  After a review of the existing theory of non-inertial frames and mathematical
observers in Minkowski space-time we give the explicit expression of a family
of such frames obtained from the inertial ones by means of point-dependent
Lorentz transformations as suggested by the locality principle. These
non-inertial frames have non-Euclidean 3-spaces and contain the differentially
rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to
replace mathematical accelerated observers with dynamical ones (their
world-lines belong to interacting particles in an isolated system) and of how
to define Unruh-DeWitt detectors without using mathematical Rindler uniformly
accelerated observers. Also some comments are done on the transition from
relativistic classical mechanics to relativistic quantum mechanics in
non-inertial frames.
