New Formulation of Physics based on a Complex Terrain Model — II: Reconstruction of Special Relativity through Complex Projection —

In this second report of the series, we demonstrate that the fundamental postulates
of Special Relativity—(1) the constancy of the speed of light and (2) Lorentz transforma-
tions—emerge naturally from the projection equation.
Within this framework, the mass MR in the real manifold is proportional to MC sec2 η,
where η denotes the projection angle and MC is the mass defined along the complex geodesic.
The right-hand side implies that, for a massless particle such as the photon, the projection
angle ηp must approach π/2, corresponding to null propagation along the imaginary axis.
This geometric constraint yields the constancy of the speed of light.
Furthermore, we show that the Lorentz transformation matrix arises directly from the
projection angle η, and that length contraction and time dilation follow as natural conse-
quences of the projection structure.