Elementary charge e
The elementary charge e is, in the τ-framework, a Layer-3 SI quantity built from the dimensionless EM coupling α (a τ-prediction) and the Tier-I unit conversions (c, ℏ, ε₀). It is exact by 2019 SI definition and consistent with the τ-cascade through the algebraic identity e² = 4π ε₀ ℏ c α.
τ-Definition
The elementary charge e is, in the τ-framework, a Layer-3 SI quantity built from the dimensionless EM coupling α (a τ-prediction) and the Tier-I unit conversions (c, ℏ, ε₀). It is exact by 2019 SI definition and consistent with the τ-cascade through the algebraic identity e² = 4π ε₀ ℏ c α.
Categorical invariant. e² / (4π ε₀ ℏ c) = α — the EM-coupling readout that fixes e once α and the unit-conversions are fixed.
Primary registry anchor:
IV.D84
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
IV.D407— α = (11/15)² ι_τ⁴ — EM-sector coupling -
IV.D84— Electric Charge — e fixed by α via e² = 4π ε₀ ℏ c α -
V.T142— E₁ Completeness — e is Layer-3 SI output of the cascade
Lean modules referenced:
TauLib.BookIV.Calibration.SIReference,
TauLib.BookV.Coda.ConstantsLedger
SI Translation
Numerical value: 1.602176634e-19 ± 0 C
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math)
- Layer 1: α = (11/15)² ι_τ⁴
- Layer 3: e = √(4π ε₀ ℏ c α) — Layer-3 SI output
- Numerical: e is exact by 2019 SI definition (e fixes the ampere); the τ-framework adopts this verbatim
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex
Lean Coverage
See Also
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.