Quaternion Model of Relativity: Solutions for Non-Inertial Motions and New Effects

Original method to construct models, formulate equations and find solutions for wide range of relativistic cinematic problems is suggested. This version of relativity theory is extracted from quaternion mathematics as natural consequence of SO(3, C)-invariance of quaternion multiplication rule. Quaternion units serve as relativistic frames used to measure components of basic bi-quaternion vector whose space and time parts are found in two reciprocally imaginary 3-dimensional spaces. A set of rotational equations, main instrument of the model, ties the frames by the subgroup SO(1, 2) subset of SO(3, C) leaving the basic bi-quaternion vector form-invariant. All cinematic effects of Special Relativity follow from the rotational equations with constant transformation parameters. Localization of the parameters leads to simple description of non-inertial Q-frames motion. New solutions for inverse Tomas precession, relativistic oscillator and effect of relativistic position shift of fast satellites of Solar System planets observed from the Earth are considered in detail. The theory is shown to admit a plausible explanation of Pioneer Anomaly as of a pure relativistic effect.