Motion and Special Relativity in Complex Spaces

A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M4 model for special relativity (SR) to complex C4 space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C4 one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M4 real space-time can be recovered. This means all the SR theory is preserved in the real subspace M4 of the space-time C4 while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C4 model to the C3 “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C3 alone. On the other hand, the complex time defined within the C3 theory is interpreted and modeled by the single separate C1 complex plane. The possibility for application of the C3 model to quantum mechanics is suggested. As such, the model C3 seems to have unifying abilities for application to different physical theories.