Synchronization and Inertial Frames

In classical mechanics a procedure for simultaneous synchronization in all inertial frames is consistent with the Galilean transformation. However, if one attempts to achieve such synchronization utilizing light signals , then he will be facing on one hand a break down of absolute simultaneity, and on the other hand, a self-contradictory transformation that has Lorentz transformation, or the confinement of Lorentz transformation to the velocity of light, as the only possible ways that resolve the contradiction. The current work constitutes a smooth transition from traditional to relativistic vision of mechanics, and therefore is quite appealing from pedagogical point of view. 1. Introduction Time in Newtonian mechanics is considered as an absolute entity, so that one can choose an instant t 0 which can be taken as the initial time in all inertial frames, and such that when an event occurs at an instant t in one inertial frame then it occurs also at the same instant t in all inertial frames. The inquiry of how, in principle, can one synchronize the clocks in all inertial frames receives a number of plausible answers. One possible hypothetical procedure is as follows: it is sufficient to synchronize clocks in one inertial frame, say S, with a master clock at some point in S, say the origin O, using a stream of particles emitted radially from O with the same velocity C, so that on first receiving the stream, an observer at a point P sets his clock on t = t 0 +