Lorentz Transformation, Poincaré Vectors and Poincaré Sphere in Various Branches of Physics

Fuzzy Algebraic Modeling of Spatiotemporal Timeseries’ Paradoxes in Cosmic Scale Kinematics

This paper introduces the prototype of a generic fuzzy algebraic framework, that aims to serve as a holistic modeling approach of kinematics. Moreover, it detects paradoxes and uncertainties when the involved features of the timeseries have “unconventional” values. All well accepted models are perfectly capturing and clearly describing the spatiotemporal characteristics of a moving object’s (MO) status, when its actual distance from the observer is conventional, i.e., “insignificant compared to the magnitude of light years”. Let us consider the concept that emerges by the following Boolean expression1 (BE1): “Velocity is significant compared to the speed of light (SIV_cSL) AND distance between observer and moving body is significant compared to light years (SID_cLY)”. The only restriction in the above BE1 Boolean expression is that velocity would always be less than C. So far, BE1 is not considered to be true in the models that are employed to build our scientific physics studies. This modeling effort performs mining of kinematics phenomena for which BE1 is true. This approach is quite innovative, in the sense that it reveals paradoxes and uncertainties, and it reaches the following conclusions: When a particle is moving inside hypersurfaces characterized by any type of BE1′s negation, our existing kinematics’ models can survive. In the opposite case, we are gradually led to paradoxes and uncertainties. The gradual and smooth transition from the one state to the other as well as the importance of the aforementioned limitations, can be inferred-modeled by employing fuzzy logic.

On the enpolarization/depolarization effects of deterministic devices

A Poincaré sphere geometric approach to the enpolarization/depolarization effects of dichroic devices/media is presented. The degree of polarization (DoP) of the emergent light is expressed as a function of two parameters: the DoP of the incident light and the dichroic strength of the device. The polar plots of this dependence give an intuitive grasp on how the alternation of the two effects depends on the competition between these parameters. The same approach can be transposed in an adapted terminology in various fields of physics, in all the problems whose underpinning mathematics is that of Lorentz transformation.