8 0 D O C . 1 0 R E V I E W O F S PA C E – T I M E – M AT T E R
Published in Die Naturwissenschaften 6 (1918): 373. Published 21 June 1918.
Weyl 1918b .
Similar praise can be found in Einstein to Hermann Weyl, 8 March 1918 and 3 July 1918 (Vol.
8, Docs. 476 and 579). The first edition of Weyl’s book was almost sold out by November 1918,
which, Weyl suggested, was due in no small measure to Einstein’s glowing review (see Hermann
Weyl to Einstein, 16 November 1918 [Vol. 8, Doc. 657]). An unaltered second edition was published
the following year (Weyl 1919b). The book went through substantial revisions in subsequent editions
(Weyl 1919d, 1921, 1923).
Gerhard Hessenberg (1874–1925) was Professor of Mathematics at the Technische Hochschule
Breslau (the present-day Wroc
aw). In Levi-Civita 1917a and Hessenberg 1917 the notion of parallel
displacement was introduced and used to give a geometrical interpretation of the Riemann curvature
tensor. Weyl’s treatment of curvature in terms of parallel displacement was singled out for special
praise in the first of the two letters from Einstein to Weyl mentioned in the preceding note. In his
course on general relativity in the summer semester of 1919, Einstein used the notion of parallel dis-
placement to derive the expression for the Riemann curvature tensor (Doc. 19, [p. 10] and [p. 25]; for
discussion, see Doc. 19, notes 16–21).
The variational method used in Weyl 1918b to find various static spherically symmetric solutions
of Einstein’s field equations, with and without the cosmological constant, was first used in Weyl 1917.
Einstein adopted this method in his course on general relativity in the summer semester of 1919 (Doc.
19, [p. 24]; for discussion, see Doc. 19, note 88).
The final section of Weyl 1918b (sec. 33) is on cosmology. Discussion of the page proofs of
Weyl’s book in the correspondence between Einstein and Weyl of April–May 1918 focused on this
section (see Hermann Weyl to Einstein, 19 May 1918 [Vol. 8, Doc. 544], note 1). Weyl’s analysis was
important for Einstein’s understanding of the De Sitter solution (see Einstein 1918c [Doc. 5], note 8).
The discussion of energy-momentum conservation in sec. 27 of Weyl’s book follows Weyl 1917
and Klein, F. 1917. In this approach, energy-momentum conservation emerges as an identity (see the
discussion with Felix Klein, referred to in Einstein 1918c [Doc. 5], note 5). As Einstein wrote to
Klein, referring to Weyl’s book: “He derives the energy law with the same variational trick you used
in your recent article” (“Den Energiesatz der Materie leitet er mit demselben Variations-Kunstgriff ab
wie Sie in Ihrer neulich erschienenen Note.” Einstein to Felix Klein, 24 March 1918 [Vol. 8, Doc.
492]). Einstein used this same “variational trick” in his course on general relativity in the summer
semester of 1919 (Doc. 19, [pp. 13–17]; for discussion, see Doc. 19, notes 43–46).
In the introduction, Weyl elaborates on his philosophical views, aligning himself with phenom-
enologists Franz Brentano (1838–1917) and Edmund Husserl (1859–1938) and distancing himself
from positivism (Weyl 1918b, pp. 3–4). For a discussion of Weyl’s philosophical views, see Scholz
1995, which emphasizes the influence of Johann Gottlieb Fichte (1762–1814) and attributes the influ-
ence of phenomenology to Weyl’s wife, Helene Weyl née Joseph (1893–1948), who had been one of
In Einstein 1918g (Doc. 8), Einstein argued that the unified theory of gravity and electromagne-
tism proposed in Weyl 1918a is incompatible with the notion that rods and clocks directly measure
the line element. The first edition of Weyl’s book does not include a discussion of his unified theory.
In the third edition, however, Weyl, rather than following Einstein’s advice to emphasize the direct
physical significance of the line element, added an exposition of his own theory in which the line ele-
ment is determined only up to a gauge factor (Weyl 1919c, secs. 34–35).