Subluminal and superluminal transformations in six-dimensional special relativity

A real six-dimensional space-time (three space and three time dimensions) scheme is used to discuss both subluminal and superluminal transformations between the inertial frames of observers. Properties of the linear transformations are derived by using the relative matrix velocities between frames. A link with the usual four-dimensional subluminal scheme is obtained by averaging over all possible orientations of the three time axes of each observer. An insight into the effect of working with three time co-ordinates is gained by considering an example which is the subluminal six-dimensional equivalent of the four-dimensional case of two frames which are in standard configuration