D O C . 1 9 R E L AT I V I T Y L E C T U R E N O T E S 1 7 7

AD. [3 009]. These lecture notes are preserved in the same notebook that contains Doc. 12. They con-

sist of 25 unnumbered consecutive pages, beginning on the sixth page of the notebook, one line of

which also appears in Doc. 12, [p. 6]. Numbering is here provided in the margins in square brackets.

A set of student notes (PPiU, HR-028-01-04, HR-028-01-03, HR-028-01-01), taken by Hans Rei-

chenbach (1891–1953), is used in the annotation of this document.

[1]For the first four weeks of the course, Einstein dated the notes for his lectures (“5.V” and “12.V”

on [p. 1], “19.V” on [p. 3], “20.V” on [p. 5], “26” on [p. 7], “27” on [p. 8], and “3 & 4.VI” on [p. 10]).

No dates are recorded for the remainder of the course. The fact that Einstein inserted the notes for this

course in the notebook after the first part of the notes for Doc. 12 may indicate that Einstein started

working on these notes as early as January 1919 while in Zurich.

[2]The first entry in the notebook after these lecture notes is an outline for a very similar course to

be held in Zurich (part of Einstein’s notes for this course are presented in Doc. 20).

Plan für die Züricher Vorles. Sommer 1919.

1 [---t]. d. Mechanik Aequiva Hyp. Kr. d. Lichtstr. Linienversch.

2 Allgemeine Kovarianz. Doppelbed. der

7 Riemann

8 Feldgleichungen Energiesatz

9 1. Näherung

10 Merkur

This outline can be read as a table of contents for the document presented here. Einstein begins his

lecture series by pointing out that classical mechanics does not explain the equality of inertial and

gravitational mass nor the privileged status of inertial frames. He then introduces the equivalence

principle and uses it to give the simple derivations from Einstein 1911h (Vol. 3, Doc. 23) of formulas

for the redshift and the bending of light (see [pp. 1–2]). In the third lecture, Einstein motivates the

demand for general covariance, his remedy for the second defect, and introduces the metric tensor

(see [pp. 3–4]). After these introductory lectures, which are similar to the introductory sections of Ein-

stein 1916e (Vol. 6, Doc. 30), there are several lectures devoted to tensor calculus and to the derivation

of the geodesic equation (see [pp. 4–10]). These lectures essentially follow the corresponding sections

in Einstein 1914o (Vol. 6, Doc. 9) and Einstein 1916e (Vol. 6, Doc. 30). The introduction of the Rie-

mann curvature tensor given in these two papers can be found in these lecture notes as well (see [p.

11]), but it is clear from entries on [p. 10] and [p. 25]—and from Reichenbach’s notes (the last part

of the second notebook)—that Einstein also presented the new interpretation of curvature in terms of

parallel displacement given by Tullio Levi-Civita and Hermann Weyl (who are mentioned explicitly

on [p. 10]). After these mathematical preliminaries, Einstein—borrowing elements from Weyl 1918b,

but essentially following Einstein 1916o (Vol. 6, Doc. 41)—uses variational methods to derive field

equations and the law of energy-momentum conservation (see [pp. 13–17]). For the approximative

integration of the field equations, Einstein follows (with some small improvements) Einstein 1918a

(Doc. 1), pp. 17–19. The derivation of the exact solution of the field equations for a point mass and

the perihelion advance of an orbit is taken from Weyl 1918b (see [p. 21] and, for somewhat more

detail, [p. 24]). The final pages of these notes, [pp. 21-24], deal with cosmology and combine ele-

ments from Einstein 1917b (Vol. 6, Doc. 43) and Einstein 1919a (Doc. 17).

These lectures also cover the generalization of electrodynamics from special to general relativity

([p. 12]), the equations of motion for frictionless fluids ([p. 14]), and the behavior of rods and clocks

in weak gravitational fields ([p. 20]).

gμν

3

4

þ

ýAlgebraische

ü

Operationen an Tensoren

5

6

þ

ýGeodätische

ü

Linie. Differentialoperationen an Tensoren.

11

12

þ

ýKosmologisches

ü

Problem