2 0 D O C . 2 5 A P R I L 1 9 1 9
nothing higher than 1st derivatives of
.)[3]
The reasons are set forth precisely in
the proof of the paper I sent
you.[4]
Now it seems to me, though, that another un-
solved puzzle is hiding behind energy conservation, because in the current solution
there is nothing as comparably compelling as the case without gravitation.
Furthermore, I would like to relay to you an argument that allows the spherical
option to appear preferable to the elliptic
one.[5]
In the spherical world every closed
line can be contracted continuously into one point, but not in the elliptic one; i.e.,
only the spherical, not the elliptic, world is simply connected. (Because a line that
in the spherical world links one point with its antipodal point is, in the respective
elliptic one, a noncontractable closed line.)
In addition to the Euclidean line element, there are, of course, also finite spaces
of arbitrary size that can be obtained from infinity by postulating a threefold peri-
odicity, if it is further postulated that periodically lying points are identical. These
possibilities, which incidentally do not apply in the case of general relativity, suffer
from the characteristic that these spaces are connected in multiple ways.
With cordial greetings, yours very truly,
A. Einstein.
25. From Leonhard Grebe[1]
Bonn, 17 April 1919
Highly esteemed Professor,
Pursuant to your request during our discussion in Berlin, I take the liberty today
of presenting you with the following:
Together with my colleague Dr. A.
Bachem,[2]
I have been working, since my
return from the battlefield, on the redshift of spectrum lines in the solar spectrum
predicted in your investigations and, specifically, as did Schwarzschild, on the
soc[alled] cyanogen
band.[3]
In the process, as yet unexplained displacement
anomalies have emerged for the various lines of this band. While some lines exhibit
the effect to sufficient approximation, others yield deviations far above the obser-
vational error, which are all the more remarkable since they belong to lines that,
owing to their association within a single series of band lines, would lead one to
expect the same behavior. The assumption suggests itself that these deviations are
elicited by closely lying attendant lines or by asymmetries in the intensity distribu-
tion of the lines, and that Schwarzschild’s result was substantially affected by the
inclusion of these lines to obtain a
mean.[4]
gμν
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