Fig. XI
Let us first consider the case of classical science. And here it is important to realise that our graph is nothing but a description: it merely describes graphically the relationships of duration, distance and motion which we wish to represent. Hence it is for us to discover through the medium of experiment what these relationships are going to be. Only after this preliminary work has been done can we represent these relationships graphically. Now classical science, both as the result of crude experience and, later, of more refined measurements, held to the view that duration and distance were absolutes, in that their magnitudes would never be modified by our circumstances of motion. Accordingly, regardless of whether we were at rest on the embankment or in motion, the duration separating two events or the distance between two fixed points on the embankment was assumed to remain the same. Interpreted graphically, this meant that the space and time axes would never have to be changed in our graph, regardless of the motion of the embankment observer whose measurements we were seeking to represent.
Consider two point-events, such as
and
([Fig. XI]). As referred to the embankment, these two point-events represent two instantaneous events occurring on the embankment at a definite distance apart in space and in time. Suppose, now an observer leaves the origin at a time zero and moves along the embankment to the right. His world-line will be given by some such line as
. Since, regardless of his motion, these two events