I fondamenti epistemologici della Relatività Generale e la sua «eredità matematica»

Francaviglia, Mauro ; Palese, Marcella

Bollettino della Unione matematica italiana, Série 8, 8A (2005) no. 2, pp. 289-312

Résumé

We investigate some foundational aspects of General Relativity from an epistemological point of view. We stress that speaking of time when or space where dynamics take place does not make any sense. General Relativity, in fact, states the identification between space-time, which is a metric manifold and then a priori non dynamical, and matter, which satisfies some differential equations and then it is dynamical, thus establishing the non separability between space-time and matter. This distinguishes General Relativity from Newton's Mechanics, where space and time are instead absolute and then they can be separated from matter and motion. This implies a loss of physical significance of local coordinates. The intrinsic calculus on manifolds, as well as all approaches of global nature, which are independent from the choice or the change of local coordinates, are then suitable for the description of this theory and they represent the most fundamental mathematical inheritance of General Relativity itself.