The Boolean Rotation Theorem, Riemann Sphere, and Wavefunction: Twistor Geometry of Polarization and Superposition Spinors

Being either true or false, 1 or 0, the standard logic and the Boolean algebra traditionality never rotate. Thus, it can only account for polarization states but not superposition states. This paper proves the Boolean rotation theorem through complexifications. This result allows us to formulate polarization spinors as well as superpositions spinors. It provides a new understanding of the Riemann sphere of two-state systems. It also provides an alternative solution to the measurement of wavefunctions, which accounts for both the U-process and the R-process. The work reported in this paper formulates the Penrose twistor geometry of the polarization spinors and the superposition spinors.