1 4 6 D O C U M E N T 2 1 3 A U G U S T 1 9 2 1
As we already know, no invariant that can be set constant can be formed from
Hiklm and
iklm
. Should I now examine a Weyl invariant of higher order? If I have
understood correctly, eq. (1) is I = const, where I is a Weyl invariant and
I, which plays a role entirely different from field equations.[7] Because
field equations should only depend on the ratios of the gik’s. Whereas eq. (1) is for
the gik’s themselves, of course. For I( gik) is not constant but equal to const. So
perhaps it shouldn’t do any harm if (1) became of higher order, since it does cancel
out in the end.
Then another question as well.
Does it make sense to make the assumption that the manifold is embedded
within a Euclidean one with m 10 dimensions?
I tried m = 5. Then the Riemann tensor can be expressed as a tensor of 2nd rank.
The assumption that this tensor of 2nd rank be set equal to the electromagnetic ten-
sor Tik does not lead to the goal.—
Now I would like to ask: Is it interesting to investigate the independence of the
invariants that are the quadratic of the 2nd derivatives in your theory?
Another question. Do you consider the problem of finding the proof that a closed
geodetic time-line is impossible very difficult?[8] This problem is very attractive to
me.—
I now have some courage to defend myself. You feared that I would be unsuit-
able for a teaching occupation.[9] I must say: Eastern people understand me very
well.[10] I shall very certainly have success there. It is true, though, that I am a little
rusty from a lack of interaction. But that will soon pass. Teaching is my dearest
aspiration. After a short time at work I hope to be able to familiarize myself even
with the Germans. More assuredly so in Austria, even better in Prague.
Have you spoken with Prof. Weizmann about a position for me in Palestine?[11]
I would like to come to Berlin soon, if I can continue to work for you. [12]
I very much beg your pardon for the bother.
Please accept my most cordial regards, yours,
Jakob Grommer.
Cordial greetings to your wife and daughter Ilse, JG
Please do reply soon.
I had occasion to observe from another person here that in case of bad luck one
is also tormented by the prejudices of others. Also J. G.
g
I gik
1
-- - =
1
-- -