Spin (Intrinsic Angular Momentum)
Spin (IV.T17) is the τ-categorical half-integer correction to the Angular-Momentum Character: the intrinsic rotational invariant of a fermion defect-bundle, equal to ±ℏ/2 by virtue of the bundle's defect-topology, recovered as a theorem (Emergence of Spin-1/2) rather than a postulated axiom.
τ-Definition
Spin (IV.T17) is the τ-categorical half-integer correction to the Angular-Momentum Character: the intrinsic rotational invariant of a fermion defect-bundle, equal to ±ℏ/2 by virtue of the bundle's defect-topology, recovered as a theorem (Emergence of Spin-1/2) rather than a postulated axiom.
Categorical invariant. Spin(B_fermion) := half-integer correction to the angular-momentum character of B; ±ℏ/2 for elementary fermion bundles, derived from defect topology.
Primary registry anchor:
IV.T17
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D11— Physical Quantity Template — dimensional invariants -
V.D118— Angular Momentum Character — base quantity -
IV.T17— Emergence of Spin-1/2 theorem — proves half-integer correction from defect topology -
IV.D294— Planck's constant in relational units fixes ℏ as the angular-momentum quantum
Lean modules referenced:
TauLib.BookI.Kernel.ActionQuantum
SI Translation
Numerical value: 5.272859e-35 ± 0 J·s (= ℏ)
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- ℏ via IV.D294
- spin-1/2 = ℏ/2 = 5.27 × 10⁻³⁵ J·s
Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-spin-emergence.tex