Einstein time

In his analysis of simultaneity Einstein restricts himself explicitly to reference frames that are inertial. Then he considers two points in space, A and B where observers, equipped with clocks, identical in all relevant aspects, can determine the time values of events in their immediate neighborhoods. Let now a light signal (or any other electromagnetic signal) travel from point A to point B, leaving A at time $t_{A}$ according to the clock at A (clock A for short). This signal is immediately reflected at B in the direction of A, arriving back there at time ${\bar{t}}_{A}$ .

A common time in inertial frames can now be established by stating that the ‘time’ needed for the light to travel from A to B is equal to the ‘time’ it needs to travel from B to A. According to the Einstein’s synchronization rule clock B is synchronized with clock A, if

The ‘time’ of an event is in his own words: “that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.”

Ruimtetijddiagram — Fig.3.1. Einstein synchronization: time $t$ lies halfway between times $t_{A}$ and ${\bar{t}}_{A}$ .

Because of the homogeneity of space, Einstein synchronization can also be achieved by a single master clock sending out light (electromagnetic) signals, independent of the location of that clock.
Clocks that are at rest in a single inertial frame can (in principle) synchronize each other to any accuracy required.