Fermi’s coordinates and the Principle of Equivalence

Abstract

A few months before his “Laurea” in Physics at the Scuola Normale Superiore of Pisa in July 1922, Fermi, then 21 years old, submitted to the “Rendiconti of the Accademia dei Lincei” a note entitled “Sopra i fenomeni che avvengono in vicinanza di una linea oraria” (On the phenomena that occur in the neighbourhood of a time line); it was subsequently published in three parts at pages 21, 51 and 103 of volume 31 (1922)(1). This note acquired, and still retains, an extraordinary importance for the physics of gravitation, not only with respect to its foundations, in particular the Principle of Equivalence, but also in many practical applications. It reveals great technical ability in mathematical physics, in particular in the geometric representation of curved hypersurfaces (i.e. the generalization of ordinary curved surfaces to a number of dimensions greater than two; to be precise, the Riemannian manifolds) . Fermi does not treat the physical and epistemological meaning of his work at length, although in the first paragraph he does demonstrate a full comprehension of its essence. In 1922 Einstein’s theory of General Relativity, within whose frame of reference Fermi’s memoir was written, was just becoming known, the subject of controversy and doubt, and experimental tests were lacking. Of course Fermi had thoroughly studied the works by T. Levi-Civita on Riemannian manifolds, which provided the mathematical basis of the theory; and certainly he knew (and quoted) the treatise by Hermann Weyl “Raum, Zeit, Materie” (Space, Time and Matter) published by Springer in 1921, an introduction to the theory of relativity of extraordinary physical and mathematical clarity.