We construct a toy model of spacetime deformation-induced inertia effects, in which we prescribe to each and every particle individually a new fundamental constituent of hypothetical 2D, so-calledmaster space(MS), subject to certain rules. The MS, embedded in the background 4D-spacetime, is an indispensable companion to the particle of interest, without relation to every other particle. The MS is not measurable directly, but we argue that a deformation (distortion of local internal properties) of MS is the origin of inertia effects that can be observed by us. With this perspective in sight, we construct the alternativerelativistic theory of inertia. We go beyond the hypothesis of locality with special emphasis on distortion of MS, which allows to improve essentially the standard metric and other relevant geometrical structures referred to a noninertial frame in Minkowski spacetime for an arbitrary velocities and characteristic acceleration lengths. Despite the totally different and independent physical sources of gravitation and inertia, this approach furnishes justification for the introduction of theweakprinciple of equivalence (WPE), that is, the universality of free fall. Consequently, we relate the inertia effects to the more general post-Riemannian geometry.
Free fall in KvN mechanics and Einstein’s principle of equivalence
