Page:Eddington A. Space Time and Gravitation. 1920.djvu/145

VIII] The first and second pulse have to travel the same distance ($$r$$), and they travel with the same velocity ($$dr/dt$$); for the velocity of light in the mesh-system used is $$1-2m/r$$, and though this velocity depends on $$r$$, it does not depend on $$t$$. Hence the difference $$dt$$ at one end of the waves is the same as that at the other end.

Thus in the laboratory the light from a solar source should be of greater period and greater wave-length (i.e. redder) than that from a corresponding terrestrial source. Taking blue light of wave-length 4000 Å, the solar lines should be displaced 4000 x .00000212, or 0.008 Å towards the red end of the spectrum.

The properties of a gravitational field of force are similar to those of a centrifugal field of force; and it may be of interest to see how a corresponding shift of the spectral lines occurs for an atom in a field of centrifugal force. Suppose that, as we rotate with the earth, we observe a very remote atom momentarily at rest relative to our rotating axes. The case is just similar to that of the solar atom; both are at rest relative to the respective mesh-systems; the solar atom is in a field of gravitational force, and the other is in a field of centrifugal force. The direction of the force is in both cases the same—from the earth towards the atom observed. Hence the atom in the centrifugal field ought also to vibrate more slowly, and show a displacement to the red in its spectral lines. It does, if the theory hitherto given is right. We can abolish the centrifugal force by choosing non-rotating axes. But the distant atom was at rest relative to the rotating axes, that is to say, it was whizzing round with them. Thus from the ordinary standpoint the atom has a large velocity relative to the observer, and, in accordance with Chapter, its vibrations slow down just as the aviator's watch did. The shift of spectral lines due to a field of centrifugal force is only another aspect of a phenomenon already discussed.

The expected shift of the spectral lines on the sun, compared with the corresponding terrestrial lines, has been looked for; but it has not been found.

In estimating the importance of this observational result in regard to the relativity theory, we must distinguish between a failure of the test and a definite conclusion that the lines are E.S.