A geometric framework for directly visualizing relativistic effects on space and time in special and general relativity

Abstract In this paper, we first show that it is possible to establish, by rescaling the proper time axis of inertial reference frames in a space-proper time, a new geometric framework for special relativity—equivalent to the standard framework—allowing the construction of kinetic distortion diagrams which directly visualize time dilation and length contraction for inertial motions. We then show that in the presence of a Newtonian gravitational field, the curvature of spacetime given by the Schwarzschild solution can be translated into the new geometric framework by gravitational distortions, allowing the construction of gravitational distortion diagrams to directly represent Newtonian gravitational field effects on space and time. Finally, we discuss the pedagogical value of this approach, particularly through its diagrammatic representations, for teaching relativity to undergraduate students.