  A review is given of the formulation of relativistic atomic theory, in which
there is an explicit realization of the Poincare' generators, both in the
inertial and in the non-inertial rest-frame instant form of dynamics in
Minkowski space-time. This implies the need to solve the problem of the
relativistic center of mass of an isolated system and to describe the
transitions from different conventions for clock synchronization, namely for
the identifications of instantaneous 3-spaces, as gauge transformations. These
problems, stemming from the Lorentz signature of space-time, are a source of
non-locality, which induces a spatial non-separability in relativistic quantum
mechanics, with implications for relativistic entanglement. Then the classical
system of charged particles plus the electro-magnetic field is studied in the
framework of ADM canonical tetrad gravity in asymptotically Minkowskian
space-times admitting the ADM Poincare' group at spatial infinity, which allows
to get the general relativistic extension of the non-inertial rest frames of
special relativity. The use of the York canonical basis allows to disentangle
the tidal degrees of freedom of the gravitational field from the inertial ones.
The York time is the inertial gauge variable describing the general
relativistic remnant of the gauge freedom in clock synchronization. However now
each solution of Einstein's equations dynamically determines a preferred notion
of instantaneous 3-spaces. The linearization of this canonical formulation in
the weak field approximation will allow to find Hamiltonian Post-Minkowskian
gravitational waves with an asymptotic background and without Post-Newtonian
expansion in non-harmonic 3-orthogonal gauges.
