Electron spin, nutation, and wave-particle duality

We present a diagonal spacetime 4-manifold to model the wave-particle duality with derivations of the energy ratio of wave to particle to be 1 to 3, by which we calculate the least time for an electron nutation as based on its quadrupole spin states in a 720-degree rotation of its associated electromagnetic wave in a model of Zitterbewegung, wherein we also show a left-handed positron to turn into a right-handed electron by a 3-D rotation. Our motivation here is to develop more efficient use of electricity for energy and environmental concerns.