Frequency
Frequency (IV.D79) is the τ-categorical Base Circulation rate: the rate at which a defect bundle traverses its base loop on T². It is the natural conjugate to τ-time and the operational form of the energy-frequency relation E = hν, recovered in τ from the Quantum-of-Action constant (IV.D294).
τ-Definition
Frequency (IV.D79) is the τ-categorical Base Circulation rate: the rate at which a defect bundle traverses its base loop on T². It is the natural conjugate to τ-time and the operational form of the energy-frequency relation E = hν, recovered in τ from the Quantum-of-Action constant (IV.D294).
Categorical invariant. Frequency(B) := rate of base-circulation of B on T²; the τ-internal angular rate functional, conjugate to τ-time (V.D17).
Primary registry anchor:
IV.D79
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D11— Physical Quantity Template — dimensional invariants -
IV.D79— Frequency as Base Circulation — rate of motion on the base loop -
V.D17— Proper Time (Arc Length) provides the τ-time scale conjugate to ν -
IV.D294— Planck's constant in relational units fixes the conversion ν → E
Lean modules referenced:
TauLib.BookIV.Calibration.DimensionlessCouplings,
TauLib.BookI.Kernel.ActionQuantum
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- ℏ via Planck's constant in relational units (IV.D294)
- ν = E/h on each spectral line
Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-frequency.tex