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62
Relativity: The Special and General Theory
light in Section 21; nor in interpreting the empirical law of the equality of inertial and gravitational
mass ; but it has also already explained a result of observation in astronomy, against which
classical mechanics is powerless.
If we confine the application of the theory to the case where the gravitational fields can be regarded
as being weak, and in which all masses move with respect to the coordinate system with velocities
which are small compared with the velocity of light, we then obtain as a first approximation the
Newtonian theory. Thus the latter theory is obtained here without any particular assumption,
whereas Newton had to introduce the hypothesis that the force of attraction between mutually
attracting material points is inversely proportional to the square of the distance between them. If we
increase the accuracy of the calculation, deviations from the theory of Newton make their
appearance, practically all of which must nevertheless escape the test of observation owing to their
smallness.
We must draw attention here to one of these deviations. According to Newton's theory, a planet
moves round the sun in an ellipse, which would permanently maintain its position with respect to
the fixed stars, if we could disregard the motion of the fixed stars themselves and the action of the
other planets under consideration. Thus, if we correct the observed motion of the planets for these
two influences, and if Newton's theory be strictly correct, we ought to obtain for the orbit of the
planet an ellipse, which is fixed with reference to the fixed stars. This deduction, which can be
tested with great accuracy, has been confirmed for all the planets save one, with the precision that
is capable of being obtained by the delicacy of observation attainable at the present time. The sole
exception is Mercury, the planet which lies nearest the sun. Since the time of Leverrier, it has been
known that the ellipse corresponding to the orbit of Mercury, after it has been corrected for the
influences mentioned above, is not stationary with respect to the fixed stars, but that it rotates
exceedingly slowly in the plane of the orbit and in the sense of the orbital motion. The value
obtained for this rotary movement of the orbital ellipse was 43 seconds of arc per century, an
amount ensured to be correct to within a few seconds of arc. This effect can be explained by
means of classical mechanics only on the assumption of hypotheses which have little probability,
and which were devised solely for this purponse.
On the basis of the general theory of relativity, it is found that the ellipse of every planet round the
sun must necessarily rotate in the manner indicated above ; that for all the planets, with the
exception of Mercury, this rotation is too small to be detected with the delicacy of observation
possible at the present time ; but that in the case of Mercury it must amount to 43 seconds of arc
per century, a result which is strictly in agreement with observation.
Apart from this one, it has hitherto been possible to make only two deductions from the theory
which admit of being tested by observation, to wit, the curvature of light rays by the gravitational
field of the sun,¹
)
and a displacement of the spectral lines of light reaching us from large stars, as
compared with the corresponding lines for light produced in an analogous manner terrestrially
(i.e. by the same kind of atom). ²
)
These two deductions from the theory have both been confirmed.
Next: Part III: Considerations on the Universe as a Whole
Footnotes
1
)
First observed by Eddington and others in 1919. (Cf.
Appendix III, pp. 126?129).