Page:Eddington A. Space Time and Gravitation. 1920.djvu/142

is in any case scarcely trustworthy to 5″ owing to the inevitable errors of observation, the improvement is not very important. The main conclusion is that Einstein's theory brings Mercury into line, without upsetting the existing good accordance of all the other planets.

We have tested Einstein's law of gravitation for fast movement (light) and for moderately slow movement (Mercury). For very slow movement it agrees with Newton's law, and the general accordance of the latter with observation can be transferred to Einstein's law. These tests appear to be sufficient to establish the law firmly. We can express it in this way.

Every particle or light-pulse moves so that the quantity $s$ measured along its track between two points has the maximum possible value, where $ds^{2}=-(1-2m/r)^{-1}dr^{2}-r^{2}d\theta ^{2}+(1-2m/r)\,dt^{2}$. And the accuracy of the experimental test is sufficient to verify the coefficients as far as terms of order $m/r$ in the coefficient of $dr^{2}$, and as far as terms of order $m^{2}/r^{2}$ in the coefficient of $dt^{2}$^[1].

In this form the law appears to be firmly based on experiment, and the revision or even the complete abandonment of the general ideas of Einstein's theory would scarcely affect it.

These experimental proofs, that space in the gravitational field of the sun is non-Euclidean or curved, have appeared puzzling to those unfamiliar with the theory. It is pointed out that the experiments show that physical objects or loci are "warped" in the sun's field; but it is suggested that there is nothing to show that the space in which they exist is warped. The answer is that it does not seem possible to draw any distinction between the warping of physical space and the warping of physical objects which define space. If our purpose were merely to call attention to these phenomena of the gravitational field as curiosities, it would, no doubt, be preferable to avoid using words which are liable to be misconstrued. But if we wish to arrive at an understanding of the conditions of the gravitational field, we cannot throw over the vocabulary appropriate for that purpose, merely because there may be some who insist on investing the words with a metaphysical meaning which is clearly inappropriate to the discussion.

1. Appendix, Note 10.