Euclidean Complex Relativistic Mechanics: A New Special Relativity Theory

Abstract

Relativity Theory (RT) was fundamental for the development of Quantum Mechanics (QMs). Special Relativity (SR), as is applied until now, cancels the transitive attribute in parallelism, when three observers are related, because Lorentz Boost (LB) is not closed transformation. In this presentation, considering Linear Spacetime Transformation (LSTT), we demand the maintenance of Minkowski Spacetime Interval (S2). In addition, we demand this LSTT to be closed, so there is no need for axes rotation. The solution is the Vossos Matrix (ΛB) containing real and imaginary numbers. As a result, space becomes complex, but time remains real. Thus, the transitive attribute in parallelism, which is equivalent to the Euclidean Request (ER), is also valid for moving observers. Choosing real spacetime for the unmoved observer (O), all the natural sizes are real, too. Using Vossos Transformation (VT) for moving observers, the four-vectors’ zeroth component (such as energy) is real, in contrast with spatial components that are complex, but their norm is real. It is proved that moving (relative to O) human O' meter length, according to Lorentz Boost (LB). In addition, we find Rotation Matrix Vossos-Lorentz (RBL) that turns natural sizes’ complex components to real. We also prove that Speed of Light in Vacuum (c) is invariant, when complex components are used and VT is closed for three sequential observers. After, we find out the connection between two moving (relative to O) observers: X"= ΛLO"(o) ΛLO(O') X', using Lorentz Matrix (ΛL). We applied this theory, finding relations between natural sizes, that are the same as these extracted by Classic Relativity (CR), when two observers are related (i.e. relativistic Doppler shift is the same). But, the results are different, when more than two observers are related. VT of Electromagnetic Tensor (Fμv), leads to Complex Electromagnetic Fields (CEMFs) for a moving observer. When the unmoved observer O and a moving observer O' are related, O measures the same Real Electromagnetic Fields (REMFs) as those are given, using LB, but O' measure CEMFs with the same formula. Complex Electromagnetic Tensor (F'B) turns to Real Electromagnetic Tensor (F') using the formula . When there are two moving (relative to O) observers O' and O", their real electromagnetic tensors are related, using the form F" = ΛLO"(O) ΛLO(O) F' [ΛLO"(O') ΛLO(O')]T. In addition, we prove that the relation between two moving (relative to O) observers, when they use Real Coordinates (RCs), causes a real rotation between their frames. The turn is opposite to the turn of Thomas and has a little different measure, when the velocities are small. We apply these to the Uniform Circular Motion (UCM) and to the Hydrogen Atom (H), considering that the Proton (p) is the unmoved observer O and the laboratory observer O' has infinitesimal velocity. Using Perturbation Theory (PT) we calculate the position of the fine structure peaks of the atomic spectrum. The result is better not only than this extracted using P. Dirac Theory, but also than that extracted using L. H. Thomas Method.