Modeling of Nanostructures

A dynamical derivation of the Dirac wave equation is developed by unifying the torsion and curvature of spacetime in a six-dimensional hyperspacetime supporting closed-circuit affine geodesics that form stable atomic orbitals of a spinning electron. The physical basis of spin is mechanically established. Causality is restored to atomistic phenomena by providing a spatiotemporal basis of Heisenberg's uncertainty by unifying spacelike spacetime with timelike spacetime. The discrete singularities of quantum theory are reconciled with the continua of relativity theory by unifying discrete line-continua in spacelike spacetime with the space-continuum of timelike spacetime. Spacelike and timelike spatiotemporal manifolds are established as being physically coupled by an exchange force that results from a self-generated electromotive force due to the path-dependent parallel-transport of momentum along a closed-circuit affine geodesic in flat spacelike spacetime. The self-generated electromotive force in flat spacelike spacetime accounts for the stability of a spinning electron by compensating the dissipative radiation of the rotating charge.