Hence we conclude that the space and time directions
and
are no longer absolute; every observer will have to measure time along his world-line and space along a line orthogonal to this world-line.[164] It follows that there exist an indefinite number of time directions given by the world-lines of the various observers, and a correspondingly indefinite number of space directions.
A first consequence of this novelty is that simultaneity can no longer be absolute. For whereas, in the classical graph, all events on the same horizontal or space direction were simultaneous for all observers, we now realise that with this variation in the space directions, or lines of simultaneous occurrence, the absoluteness of simultaneity must vanish. For instance, all the point-events lying on
which are therefore simultaneous with the time zero for the moving observer, appear to be unfolding themselves in succession for the stationary observer.
Also it follows that as, according to relativity, no observer can travel faster than light, all the permissible world-lines of the observers (passing through
