Arthur Eddington

“ It seems reasonable to suppose that a vibrating atom is an ideal type of clock. The beginning and end of a single vibration constitute two events, and the interval between two events is an absolute quantity independent of any mesh-system. ”

“ Hence it is not clear that there is any absolute interval corresponding to the vibration of an atom; an absolute interval only exists between two events absolutely defined.
It is unlikely that any of these three possibilities can negative the expected shift of the spectral lines. The uncertainties introduced by them are, so far as we can judge, of a much smaller order of magnitude. But it will be realised that this third test of Einstein's theory involves rather more complicated considerations than the two simple tests with light-waves and the moving planet. ”

“ A clock cannot pay any heed to the mesh-system used; but it may be affected by the kind of space-time around it [5] . The terrestrial atom is in a field of gravitation so weak that the space-time may be considered practically flat; but the space-time round the solar atom is not flat. It may happen that the two atoms actually detect this absolute difference in the world around them and do not vibrate with the same interval —contrary to our assumption above. Then the prediction of the shift of the lines in the solar spectrum is invalidated. ”

“ The glare from the light of the planet ruins any chance of success.
Most astronomers, who look into the subject, are entrapped sooner or later by a fallacy in connection with double stars. It is thought that when one component passes behind the other it will appear displaced from its true position, like a star passing behind the sun; if the size of the occulting star is comparable with that of the sun, the displacement should be of the same order, 1′′.7. This would cause a very conspicuous irregularity in the apparent orbit of a double star. ”

“ Since certain stars are perhaps ten times more massive than the sun, without the radius being unduly increased, they should show a greater shift of the spectral lines and might be more favourable for the third crucial test. Unfortunately the predicted shift is indistinguishable from that caused by a velocity of the star in the line-of-sight on Doppler's principle. Thus the expected shift on the sun is equivalent to that caused by a receding velocity of 0.634 kilometres per second. In the case of the sun we know by other evidence exactly what the line-of-sight velocity should be ”

“ 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. ”

“ I do not think that any "simple explanation" of this property of the inverse-square law has been given; and it seems fair to remind those, who complain of the difficulty of understanding Einstein's prediction of the advance of the perihelion, that the real trouble is that they have not yet succeeded in making clear to the uninitiated this recondite result of the Newtonian theory. The slight modifications introduced by Einstein's law of gravitation upset this fine adjustment, so that the oscillation between the extremes occupies slightly more than a revolution. ”

“ It is true that every atom is continually undergoing collisions, but it is just possible that the average solar atom has a different period from the average terrestrial atom owing to this systematic difference in its history. ”

“ If they are two absolute events, like the explosions of two detonators, then the interval between them will be a definite quantity, and our argument applies. But if, for example, an atomic vibration is determined by the revolution of an electron around a nucleus, it is not marked by any definite events. A revolution means a return to the same position as before; but we cannot define what is the same position as before without reference to some mesh-system. ”

“ The exact prediction of Einstein's law is that in one revolution of the planet the orbit will advance through a fraction of a revolution equal to , where is the speed of the planet and the speed of light. The earth has 1/10,000 of the speed of light ”

“ These theoretical uncertainties are apart altogether from the great practical difficulties of the test, including the exact allowance for the unfamiliar circumstances of an absorbing atom in the sun's atmosphere.
Outside the three leading tests, there appears to be little chance of checking the theory unless our present methods of measurement are greatly improved. It is not practicable to measure the deflection of light by any body other than the sun. The apparent displacement of a star just grazing the limb of Jupiter should be 0′′.017. ”