502 DOC. 17 PROBLEM

OF GRAVITATION

[18]In his

discussion of scalar theories of

gravity in

Einstein and Grossmann

1913

(Doc. 13),

part

1, §7,

Einstein

put

forward

an

argument

against

such theories without

taking

this

possibility

into

account;

see

also the discussion

on p.

1253

below.

[19]In

Einstein

and Grossmann 1913

(Doc.

13),

part

1,

§4,

a

similar

approach

is

followed.

[20]"dt"

should be "dt."

[21]See

Laue 1911a,

p.

74

or

Laue

1913,

p.

85; see

also Einstein and Grossmann

1913 (Doc.

13),

part

1, §7.

For the

significance

of Laue's scalar

in the

second version of Nordström's

theory,

see

Nordström

1913b,

§1.

[22]"K"

in

the

numerator

should

be

"x."

[23]See

Laue

1911a,

p.

169,

or

Laue

1913,

p.

209.

The summation

signs

should

be

omitted.

[24]See

Einstein and Grossmann

1913

(Doc. 13),

part

1,

§7.

Einstein retracted his

argument

against

scalar theories

in

the

comments

added

to the

republication

of

this

paper

(see

Einstein

1914d

[Doc. 26], p.

261).

Nordström discussed

the

problem

of the

dependence

of the

length

dimensions

on

the

gravitational

field in

Nordström

1913b,

§4.

[25]See

Nordström

1913b,

p.

538,

for Nordström's version of Einstein's

equation

(7).

This

equation

is

quoted

in

Einstein and Besso's

manuscript

on

the

motion of the

perihelion

of

Mercury

(Doc. 14), on [p. 52].

[26]For Einstein's method of

demonstrating

that the conservation laws hold

in Nordström's

theory,

see

Einstein and Grossmann

1913

(Doc. 13), §5.

[27]For

a more

detailed

explanation

of

this

argument,

see

Einstein 1914c

(Doc.

24).

Nord-

ström's

original theory

did

not

satisfy

the

equivalence principle

(see

Nordström

1912,

p.

1129,

where

he

acknowledges

a

letter

by

Einstein

pointing out

this

consequence

of

the

theory;

see

also Nordström

1913a).

Einstein further discussed the role of

the

equivalence

of

energy

and

gravitational

mass

in

Nordström's

theory

in

Einstein

1914h

(Doc. 31),

p.

344.

[28]The

two

types

of clocks

were

earlier described

in

Einstein 1912c

(Doc.

3), §3. During

Nordström's visit

to

Zurich

in late

June

1913,

Einstein

and

Nordström

jointly

worked

on a

calculation related

to

a

comparison

between these

two

clocks

(see

the

entry

for

29

June

in

Ehrenfest's

Diary

"I," NeLR,

Ehrenfest

Archive, Notebooks, ENB: 4-15).

[29]In

a

letter

to

Erwin Freundlich of

mid-August

1913

(Vol. 5,

Doc. 468),

Einstein called

Nordström's

theory "very

reasonable"

("sehr

vernünftig")

and

commented that

it

showed how

to

achieve results without the

use

of

the

equivalence hypothesis.

See

also Einstein and Fokker

1914 (Doc.

28),

p.

328,

for another

positive

evaluation of Nordström's

theory.

[30]Einstein

1911h

(Vol. 3,

Doc.

23).

[31]The

following provides

the first

popular explanation

of

the

principle

of

equivalence.

Einstein's

thought experiment

is

taken

up

and criticized

by

Gustav Mie

in

the discussion

fol-

lowing

the lecture

(see

Einstein

et

al. 1913

[Doc. 18],

p.

1264).

[32]For

a

historical discussion of

the principle

of

equivalence,

see

Norton

1985.

[33]Einstein and

Grossmann 1913

(Doc.

13).

[34]This

section summarizes Einstein and Grossmann

1913

(Doc. 13),

part

1,

§§2-4.

[35]In

Einstein's

presentation

of the four-dimensional formulation of

special relativity

in

his

unpublished manuscript

on

special relativity (Doc.

1),

he had

followed Minkowski

in

using

an

imaginary

time coordinate.

[36]In §2

of Einstein 1912d

(Doc. 4)

Einstein referred

to

such devices

as

"pocket"

("Taschen")

instruments. The

concept

of

a

natural

length

was

introduced

in

part

1,

§3,

of

Einstein and Grossmann

1913

(Doc. 13).

[37]All denominators "dxs" should

be

"ds" and there should

be

no

summation

with

respect

to

s.

[38]The

signs

of

all terms

on

the

right-hand

side with the

exception

of those of

the

last line

should

be

negative,

as was

pointed

out in

Einstein and Fokker 1914

(Doc.

25),

p.

323.

[39]Ricci

and Levi-Civita

1901.

[40]Christoffel

1869.

[41]See

Einstein and Grossmann

1913 (Doc.

13), part 2,

and

also Grossmann

1913

for

expo-

sitions of the mathematical method.

[42]Kottler 1912.

This

paper

was

earlier cited

in

Einstein and Grossmann

1913

(Doc. 13),

p.

23.