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 4 5 7

By 1921 several leading researchers, beginning with Eddington 1918, had realized that the equations

of motion in general relativity followed from the field equations (which is not generally the case in

other field theories or in Newtonian theory) via the relation (see Havas 1989 for a histor-

ical discussion). Einstein later stated in Einstein et al. 1937, p. 65, that he was unhappy with this ap-

proach to the problem of motion, because of its dependence on the particular model of matter entering

into the energy-momentum tensor. In his work on the problem of motion from 1927 on, he consistent-

ly based his approach on the vacuum field equations, with singularities in place of material bodies and

(from 1937) employing integration around closed surfaces to excise the singularities from the space-

time (see Havas 1989, 1993 and Earman and Eisenstaedt 1999 for historical discussions; see Ander-

son 1997 for a contrasting assessment of Einstein’s contributions to the problem of motion). Note that

Einstein 1922c (Doc. 71), p. 33, fn. 1, is sharply critical of the singularity model of matter. This model

had already been proposed, in the context of general relativity, in Eddington 1918a.

[7]“ ” should be “ .”

[8]On the right-hand side of this equation, “ ” should be “ .”

[9]Although Einstein specifies his choice of units here, he had already written the following page

and a half of equations in conventional units, as is indicated by his crossing out all factors of c (except

in one case in the middle of the next line and one on the next page [see note 12]).

[10]Here , where v is the relative velocity of the two frames.

[11]“il” should be “il,” with i the imaginary unit and l the flux of the energy density of the electro-

magnetic field.

[12]In the middle of this line, Einstein changes retroactively to units with (see note 9), but

forgot to delete the factor of after the word “Punkte” opposite the figure immediately above. To

the left of the small vertical line, “ ” should be “ .”

[13]For a brief explanation of the derivation of the electromagnetic energy-momentum tensor, see

Doc. 12, [p. 7], notes 33 and 34.

[14]Poincaré 1906. See Einstein 1919a (Doc. 17), note 11, for background and references to the so-

called Poincaré stresses.

[15]See Einstein 1922c (Doc. 71), pp. 68–70, for a discussion of this “cosmic pressure,” which Ein-

stein saw as a possible substitute for his cosmological term, introduced in Einstein 1917b (Vol. 6, Doc.

43). See Einstein 1918d (Doc. 3) for his earlier opposition to this approach to cosmology.

T μν;ν 0 =

bμdν bμdxν

∂xν

∂

∂xτ

∂

w 1

v2

c2

---- - – =

c 1 =

c2

E

m

1 q2 –

-------------- – E

m

1 q2 –

------------------ =