338

DOC.

30 FOUNDATION OF

GENERAL RELATIVITY

Published

in Annalen

der

Physik

49

(1916):

769-822. Received

20

March

1916, published

11

May

1916. A

manuscript

of

46 pages is

in

the Schwadron Collection

at

the Hebrew

University

of

Jerusalem. There

are no

significant

variations from the

printed

version.

[1]This paper gives

a

full overview of the

final

version of the

general theory

of

relativity

after its latest revisions

as

published

in

Einstein's

papers

of November

1915,

Einstein

1915f,

1915g, 1915h,

and 1915i

(Docs.

21, 22, 24, and

25).

It

was

also

published separately

as

Ein-

stein

1916f. In mid-January 1916

Einstein had still

expressed

doubts about his

ability to

write

such

a

paper,

calling

his

writings

"correct but

quite indigestible" ("zwar richtig

aber reichlich

unverdaulich."

Einstein

to

H. A. Lorentz,

17 January

1916),

but

two

months later

he sent

the

manuscript

of the

paper

to

the editor

of

the Annalen

der

Physik,

Wilhelm

Wien

(see

Einstein

to

Wilhelm

Wien,

18

March

1916).

[2]Although the

term

"special

theory

of

relativity" ("spezielle Relativitätstheorie") already

occurs

in

Einstein

1915f (Doc. 21)

and Einstein

1915i

(Doc.

25),

this

is

Einstein's

first

system-

atic

usage

of

it.

The

term

"special principle

of

relativity" ("spezielles Relativitätsprinzip"),

which

is

used

on p.

770,

appears

here for the first

time.

[3]See

Minkowski

1908. See also, e.g.,

Einstein's

own

exposition

of

special relativity

in

an

unpublished manuscript

from

1912

to

1914 (see Vol.

4,

Doc.

1).

[4]See Vol.

4,

the editorial

note,

"Einstein's Research Notes

on a

Generalized

Theory

of Rel-

ativity," pp. 195-196,

and Reich

1994

for discussions of the mathematical

background

of

gen-

eral

relativity.

[5]See

also Einstein and Grossmann 1913

(Vol. 4,

Doc.

13)

and Einstein 1914o

(Doc.

9)

for

earlier

expositions

of these mathematical tools.

[6]Several months earlier Einstein

expressed

himself somewhat

differently,

claiming

that

Grossmann "did

not

contribute

substantially to

the results"

("trug

aber materiell nichts

zu

den

Ergebnissen

bei." Einstein

to

Arnold

Sommerfeld,

15 July 1915).

See also

Vol.

4,

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Collaboration with Marcel

Grossmann,"

pp.

295-296,

for

a

discussion of Marcel Grossmann's

part

in

the

development

of

general relativity.

[7]See

Mach 1897. See also Einstein 1916c

(Doc. 29),

note 4,

for

more on

the role of Mach's

ideas

in

Einstein's

thinking.

[8]This

"equivalence principle"

had

played

an

important

heuristic role

in

Einstein's search

for

a

relativistic

theory

of

gravitation.

It

was

first formulated

in

Einstein

1907j (Vol. 2,

Doc.

47), §17;

see

also

Vol.

4,

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Static

Field,"

pp. 122-124,

for

a

discussion.

In

Einstein

1916p

(Doc. 40)

Einstein

gives

a

further elu-

cidation

in

response to

criticism

by

Friedrich

Kottler.

[9]See

Eötvös 1891.

[10]See

Stachel 1980 for

a

discussion of the role that the

problem

of the

rigidly rotating

disk

played

in

the

development

of

general relativity.

[11]This

point

was

first

emphasized by

Einstein

in

his

correspondence

with Paul Ehrenfest

and Michele

Besso

(see

Einstein

to

Paul

Ehrenfest, 26

December

1915,

and

5 January 1916;

and

Einstein

to

Michele

Besso,

3 January

1916).

[12]This

is

the first time Einstein introduces his "summation convention"

in print.

He had

used it earlier

in

his

correspondence

(see

Einstein

to

Paul

Ehrenfest, 24 January

1916).

[13]See

Ricci and Levi-Civita 1901.

[14]"guv"

in

the first

term

on

the

right-hand

side should

be

"guo."

[15]"guv"

in

the first and second

terms

should be "guo"; "xo"

in

the second

term

should

be

"xv"

in

both

cases;

all "y"

in

the second and third

terms

should

be

"s."

[16]"guv"

on the

left-hand side should be

"guv"

[17]"y"

should be

"g."

[18]"gua"

should be

"gua."

[19]"(31)"

should be

"(32)."

[20]"guv"

should be "gta."

[21]In

this line

as

well

as

three lines below

Rpuot

denotes the Riemann-Christoffel

tensor.