In two respects this
result is of great importance.
In the first place, it can be compared with the reality. Although a
detailed examination of the question shows that the curvature of light
rays required by the general theory of relativity is only exceedingly
small for the gravitational fields at our disposal in practice, its
estimated magnitude for light rays passing the sun at grazing
incidence is nevertheless 1.7 seconds of arc. This ought to manifest
itself in the following way. As seen from the earth, certain fixed
stars appear to be in the neighbourhood of the sun, and are thus
capable of observation during a total eclipse of the sun. At such
times, these stars ought to appear to be displaced outwards from the
sun by an amount indicated above, as compared with their apparent
position in the sky when the sun is situated at another part of the
heavens. The examination of the correctness or otherwise of this
deduction is a problem of the greatest importance, the early solution
of which is to be expected of astronomers.[2]*
In the second place our result shows that, according to the general
theory of relativity, the law of the constancy of the velocity of
light in vacuo, which constitutes one of the two fundamental
assumptions in the special theory of relativity and to which we have
already frequently referred, cannot claim any unlimited validity.
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