Fine-structure constant α
The fine-structure constant α is, in the τ-framework, the τ-effective dimensionless coupling of the electromagnetic sector — derived as α = (11/15)² · ι_τ⁴ at enrichment layer E₁. It is *not* a free parameter: it is fully determined by the master constant ι_τ. The τ-prediction agrees with CODATA to 9.8 ppm, and the formula entails the gauge hierarchy α/α_G ~ 10³⁶ via α_G = α¹⁸ √3 (1 − (3/π)α).
τ-Definition
The fine-structure constant α is, in the τ-framework, the τ-effective dimensionless coupling of the electromagnetic sector — derived as α = (11/15)² · ι_τ⁴ at enrichment layer E₁. It is *not* a free parameter: it is fully determined by the master constant ι_τ. The τ-prediction agrees with CODATA to 9.8 ppm, and the formula entails the gauge hierarchy α/α_G ~ 10³⁶ via α_G = α¹⁸ √3 (1 − (3/π)α).
Categorical invariant. α = (11/15)² · ι_τ⁴ — the EM-sector readout of ι_τ⁴ at the holonomy crossing.
Primary registry anchor:
IV.D104
τ-Derivation Chain
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I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
IV.D104— τ-Native fine-structure constant — α as ι_τ⁴ readout -
IV.D407— Fine-Structure Constant — α = (11/15)² ι_τ⁴ ≈ 0.0072974 (9.8 ppm) -
V.T154— G–α Bridge — α_G = α¹⁸ √3 (1 − (3/π)α), the unique zero-parameter identity linking gravity and electromagnetism
Lean modules referenced:
TauLib.BookIV.Calibration.DimensionlessAlpha,
TauLib.BookV.Coda.GAlphaBridge
SI Translation
Numerical value: 0.0072973525693 ± 1.1e-12 dimensionless
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e)
- Layer 1 (dimensionless): α = (11/15)² ι_τ⁴ — pure τ-prediction, no anchor needed
- α⁻¹ τ-predicted: 137.04 | CODATA: 137.035 999 084(21) | Deviation: 9.8 ppm
- α propagates into R_∞, a_0, λ_C, and (via the G–α bridge) into α_G
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex
Lean Coverage
See Also
Related glossary entries
Referenced by
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PG-C06-elementary-chargeElementary charge e -
PG-C07-vacuum-permittivityVacuum permittivity ε₀ -
PG-C09-electron-massElectron mass m_e -
PG-C11-rydberg-constantRydberg constant R_∞ -
PG-C12-bohr-radiusBohr radius a_0 -
PG-C14-gravitational-fine-structureGravitational fine-structure constant α_G -
PG-C16-weinberg-angleWeak mixing angle sin²θ_W -
PG-C17-strong-couplingStrong coupling constant α_s
Cross-domain bridges
This glossary term sits on the boundary between domains. The τ-framework's cross-domain pivots are the structural junctions where physics, life, and metaphysics readouts meet.
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PG-C05-fine-structure-alphaFine-structure constant α →MathG-D01-iota-tauMaster constant ι_τ -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-D02-tau-categoricalτ-categorical structure -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-D07-4-plus-1-sector4+1 Sector Decomposition -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-D08-five-generators-defFive Generators (definition) -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-K01-universe-postulateThe Universe Postulate (K0) -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-K02-five-generatorsThe five canonical generators (K1–K5) -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-K03-no-omega-axiomThe no-ω axiom (K6) -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-L01-idempotent-decompositionIdempotent Decomposition Lemma -
PG-C05-fine-structure-alphaFine-structure constant α →MathG-O01-tau-objectGeneric τ-object