FOR A NEW IMPULSE TO RESEARCH ON SPECIAL RELATIVITY Notes on the mathematical formalism of Special Relativity

Special Relativity has been continually taught and studied, for a long time now, essentially without modifications and without substantial developments. As if this theory were a closed chapter. On the contrary, it is full of stimuli and also problems and critical issues. This work shows the necessity of a strong resumption of the research on Special Relativity, which could be very productive both for General Relativity and for fundamental physics tout court. An analysis is conducted of some essential points of its mathematical formalism and of the physical interpretations derived from it. The common thread of the reasoning is constituted by the concept of proper time in the theory, starting from Einstein and Minkowski, up to the discussion on the 'lenght' of proper time, that means the question of geodesics in the curved space, that is in General Relativity. A family of themes far from being exausted. The conclusion is that we don't have a complete and definitive theory of space-time relations at all and that much remains to be done for a satisfying understanding of space and time.