A Physicist Viewpoint on Space - time , Simultaneity , and Accelerated

The Newtonian notions of 3-space and time have been replaced by Minkowski space-time, a pseudo-Rimennian 4-manifold with Lorentz signature, because of the overcoming of the absolute notion of simultaneity. Even if the chrono-geometrical structure of Minkowski's space-time is xed and non-dynamical, the establishment of a metrology (rods and clocks) is necessarily observer-dependent and requires the choice of a convention about the synchronization of distant clocks. Lacking this, the notions of 3-space, one-way velocity of light and spatial distance between space-like-separated events are not de nable. Therefore while the world is 4-dimensional, the notion of 3-space is observer-dependent. Any inertial observer with Cartesian 4-coordinates, using light signals and Einstein's convention de nes the spacelike hyper-planes of constant time as simultaneity 3-spaces. As shown by the lasting debate about the conventionalism of simultaneity, other possibilities are open for both inertial and non-inertial observers. These unorthodox choices lead to di erent local description of phenomena (the 1+3 point of view). Since actual observers are always accelerated, a big e ort has been undertaken to the e ect of building associated 4-coordinate systems that generalize Fermi coordinates. Yet, all of them failed in de ning a good notion of simultaneity. This fact is exemplarily shown by the lack of consensus about the de nition of a satisfactory relativistic rotating 4-coordinate system with a well de ned notion of 3-space (see the unending debate about the rotating disk and the Sagnac e ect). A possible way out [1] from these problems is the 3+1 point of view together with M ller's conditions for the admissibility of the notion of simultaneity and thereby of 3space. Accordingly, in order to describe relativistic system in 3-space, one has to make a 3+1 splitting of Minkowski space-time by means of an arbitrary, admissible, foliation whose leaves are just space-like 3-spaces. Then, each 3-space is both a simultaneity surface (i.e., a convention for the synchronization of clocks) and a Cauchy surface for the equations of motion on which the initial data for the predictable evolution must be given. This approach allows to associate admissible notions of simultaneity to arbitrary accelerated observer. A particular development has been the formulation [2] of isolated relativistic systems (particles, strings, elds) as "parametrized Minkowski theories". In this approach all the admissible foliations and the associated notions of simultaneity are "gauge equivalent" because of a special type of general covariance. Since the high precision of the new atomic clocks (10 15 10 ) allow to test relativistic e ects till the order 1=c, this approach turns out to be relevant [1] for space navigation (recall the Global Positioning System). Since in general relativity the chrono-geometrical structure of space-time becomes dynamical, a new problem arises from the so-called Hole Argument. Actually, as shown in