Page:Eddington A. Space Time and Gravitation. 1920.djvu/65

III] world in more detail, it is necessary to return to real time, and face the difficulties of a strange geometry.

Consider a particular observer, $$S$$, and represent time according to his reckoning by distance up the page parallel to $$OT$$. One dimension of his space will be represented by horizontal distance parallel to $$OX$$; another will stand out at right angles from the page; and the reader must imagine the third as best he can. Fortunately it will be sufficient for us to consider only the one dimension of space $$OX$$ and deal with the phenomena of "line-land," i.e. we limit ourselves to motion to and fro in one straight line in space.

The two lines $$U^\prime OU$$, $$V^\prime OV$$, at 45&deg; to the axes, represent the tracks of points which progress 1 unit horizontally (in space) for 1 unit vertically (in time); thus they represent points moving with unit velocity. We have chosen the velocity of light as unit velocity; hence $$U^\prime OU$$, $$V^\prime OV$$ will be the tracks of pulses of light in opposite directions along the straight line.

Any event $$P$$ within the sector $$UOV$$ is indubitably after the event $$O$$, whatever system of time-reckoning is adopted. For it would be possible for a material particle to travel from $$O$$ to $$P$$, the necessary velocity being less than that of light; and no E.S.