Аннотация

Diagonal quadratic forms of any dimension, built on a sign-indefinite metric, are represented as squares of six-dimensional (6D) bi-quaternion (BQ) vectors having a definable norm. In particular, the line element of 4D Minkowski space-time is written as a square of BQ-vector whose spatial and temporal parts are mutually orthogonal. Lorentz transformations of BQ-vector components with simultaneous SO(3,C) transformations of the quaternion frame yield a correlation between matrix representations of these groups, distinguishing the SO(1,2) subgroup of mixed space-time rotations. The admitted variability of the subgroup parameters leads to a BQ-vector formulation of relativity theory, comprising all features and effects of Special Relativity with an additional ability to describe motion of arbitrary non-inertial frames. Abandoning the requirement of BQ-vector norm existence leads to an unconventional 6D model of relativity, such that the imaginary part of a space-time interval is observed on the light cone.