The Space and Time Continuum Model

This study presents the Space and Time Continuum Model, a local formulation of relativistic kinematics. The model results from the limiting condition of a finite local measurement process of space and time in homogeneous and isotropic media and quantifies into an initial value problem incorporating four space and time advection equations. The advection equations' general non-linear solutions, obtained by the method of characteristics, represent space and time flow as invariant-profile space and time waves. As spatial and temporal transformations, the general solutions shape into linear ones that reflect the current formulation of space and time measurement, distinguishing between stationary and moving reference frames. That distinction eliminates itself with additional consideration of the measurement process, proving that inertial reference frames, as aggregates of synchronized clocks where the law of inertia is valid,  are equivalent in measuring space and time through a set of extended Poincare transformations. Furthermore, the derivation of the characteristic curves of those transformations completes their interpretation as pairs of space and time waves with constant amplitude and opposite constant phases along those curves. Thus, the Space and Time Continuum Model interprets current relativistic kinematics and broadens the theory by deriving the extended Poincare transformations.