4 5 6 D O C . 6 3 S P E C I A L A N D G E N E R A L R E L AT I V I T Y

Für Vakuum . Differentialgesetz der Energie Übergn. zu Integr. muss

allgemein gelten. .

Flüssigkeiten

Divergenz liefert Euler’sche Gleichungen.

Phänomenologische Darstellung der Materie.

Bemerkung über Elektron. Poinákñcarés Druck

P[14]

Kosmischer Druck mit unbekanntem

Nullpunkt.[15]

ADft. [2 085]. The manuscript consists of nine unnumbered pages. Page numbers are here provided

in the margin in square brackets.

[1]This document is dated on the assumption that it is an aborted draft for Einstein 1922c (Doc. 71)

(see note 4). In Einstein to Paul Ehrenfest, 1 September 1921, Einstein remarks that he has barely

begun working on the manuscript.

[2]For more on the distinction between kinematical and physical relativity of motion, see the type-

script of the second Princeton lecture, Appendix C, [p. 1].

[3]See Einstein 1922c (Doc. 71), p. 2–3, where Henri Poincaré’s book (Poincaré 1902) is also dis-

cussed. See also Einstein’s discussion of Poincaré in Einstein 1921c (Doc. 52), pp. 7–10.

[4]The fact that the fourth lecture deals with general relativity suggests that this manuscript is an

early draft of Einstein 1922c (Doc. 71). Both in the actual lecture series and in the manuscript for Ein-

stein 1922c (Doc. 71), the discussion of general relativity begins in the fourth lecture (see Doc. 71,

note 66). The topics discussed here bear considerable resemblance to those covered in lectures 3 and

4 of Doc. 71 (see, for instance, note 15).

[5]See Doc. 19, [pp. 10-11], and note 20, for a fuller treatment of parallel transport.

[6]Einstein had recognized the connection between the field equations, energy-momentum conser-

vation, and the geodesic equation early on. The field equations of Einstein and Grossmann 1913 (Vol.

4, Doc. 13) guarantee that , the covariant divergence of the energy-momentum tensor for mat-

ter, vanishes in all so-called adapted coordinates (see Einstein and Grossmann 1914b [Vol. 6, Doc.

2]). The field equations of the final theory guarantee that in all coordinate systems by

virtue of the contracted Bianchi identities. As Einstein pointed out in Einstein and Grossmann 1913

(Vol. 4, Doc. 13), sec. 4, the geodesic equation governing the motion of a point mass can be obtained

from by setting (the energy-momentum tensor for pres-

sureless dust) and integrating over the worldtube of the particle, i.e., the region with nonvanishing

matter density ρ (see also Doc. 19, [p. 14]).

This is the first time that Einstein explicitly states that the field equations imply the equations of

motion for particles in a gravitational field. He did not include a similar statement in the published

version of the Princeton lectures (see Einstein 1922c (Doc. 71), pp. 50–52, where he discusses the

geodesic equation). In fact, he did not address this issue in print until Einstein and Grommer 1927.

[p. 9]

∂Tμν

∂xν

----------- - 0 =

∂å

Tμν

∂xν

------------------ 0 =

Tμν +σ

dσ

dxμdxν

dσ

pδμν + =

x

∂x

∂P

0 = –

– – – – – –

– – – – – –

T

μν

;ν

T

μν

;ν

0 =

T

μν;ν

0 = T

μν

ρ( dxμ ds)( ⁄ dxν ds) ⁄ =