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

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III]
THE WORLD OF FOUR DIMENSIONS
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dimensional world in more detail, it is necessary to return to real time, and face the difficulties of a strange geometry.

Consider a particular observer, , and represent time according to his reckoning by distance up the page parallel to . One dimension of his space will be represented by horizontal distance parallel to ; 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 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 , , at 45° 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 , will be the tracks of pulses of light in opposite directions along the straight line.

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

E.S.
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