Einstein's physical geometry at play: inertial motion, the boostability assumption, the Lorentz transformations, and the so-called conventionality of the one-way speed of light

Abstract: In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a non-conventional view on Euclidean geometry (as the geometry associated to inertial motion and inertial reference frames) and on the uniform time. Also, by taking into account the implications of the view of geometry as a physical geometry, it is presented a critical reassessment of the so-called boostability assumption (implicit according to Einstein in the formulation of the theory) and also of 'alternative' derivations of the Lorentz transformations that do not take into account the so-called 'light postulate'. Finally it is addressed the issue of the eventual conventionality of the one-way speed of light or, what is the same, the conventionality of simultaneity (within the same inertial reference frame). It turns out that it is possible to see the (possible) conventionality of distant simultaneity as a case of conventionality of geometry (in Einstein's reinterpretation of Poincar\'e's views). By taking into account synchronization procedures that do not make reference to light propagation (which is necessary in the derivation of the Lorentz transformations without the 'light postulate'), it can be shown that the synchronization of distant clocks does not need any conventional element. This implies that the whole of chronogeometry (and because of this the physical part of the theory) does not have any conventional element in it, and it is a physical chronogeometry.