340

DOC. 13 GENERALIZED THEORY OF RELATIVITY

Published

by

Teubner,

Leipzig.

Submitted before

28

May 1913, published

before 25

June

1913

(see

Einstein

to Paul Ehrenfest, 28

May

1913

[Vol. 5,

Doc.

441],

where Einstein

anticipates

publication

within

a

few weeks;

Einstein

to

Ernst

Mach, 25

June

1913

[Vol.

5,

Doc.

448],

where he

assumes

that

Mach

has

received

a

copy

of

the

paper;

and

Einstein

to

Jakob

Laub, 22

July

1913

[Vol. 5,

Doc. 455], in

which

he

mentions that the work

on

generalized relativity was

completed a

few

months

earlier).

[1]Einstein

1911h

(Vol.

3,

Doc.

23),

Einstein 1912c

(Doc. 3),

and Einstein 1912d

(Doc. 4).

[2]The term

"equivalence hypothesis" ("Äquivalenzhypothese") appeared

for the

first

time

in

Einstein 1912c

(Doc.

3),

p.

355,

but the

underlying

idea

was

used

by

Einstein

since

1907 in

attempts

to

generalize special relativity

(see

Einstein

1907j

[Vol. 2,

Doc.

47]).

For

a

comprehensive

discussion of Einstein's views

on

the

equivalence principle,

see

Norton

1985.

[3]Eötvös 1891

(a Hungarian

version

was

first

published

as

Eötvös

1890)

and Hess

1891.

This

is

the

first

time Einstein referred

to

Eötvös's

experiments

in

print;

in

July

1912

Einstein

was

still

unaware

of them

(see

Einstein

to

Wilhelm

Wien,

10 July

1912

[Vol. 5,

Doc. 413];

Illy

1989

suggests

that Einstein's

knowledge

of Eötvös's work derives from Wien's

answer

to

this

letter,

which

is not

preserved).

[4]For the

derivation of

this

relationship

between

mass

and

energy,

see

Einstein 1905s

(Vol.

2,

Doc.

24)

and Einstein 1906e

(Vol. 2,

Doc.

35).

[5]In

1912

Langevin

had

drawn Einstein's attention

to

this

consequence

(see

Einstein

1912h

[Doc. 8],

p.

1062,

fn.

1).

In

a

letter

to

Wilhelm Wien of the

same

year

Einstein

inquired

about

the

possibility

of

testing

the

equality

of

gravitational

and

inertial

mass

for radioactive substances

(see

Einstein to

Wilhelm

Wien,

10 July

1912

[Vol. 5,

Doc.

413]).

[6]Planck

1906a.

[7]There should

be

no

factor

m

after the

first

equal

sign.

[8]For

an

overview of these earlier

papers,

see

the editorial

note,

"Einstein

on

Gravitation

and

Relativity:

The Static

Field,"

pp.

122-128. The static

case

is

discussed

in

Einstein's

research

notes

on a

generalized theory

of

relativity

(Doc.

10) on

[p.

42];

see

also

[pp.

1-2]

for

references

to

the

static

case.

[9]See

Einstein 1912d

(Doc. 4),

p.

458.

[10]This

conclusion

was

earlier drawn

in

Einstein 1912e

(Doc. 7),

p.

39.

Immediately

after

the

publication

of

the

present paper,

Einstein

pointed

Mach's attention

to

the above

paragraph

(see

Einstein

to

Ernst

Mach, 25

June

1913

[Vol. 5,

Doc. 448]).

[11]The present paper

is

the

first

published

work

in

which Einstein makes

systematic

use

of

Minkowski's

four-dimensional

formalism; he

did,

however,

expound

this formalism

in

his

unpublished manuscript

on

special relativity (Doc.

1).

[12]For

a

brief historical discussion of Einstein's

recognition

of the non-Euclidean character

of the metric

in the

general case,

see

the editorial note, "Einstein's Research

Notes

on a

Gen-

eralized

Theory

of

Relativity,"

pp.

193-194.

[13]This is the

four-dimensional

representation

of

the

theory

of the static

field

developed

in

Einstein

1912d

(Doc. 4).

Formulas similar

to

the

ones on

this

page

also

appear

on [p.

10],

[p.

40],

and

[p. 42]

of Einstein's research

notes

on a

generalized theory

of

relativity (Doc. 10).

[14]"d1x"

in

the second

equality

should be

"dx1."

[15]For

a

history

of

the tensor

concept, see

Reich

1994, and

also Norton

1992a,

pp.

302-310;

see

also the discussion

in

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Col-

laboration

with Marcel

Grossmann,"

pp.

295-296.

[16]Einstein

1911h

(Vol. 3,

Doc.

23), §3.

[17]For

a

description

of the roles

played

by

the

line

element and the Gaussian

theory

of

surfaces

as starting points

for Einstein's

approach

to

the mathematical

problems posed

by a

generalized

theory

of

relativity,

see

the

editorial

note,

"Einstein's Research Notes

on a

Gen-

eralized

Theory

of

Relativity,"

pp.

193-194.

[18]The

existence of such

an

elementary system

was

later

interpreted

as

the

expression

of

a

generalized principle

of

equivalence

(see,

e.g.,

Pauli

1921, sec.

51);

for

a

discussion of the

problematic

character of

this

interpretation,

see

Norton

1985, sec.

9.