Author(s)

Jerzy K. Filus

Department of Mathematics and Computer Science, Oakton College, Des Plaines, IL, USA.

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.

Special Relativity, Complex Space and Time Models and Dramatic SR Simplification, Complex Time and Space Separation, Complex Time Interpretation

Filus, J. (2024) Motion and Special Relativity in Complex Spaces. Journal of Applied Mathematics and Physics, 12, 330-361. doi: 10.4236/jamp.2024.121025.