A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 2. Alternative completion of Bressan's work, fit for extension to special relativity

Montanaro, Adriano

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 81 (1987) no. 1, pp. 47-54

Résumé

The work [3] of axiomatization of various classical theories on continuous bodies from the Mach-Painlevè point of view, is completed here in a way which -unlike [4]- is suitable for extension to special relativity. The main reason of this is the fact that gravitation can be excluded in all the theories on continuous bodies considered here. Following [1], the notion of (physical) equivalence among affine inertial frames, and that of (physical isotropy of these frames are introduced; it is shown that the isotropic inertial frames equivalent to a fixed frame of this kind are those linked to this frame by a (proper) Galilean transformation. As in Part 1, the Euclidean physical metric on inertial spaces is consequently determined, without introducing it as a primitive notion. The treatment of Part 2 is referred to thermodynamic theories for continuous bodies and, as a particular case, to purely mechanic theories. In this last case, the primitive concepts are only the purely kinematical ones, presented in [3].