Planck's Constant from Incommensurable Sectors on Fl₁,₂(ℂ³) × ℂP¹
Year: 2026
Type: preprint
Abstract: This paper proposes a structural origin for ℏ by identifying it as the dimensional mediator between two incommensurable symplectic sectors of the possibility manifold M = Fl₁,₂(ℂ³) × ℂP¹. In the symmetric Kähler–Einstein normalization, the flag sector (carrying Standard Model charge structure) and the recording sector (carrying binary quantum-state structure) possess primitive symplectic periods in the ratio: (1, 1, π) Because π ∉ ℚ, the Kostant–Souriau–Weil integrality criterion implies that no single ordinary prequantum line bundle exists over M. A universal quantization scale is therefore mathematically required to mediate between these incompatible sectors. This scale is identified with Planck’s constant ℏ. The resulting structural relation is: κ / ℏ = π where κ is the Fubini–Study period of the ℂP¹ recording sector. In this reading, one complete recording act consumes π action quanta. The paper further shows that local Kähler quantization reproduces standard quantum commutator structure with the same ℏ: Heisenberg algebra on local flag charts Exact SU(2) spin algebra on ℂP¹ Standard uncertainty relations emerging sectorwise Thus ℏ appears simultaneously as: Global geometric: commensuration between sectors Local algebraic: deformation parameter of quantum commutators Dimensional physical: the unit converting charge-lattice action into recording-lattice action Within the broader program in which M = Fl₁,₂(ℂ³) × ℂP¹ also yields Standard Model charge structure, coupling relations, three generations, and prior geometric derivations of constants, this work positions Planck’s constant not as primitive, but as emergent from manifold structure.
Author: Kirk, Harold D.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155384096