Page:Eddington A. Space Time and Gravitation. 1920.djvu/148

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 $ds$—contrary to our assumption above. Then the prediction of the shift of the lines in the solar spectrum is invalidated. Now it is very doubtful if an atom can detect the curving of the region it occupies, because curvature is only apparent when an extended region is considered; still an atom has some extension, and it is not impossible that its equations of motion involve the quantities $B_{\mu \nu \sigma }^{\rho }$ which distinguish gravitational from flat space-time. An apparently insuperable objection to this explanation is that the effect of curvature on the period would almost certainly be represented by terms of the form $m^{2}/r^{2}$, whereas to account for a negative result for the shift of the spectral lines terms of much greater order of magnitude $m/r$ are needed.

The second possibility depends on the question whether it is possible for an atom at rest on the sun to be precisely similar to one on the earth. If an atom fell from the earth to the sun it would acquire a velocity of 610 km. per sec., and could only be brought to rest by a systematic hammering by other atoms. May not this have made a permanent alteration in its time-keeping properties? 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.

What are the two events which mark the beginning and end of an atomic vibration? This question suggests a third possibility. 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. 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