DOC.

9

FORMAL FOUNDATION OF RELATIVITY

129

Published

in

Königlich

Preußische

Akademie der

Wissenschaften (Berlin). Sitzungsberichte

(1914):

1030-1085. Submitted

29

October

1914, published

26

November

1914.

[1]See

Einstein and Grossmann

1913

(Vol.

4.

Doc.

13),

1914b

(Doc.

2),

and

Einstein 1913c

(Vol. 4,

Doc.

17)

for Einstein's work with Marcel Grossmann

on

general

relativity

and later

developments;

see

also

Vol.

4,

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The

Collaboration with Marcel

Grossmann,"

pp.

294-301,

for

a

historical discussion.

In

a

letter

from

1915

Einstein claimed that Grossmann "did

not

contribute

substantially

to

the results"

("trug

aber materiell nichts

zu

den

Ergebnissen

bei." Einstein

to

Arnold

Sommerfeld,

15

July

1915).

[2]For historical discussions of the

present paper,

see

Norton

1984 and

Cattani and

De

Maria

1989.

[3]See

also Einstein's discussion of

the

physical

and

epistemological

reasons

to

include

non-

linear transformations in Einstein

to

H. A. Lorentz, 23 January 1915.

[4]See

Mach

1897, chap.

2.6.

See

also Einstein 1916c

(Doc.

29),

note

4,

for

more on

the role

that Mach's ideas

played

in

Einstein's

thinking.

[5]This is

a

version of the

equivalence principle,

which

was

first

formulated

by

Einstein

in

1907 (see

Einstein

1907j [Vol. 2,

Doc.

47],

§17).

It had

played

an

important

heuristic role

in

Einstein's search for

a

relativistic

theory

of

gravitation (see

Vol.

4,

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Static

Field,"

pp.

122-128,

for

a

discussion).

See

also Ein-

stein

1916p

(Doc. 40)

for further elucidation.

[6]"idt" should be "it."

[7]The

superscripts

a

should

be

subscripts.

[8]See

Ricci and Levi-Civita

1901.

[9]The

derivatives

should

be

partial

derivatives.

[10]"(2)"

should be

"(20)."

[11]Here and

in

the

equation

below the

subscript

"k" should

be

"k."

[12]The

superscript pairs

"tax,"

"Kß,"

"wß,"

and "Ka" should be

subscripts.

[13]"Faß"

should be

"Faß."

[14]"Linse"

should

be

"Linie."

[15]Note

that

equation

numbers

(23), (24), and (23a)

are

used twice

in

this

paper.

[16]See Christoffel

1869,

p.

48.

[17]See

Christoffel 1869,

p.

49.

[18]See

Christoffel 1869,

p.

57.

[19]"a-1"

should be

"al-1."

[20]There

should

be

a

minus

sign

between the

two

derivatives

in

the second

term

in

the

sec-

ond

summation.

[21]In

the

second and

third

terms

on

the

right-hand

side

a

summation

over

x

is

implied,

as

are

summations

over

a

and

x

in

the

following terms.

[22]A

summation

over a

is

implied.

[23]Following

Weyl,

V-tensors

were

later named "tensor densities"

("Tensordichten."

Weyl

1918b).

[24]See,

e.g.,

Laue

1911

for Max Laue's

formulation.

Einstein

had used Laue's

approach

ear-

lier

in

an

unpublished manuscript

on

the

special theory

of

relativity (see Vol.

4,

Doc.

1).

[25]"o

=

1" should be "a

=

2" and vice

versa.

[26]"(42)"

should

be "(42a)."

LIV

[27]In

eq.

(46)

"g"

should be

"g^v."

Earlier,

Einstein

had

denoted the

quantities

gmv as

the

components

of the

gravitational

field

(see

Einstein 1914e

[Vol. 4,

Doc.

25],

p. 177).

[28]"(44)"

should be

"(42a)."

[29]"(44)"

Should

be

"(42a)."

[30]"dx2"

should be

"dx1."

[31]"1

+

p

+

P"

in

this

equation

and in

the

one

below should

be

"1 +

pp0-1

+

P

."\