Quantization of Hyper-Complex Gauges and Space Time: Dering the Fine Structure Constant as a Dimensionless Geometric Constant Beyond 12th Digits
Abstract
Jau Tang and Qiang Tang
To derive the precise fine structure constant, we use an approach based on hypercomplex algebra, including Hamilton’s 4D quaternions, Cayley’s 8D octonions, and 16D sedenions, which have broad applications in particle physics. This framework allows us to investigate electron quantum dynamics, introducing a hypercomplex non-Abelian, non-associative gauge for the Dirac equation with internal structure. Extending 4D spacetime to a higher-dimensional lattice, we show that electron coupling to a quantized gauge field yields an effective quantized mass. This approach derives an inverse fine-structure constant of 137 from the su (2) octonion gauge and a precise experimental match of 137.035999206 from the (su(2) ⊕ su(2) ⊕ su(2)) × S3 ⊕ su(2) sedenion gauge. These gauges dictate lepton masses in higher-dimensional generalized Einstein’s massenergy relation. The fundamental constant, linked to Pythagorean primes, governs electron- photon interactions and plays a crucial role across physics.
