  All existing 4-coordinate systems centered on the world-line of an
accelerated observer are only locally defined like it happens for Fermi
coordinates both in special and general relativity. As a consequence, it is not
known how non-inertial observers can build {\it equal-time surfaces} which a)
correspond to a conventional observer-dependent definition of synchronization
of distant clocks; b) are good Cauchy surfaces for Maxwell equations. Another
type of coordinate singularities are those connected to the relativistic
rotating coordinate systems (the rotating disk).We show that the use of
Hamiltonian methods based on 3+1 splittings of space-time allows to define as
many observer-dependent globally defined radar 4-coordinate systems as nice
foliations of space-time with space-like hyper-surfaces admissible according to
M$\o$ller (for instance only differentially rotating relativistic coordinate
system are allowed). All these conventional notions of an {\it instantaneous
3-space} for an arbitrary observer can be empirically defined by introducing
generalizations of Einstein ${1\over 2}$ convention for clock synchronization
in inertial frames. Each admissible 3+1 splitting corresponds to a non-rigid
non-inertial frame centered on the observer. When there is a Lagrangian
description of an isolated relativistic system, its reformulation as a
parametrized Minkowski theory allows to show that all the admissible
synchronization conventions are {\it gauge equivalent}, as it also happens in
canonical metric and tetrad gravity, where, however, the chrono-geometrical
structure of space-time is dynamically determined.
