Prior to Einstein, a meter was defined to pertain to all observers. Worded differently, prior to Einstein, a meter was defined to be the same for all observers. But in Einstein?s space transformation, he is proposing that a meter for one observer not correspond with a meter for another observer. Einstein cannot make this proposal without first defining a meter for S and then for S?. In other words, Einstein must redefine meters per each observer, rather than per all observer (like it was defined before him).
To this purpose, Einstein says that increments of space and time (such as a meter or second) and events in space and time can only be defined for an observer by measuring devices. The measuring devices he mentions in his relativity paper of 1905 are "rigid rods" and "synchronized clocks". According to Einstein, the clocks have to be synchronized for an observer in order to be good clocks for that observer. And according to Einstein, the clocks have to be synchronized by light signals. Einstein finds that the clocks can only be synchronized for an observer as long as the rods and clocks are placed at rest to the observer. Therefore, increments of space and time and events in space and time can only be properly defined for an observer by certain measuring devices placed at rest to the observer.