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gravitational field in which it is situated.
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Relativity: The Special and General Theory
The frequency of an atom situated on the surface of a heavenly body will be somewhat less than
the frequency of an atom of the same element which is situated in free space (or on the surface of
a smaller celestial body).
Now � = - K (M/r), where K is Newton's constant of gravitation, and M is the mass of the heavenly
body. Thus a displacement towards the red ought to take place for spectral lines produced at the
surface of stars as compared with the spectral lines of the same element produced at the surface of
the earth, the amount of this displacement being
For the sun, the displacement towards the red predicted by theory amounts to about two millionths
of the wave-length. A trustworthy calculation is not possible in the case of the stars, because in
general neither the mass M nor the radius r are known.
It is an open question whether or not this effect exists, and at the present time (1920) astronomers
are working with great zeal towards the solution. Owing to the smallness of the effect in the case of
the sun, it is difficult to form an opinion as to its existence. Whereas Grebe and Bachem (Bonn), as
a result of their own measurements and those of Evershed and Schwarzschild on the cyanogen
bands, have placed the existence of the effect almost beyond doubt, while other investigators,
particularly St. John, have been led to the opposite opinion in consequence of their measurements.
Mean displacements of lines towards the less refrangible end of the spectrum are certainly
revealed by statistical investigations of the fixed stars ; but up to the present the examination of the
available data does not allow of any definite decision being arrived at, as to whether or not these
displacements are to be referred in reality to the effect of gravitation. The results of observation
have been collected together, and discussed in detail from the standpoint of the question which has
been engaging our attention here, in a paper by E. Freundlich entitled "Zur Pr�fung der
allgemeinen Relativit�ts-Theorie" (Die Naturwissenschaften, 1919, No. 35, p. 520: Julius Springer,
Berlin).
At all events, a definite decision will be reached during the next few years. If the displacement of
spectral lines towards the red by the gravitational potential does not exist, then the general theory
of relativity will be untenable. On the other hand, if the cause of the displacement of spectral lines
be definitely traced to the gravitational potential, then the study of this displacement will furnish us
with important information as to the mass of the heavenly bodies. [A]
Next: Appendix IV: The Structure of Space According to the General Theory of Relativity
Footnotes
1)
Especially since the next planet Venus has an orbit that is almost an exact circle, which makes it
more difficult to locate the perihelion with precision.
[A]
The displacentent of spectral lines towards the red end of the spectrum was definitely
established by Adams in 1924, by observations on the dense companion of Sirius, for which the
effect is about thirty times greater than for the Sun. R.W.L.  translator
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Relativity: The Special and General Theory
Relativity: The Special and General Theory
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Relativity: The Special and General Theory
Albert Einstein: Relativity
Appendix
Appendix IV
The Structure of Space According to the General Theory of
Relativity
(Supplementary to Section 32)
Since the publication of the first edition of this little book, our knowledge about the structure of
space in the large (" cosmological problem ") has had an important development, which ought to be
mentioned even in a popular presentation of the subject.
My original considerations on the subject were based on two hypotheses:
(1) There exists an average density of matter in the whole of space which is everywhere the same
and different from zero.
(2) The magnitude (" radius ") of space is independent of time.
Both these hypotheses proved to be consistent, according to the general theory of relativity, but
only after a hypothetical term was added to the field equations, a term which was not required by
the theory as such nor did it seem natural from a theoretical point of view (" cosmological term of
the field equations ").
Hypothesis (2) appeared unavoidable to me at the time, since I thought that one would get into
bottomless speculations if one departed from it.
However, already in the 'twenties, the Russian mathematician Friedman showed that a different
hypothesis was natural from a purely theoretical point of view. He realized that it was possible to
preserve hypothesis (1) without introducing the less natural cosmological term into the field
equations of gravitation, if one was ready to drop hypothesis (2). Namely, the original field
equations admit a solution in which the " world radius " depends on time (expanding space). In that [ Pobierz całość w formacie PDF ]