Vacuum permittivity ε₀
Vacuum permittivity ε₀ is, in the τ-framework, a Tier-I (Established) unit-conversion entry of the constants ledger — the dimensional factor Q²/(M L³ H²) that, together with c and μ₀, satisfies the algebraic identity c² = 1/(ε₀ μ₀). It is exact in the τ-cascade and fixed by 2019 SI definitions (e and c are exact).
τ-Definition
Vacuum permittivity ε₀ is, in the τ-framework, a Tier-I (Established) unit-conversion entry of the constants ledger — the dimensional factor Q²/(M L³ H²) that, together with c and μ₀, satisfies the algebraic identity c² = 1/(ε₀ μ₀). It is exact in the τ-cascade and fixed by 2019 SI definitions (e and c are exact).
Categorical invariant. ε₀ = Q² / (M L³ H²) — the dimensional EM-coupling readout that closes the (E, B) ↔ (M, L, T, Q) projection.
Primary registry anchor:
IV.D36
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
IV.D36— Vacuum Permittivity — dimensional factor Q²/(M L³ H²) -
V.T142— E₁ Completeness — ε₀ is one of six Tier-I unit conversions; c² = 1/(ε₀ μ₀) holds exactly
Lean modules referenced:
TauLib.BookIV.Calibration.SIReference,
TauLib.BookV.Coda.ConstantsLedger
SI Translation
Numerical value: 8.8541878128e-12 ± 1.3e-21 F m⁻¹
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: ε₀ = e²/(4π ℏ c α) — exact within τ-cascade once α, e, ℏ, c are fixed
- c² = 1/(ε₀ μ₀) is entry #6 of the ledger, scope label E (Established)
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex