Generalized Dirac Equation in Quantized Octonion-Sedenion Spacetime: Deriving the Fine Structure Constant beyond ex-perimental precision
Abstract
Jau Tang, Chien-Cheng Chang and Qiang Tang
Using hypercomplex algebra, we introduce a novel framework for understanding the fine-structure constant (α) through mass-spacetime quantization. By extending the Dirac equation beyond Minkowski spacetime and incorporating a 12-dimensional (12D) internal spacetime structure derived from octonion and sedenion algebra, we propose that mass emerges from internal dynamics rather than the Higgs mechanism. Our theoretical formulation yields a value of 1/α = 137.03599920605017, achieving remarkable agreement beyond the 12th decimal place of the experimental inverse fine structure constant. This result suggests that α is not merely a phenomenological parameter but an emergent geometric constant, akin to π or the Euler constant. Moreover, our approach naturally connects mass quantization to internal spacetime symmetry, providing deeper insights into the fundamental nature of elementary particles and forces. By challenging conventional assumptions of the Standard Model, this framework opens new avenues for exploring quantum gravity and grand unification beyond existing theories.
