Sidelights on Relativity · Albert Einstein
GEOMETRY AND EXPERIENCE
We must carefully bear in mind that our statement as to the growth of the disc-shadows, as they move away from _S_ towards infinity, has in itself no objective meaning, as long as we are unable to employ Euclidean rigid bodies which can be moved about on the plane _E_ for the purpose of comparing the size of the disc-shadows. In respect of the laws of disposition of the shadows _L'_, the point _S_ has no special privileges on the plane any more than on the spherical surface. The representation given above of spherical geometry on the plane is important for us, because it readily allows itself to be transferred to the three-dimensional case. Let us imagine a point _S_ of our space, and a great number of small spheres, _L'_, which can all be brought to coincide with one another. But these spheres are not to be rigid in the sense of Euclidean geometry; their radius is to increase (in the sense of Euclidean geometry) when they are moved away from _S_ towards infinity, and this increase is to take place in exact accordance with the same law as applies to the increase of the radii of the disc-shadows _L'_ on the plane.
Ideas discussed in this chapter
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