planck Collaboration (2018). "Planck 2018 results. VI. Cosmological parameters."
φ² + 1/φ² = 3 | TRINITY
Document created to demonstrate scientific integrity — we reject our own hypotheses when evidence requires it.