8 8 D O C U M E N T 5 9 J U N E 1 9 1 9
führt. Weyl will über seine Gedanken betreffend Gravitation u. Elektrizität spre-
chen.[5]
Mit herzlichen Grüssen Ihr
Hilbert.
AKS. [13 058]. The verso is addressed “Herrn Prof. Einstein Berlin W. 30 Haberlandstr. 5.,” and post-
marked “Göttingen 1 k 9.6.19 7–8N[achmittags].” There is a perforation for a loose-leaf binder at the
head of the document.
[1]David Hilbert (1862–1943) was Professor of Mathematics at the University of Göttingen.
[2]Einstein 1919a (Vol. 7, Doc. 17), in which Einstein proposed modified field equations with a
scalar-free gravitational part as a way to consider purely electromagnetic energy-momentum as matter
part without being forced to introduce nonlinear terms in the electromagnetic energy-momentum ten-
sor. The latter alternative was termed Gustav Mie’s path, and Hilbert 1915 was cited by Einstein in
that context (see Einstein 1919a [Vol. 7, Doc. 17], p. 351).
[3]Eq. (4a) of Einstein 1919a (Vol. 7, Doc. 17) reads
,
where is the electromagnetic field tensor, the current, the
Riemann curvature scalar, and κ a coupling constant. It follows from taking the divergence of the
gravitational field equation advanced in that paper,
,
with electromagnetic stress-energy tensor, , as explained by Einstein in
the following document.
[4]Hilbert regularly spent the time between semesters in Switzerland. The winter semester lasted
until 1 February, the summer semester started on 28 April. By the end of June, Hilbert was actually
considering leaving Göttingen for good and moving to Switzerland (see Doc. 341 and, for further dis-
cussion, Sauer 2000).
[5]Hermann Weyl did not come to Göttingen (see Hermann Weyl to David Hilbert, 12 July 1919,
GyGöU, Cod. Ms. Hilbert 431/7).
59. To David Hilbert
Berlin 11. VI. 19
Verehrter Kollege!
Ich weiss selbst nicht, ob ich mit dieser Notiz das Richtige getroffen habe.[1] Sie
kommt zurürück auf die Hypothese eines kosmischen Druckes, (ähnlich schon von
Poincaré in Betracht gezogen, um das Elektron begreiflich zu machen), der nur bei
mir eliminiert ist.[2] Die Gleichung (4a) ist richtig gebildet. Schreibt man (1a) in
der Form
,
so verschwindet bei Divergenzbildung (im Sinne der allgem. Kov. Theorie) die lin-
ke Seite identisch, das erste Glied der rechten Seite liefert
φσαJα
1
4κ∂xσ
--------------
∂R
- + 0 =
φσα Jα –gφαβ),β ( –g ⁄ = R gikRik =
Rik
1
4
-- -
gikR – –κTik =
Tik
1
4
-- -
gikφαβφαβ φiαφkβ – =
Rik
1
2
--gikR - – κTik
1
4
--gikR - – =