Lorentz's 1895 transformations, Einstein's equivalence principle and the perihelion shift of Mercury

Abstract

As a continuation of previous papers emphasizing the interest of historical issues for the present teaching of mechanics (Kepler's equant model, Newton's derivation of planetary motions, Lorentz's 1895 transformations applied to special relativity), we address the question of the perihelion shift of Mercury, whose explanation was a major success of Einstein in 1915. Thanks to the introduction of a general Lagrangian, we derive an expression for this shift, which can be applied to many historical attempts as well as to modern presentations. This approach, accessible to students interested in special relativity and aware of Lagrangian formalism, allows a critical discussion of the physical ideas which have contributed to the genesis of Einstein's theory of general relativity.