x l v i i i I N T R O D U C T I O N T O V O L U M E 1 2
conceptually unified way. In previous years, Einstein had been confronted with two
appealing suggestions for a modification of the original framework of general rel-
ativity. The first approach was Hermann Weyl’s “truly infinitesimal” geometry and
the interpretation of the electromagnetic potential in terms of what Weyl called the
“length connection” within his generalized geometric theory. Fascinated by Weyl’s
mathematical ideas, Einstein had soon rejected it as physically untenable on ac-
count of his “measuring rod objection.” Nevertheless, Weyl’s theory was studied as
an attractive generalization of Einstein’s general theory of relativity, especially
when Weyl included discussions of these ideas in the third and fourth editions of
his highly acclaimed and widely studied textbook SpaceTimeMatter (Weyl 1919,
1921a). In correspondence, Einstein singled out two further theories that were
based on Weyl’s generalized geometry, one by Arthur Stanley Eddington, and an-
other by Rudolf Bach (Docs. 163, 230).
The second approach aimed at a unification of the gravitational and electromag-
netic forces had been Theodor
Kaluza’s.[52]
It proposed using a metric of a five-
dimensional spacetime that contained the electromagnetic potential in its -
components (the , , played their familiar role from relativity).
Kaluza showed that this theory’s affine connection can be interpreted as containing
the electromagnetic field, and that for a linearized metric, the Ricci tensor would
yield the linearized field equations for gravity along with the Maxwell equations.
Einstein had learned about Kaluza’s theory through a manuscript that Kaluza had
sent him in 1919. As with Weyl’s approach, he was initially fascinated and pro-
posed to submit an article by Kaluza for publication in the proceedings of the Prus-
sian Academy (Vol. 9, Doc. 26). Yet, here as well, Einstein would soon come across
a fundamental objection. Kaluza’s framework implied the existence of a -com-
ponent whose interpretation was unclear. But one of the consequences of Kaluza’s
theory is that the -component constitutes the leading term in the equation of
motion of particles carrying an elementary charge. This implies an influence great-
er by many orders of magnitude on the motion of the electron than the empirically
observed motion would allow for. Einstein considered the objection sufficiently se-
rious to withdraw his offer to communicate the paper, and Kaluza ended up not
publishing the work (Vol. 9, Docs. 40 and 48).
Einstein and others hoped to “throw light” on the microscopic, “molecular
realm” as well (Doc. 57). One of the main concerns was to overcome the “dualism
of field and matter.” When assessing the structure of the field equations in the gen-
eral theory of relativity, Einstein held that the occurrence of the stress-energy tensor
was just a phenomenological “stopgap,” a consequence of overlooking the true mo-
lecular nature of matter (Doc. 318).
g5
g 1 4 =
g55
g55