Recently a new class of mathematical entities—the gyrovectors—came into light in physics. The most intuitive examples of gyrovectors are the relativistic allowed velocities and the Poincaré polarization vectors. Taking advantage of the (also recently elaborated) approach of degree of polarization surfaces in polarization theory, I make an analysis of the strange behavior of these entities in the interaction between the polarized light and the orthogonal dichroic polarization devices. The same approach can be applied in the theory of relativity as well as in many other branches of optics (multilayer optics, ray optics, laser cavity physics, quantum optics) where the Lorentzian character of the transformations which govern some specific problems has been recognized.
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