Page:Eddington A. Space Time and Gravitation. 1920.djvu/70

54 corresponding to the difference between the square-partitions of observer $$S$$ and the diamond-shaped partitions of observer $$S_1$$. We might say that $$S_1$$ transplants the space-time world unchanged from Fig. 5 to Fig. 6, and then distorts it until the diamonds shown become squares; or we might equally well start with this distorted space-time, partitioned by $$S_1$$ into squares, and then $$S$$'s partitions would be represented by diamonds. It cannot be said that either observer's space-time is distorted absolutely, but one is distorted relatively to the other. It is the relation of order which is intrinsic in nature, and is the same both for the squares and diamonds; shape is put into nature by the observer when he has chosen his partitions.

We can now deduce the FitzGerald contraction. Consider a rod of unit length at rest relatively to the observer $$S$$. The two extremities are at rest in his space, and consequently remain on the same space-partitions; hence their tracks in four dimensions $$PP^\prime$$, $$QQ^\prime$$ (Fig. 7) are entirely in the time-direction. The real rod in nature is the four-dimensional object shown in section as $$P^\prime PQQ^\prime$$. Overlay the same figure with $$S_1$$'s space and time partitions, shown by the dotted lines. Taking a section at any one "time," the instantaneous rod is $$P_1 Q_1$$, viz. the section of $$P^\prime PQQ^\prime$$ by $$S_1$$'s time-line. Although on paper $$P_1 Q_1$$ is actually longer than $$PQ$$, it is seen that it is a little shorter than one of $$S_1$$'s space-partitions; and accordingly $$S_1$$ judges that it is less