I N T R O D U C T I O N T O V O L U M E 1 2 x l i x
Already in 1919, Einstein had published a note in which he considered the ques-
tion: “Do Gravitational Fields Play an Essential Role in the Structure of the Ele-
mentary Particles?” (Einstein 1919a [Vol. 7, Doc. 17]). He there proposed a
modified gravitational field equation in order to account for the electron’s stability,
following up on similar ideas about internal stresses of the electron put forward by
Henri Poincaré. Occasional remarks in his correspondence suggest that Einstein
had continued pondering these questions, but in 1921 he explicitly followed up on
these issues by reconsidering both Weyl’s theory and Kaluza’s idea.
Early in 1921, Einstein had a “fortunate thought” (Doc. 71) concerning Weyl’s
theory. As he would argue in a note presented to the Academy on 3 March (Einstein
1921e [Vol. 7, Doc. 54]), Weyl’s theory was based on two fundamental ideas. Ac-
cording to the first, the ratio of metric components is a more fundamental quantity
than their absolute values, and, in fact, much of the theory’s content is already con-
tained in its conformal structure, given by the light cones , rather than by
its full metric structure, given by the line element . Weyl’s sec-
ond idea then was to generalize Riemannian geometry by postulating the existence
of transportable measuring rods, while denying that their length was independent
of the path of transport. This was achieved, in Weyl’s theory, by means of the new
concept of a “length connection” whose coefficients were interpreted as ex-
pressions of the electromagnetic potential.
Einstein now proposed to keep Weyl’s first idea, but do without the second. He
asked the Viennese mathematician Wilhelm Wirtinger, whom he had met in Vienna
earlier in the year, whether one could find a generalization of the geodesic equation
that would only depend on the conformal structure. Wirtinger replied in the affir-
mative, and showed how an equation of motion could be based on a line element
constructed from the Weyl scalar (Docs. 49, 58, 79). An attractive feature of such
a theory was that, unlike in Weyl’s earlier theory of unified gravity and electromag-
netism, there would be only electromagnetic field strengths and no electromagnetic
potentials (Docs. 57,
89).[53]
Initially, Einstein was “very curious whether these
hypotheses will hold up” (Doc. 57), and confident that one could decide readily
whether the theory would be physically correct (Docs. 58, 71). But already on 9
March, he wrote to Sommerfeld that he doubted “whether this business is physical-
ly worth anything,” adding: “The Lord does as He pleases and doesn’t follow or-
ders” (Doc. 89). A few weeks later, he lamented a general lack of “physical clues”
which Einstein, at that time, believed to be the only possible starting point for “real
progress” (Doc. 163).
Einstein also reconsidered Kaluza’s five-dimensional unified field theory. As
shown by Jakob Grommer (Doc. 283), the objective was to examine whether this
ds2 0=
ds2 g dx dx =