Poincar\'e Sphere and Decoherence Problems

Henri Poincar'e formulated the mathematics of the Lorentz transformations, known as the Poincar'e group. He also formulated the Poincar'e sphere for polarization optics. It is shown that these two mathematical instruments can be combined into one mathematical device which can address the internal space-time symmetries of elementary particles, decoherence problems in polarization optics, entropy problems, and Feynman’s rest of the universe.