A Geometric Model for the Origin of Spacetime Dimensions and Fundamental Forces from Spinor Geometry

This work proposes a novel model where the dimensional structure of spacetime and the nature of elementary particles are necessary geometric consequences of spinor rotational phase requirements. We show that three-dimensional space is the minimum topological structure capable of hosting the 720-degree (4-pi) rotational symmetry of spin-1/2 fermions without self-intersection. This rotation is defined as a dual-phase oscillation of a particle and its intrinsic, temporally-orthogonal shadow phase sharing a single mass along the time axis. We derive electric charge as the linear direction of this temporal flow, and magnetic spin as its rotational vortex. Extending this logic, a fundamental spin-1/4 particle, requiring an 8-pi (1440-degree) rotational cycle, geometrically necessitates a fourth spatial dimension. This framework is validated by the four-photon vertex in QED (Feynman's box diagram), the "dressed" net-zero structure of hadrons, and the inevitable face-to-face alignment mechanism required for particle-antiparticle annihilation.