Classical and quantum inertia: A matter of principles

A simple, general discussion of the problem of inertia is provided both in classical physics and in the quantum world. After briefly reviewing the classical principles of equivalence (weak (WEP), Einstein (EEP), strong (SEP)), I pass to a presentation of several equivalence statements in nonrelativistic quantum mechanics and for quantum field vacuum states. It is suggested that a reasonable type of preferred quantum field vacua may be considered: those possessing stationary spectra of their vacuum fluctuations with respect to accelerated classical trajectories