Page:Eddington A. Space Time and Gravitation. 1920.djvu/98

82 which specifically refer to a particular mesh-system, although the mesh-system can have nothing to do with the matter. It is worrying not to be able to express the differences of space in a purer form without mixing them up with irrelevant differences of potential. But we have neither the vocabulary nor the imagination for a description of absolute properties as such. All physical knowledge is relative to space and time partitions; and to gain an understanding of the absolute it is necessary to approach it through the relative. The absolute may be defined as a relative which is always the same no matter what it is relative to. Although we think of it as self-existing, we cannot give it a place in our knowledge without setting up some dummy to relate it to. And similarly the absolute differences of space always appear as related to some mesh-system, although the mesh-system is only a dummy and has nothing to do with the problem.

The results for two dimensions can be generalised, and applied to four-dimensional space-time. Distance must be replaced by interval, which it will be remembered, is an absolute quantity, and therefore independent of the mesh-system used. Partitioning space-time by any system of meshes, a mesh being given by the crossing of four channels, we must specify a point in space-time by four coordinate numbers, $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$. By analogy the general formula will be The only difference is that there are now ten $$g$$'s, or potentials, instead of three, to summarise the metrical properties of the mesh-system. It is convenient in specifying special values of the potentials to arrange them in the standard form