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Abstract
To investigate the origin and nature of inertia, we introduce a new concept of hypothetical
2D, so-called, "master-space" (MS), subject to certain rules. The MS, embedded in
the background 4D-spacetime, is an indispensable individual companion to the particle
of interest, without relation to every other particle. We argue that a deformation/(distortion
of local internal properties) of MS is the origin of inertia. With this perspective
in sight, we construct the alternative relativistic theory of inertia (RTI), which
allows to compute the relativistic inertial force acting on an arbitrary point-like
observer due to its "absolute acceleration". We go beyond the hypothesis of locality
with an emphasis on distortion of MS, which allows to improve essentially the standard
metric and other relevant geometrical structures related to the noninertial reference
frame of an arbitrary accelerated observer. We compute the inertial force exerted
on the photon in a gravitating system in the semi-Riemann space. Despite the totally
different and independent physical sources of gravitation and inertia, this approach
furnishes justification for the introduction of the principle of equivalence. Consequently,
we relate the inertia effects to the more general post-Riemannian geometry. We derive
a general expression of the relativistic inertial force exerted on the extended spinning
body moving in the Rieman-Cartan space.