EINSTEIN ON THE

STATIC FIELD

123

When

Einstein

realized

in

1911

that

gravitational light

deflection should

be

exper-

imentally

observable for

light rays passing

near

the

sun,

he

took

up

the

problem

of

gravitation again

and

published

this

insight

in

Einstein

1911h

(Vol.

3,

Doc.

23).[6]

He

also

used

the

occasion

to

extend

his

theoretical discussion of

gravitation.

A

conse-

quence

of

the

equivalence principle

which he

had earlier mentioned

in

passing now

became of fundamental

importance.

Since Einstein

had

found that

the

coordinate time

measured

by

local

clocks

depends

on

the

gravitational potential

O, he had

concluded

that

the

velocity

of

light

c

should

also

depend

on

the

gravitational potential according

to

the relation[7]

c

=

c0 (1

+

O/c2).

This relation

was

not

only

crucial

for

deriving

the

bending

of

light rays

but

also

implied

that

the

principle

of

the

constancy

of

the

velocity

of

light

had

to

be

modified if

grav-

itational

fields

were

taken

into

account.[8]

Hence

the

assumption

of

a

variable

speed

of

light

became

the

basis

for

Einstein's

subsequent

papers on

the static

gravitational

field.

In

late

1911

and

early

1912

Einstein invested

great

effort

in

developing a

coherent

theory

of

the static

gravitational

field.

To

a

friend

he wrote:

"I

am

working

like

a

horse."[9]

Finally, on

24

February,

he

submitted

a

paper

to

Wilhelm

Wien, the

editor

of the

Annalen der

Physik,

entitled "The

Speed

of

Light

and the

Statics of

the

Grav-

itational

Field."[10] In this

paper

Einstein

gives

a

heuristic

argument

for

a

gravitational

field

equation

which

generalizes

the

Poisson

equation

of Newtonian mechanics.

Using

the

principle

of

equivalence

he first finds that the

speed

of

light

in

a

static

gravitational

field is

a

linear function of

the

spatial

coordinates.

By

studying

the

equations

of

motion

of

a mass

point,

he

then concludes

that the

speed

of

light plays

the

role of

the

gravi-

tational

potential.

On the

basis of these considerations Einstein

suggests

a

differential

equation

for

the

speed

of

light

c

in the

presence

of

matter

which

takes

the

place

of

Poisson's

equation:[11]

Ac

=

kcp.

[6]Einstein also

began corresponding

with

contemporary astronomers to encourage tests

of

the

experimental consequences

of his

analysis

of

gravitation;

see

in

particular

his

correspon-

dence with Erwin Freundlich

and W. H.

Julius from

this

period

in Vol. 5.

[7]See

Einstein

1911h

(Vol. 3,

Doc.

23),

p.

906;

see

also Einstein

1907j (Vol. 2,

Doc.

47),

p.

461.

[8]See

Einstein

1911h

(Vol. 3,

Doc.

23),

p.

906;

see

also Einstein

to

Jakob

Laub,

10 August

1911

(Vol. 5,

Doc.

275).

[9]"ich

arbeite

wie ein

Ross"

(Einstein

to Ludwig Hopf,

after

20

February

1912

[Vol. 5,

Doc.

364];

the

same

expression

is

used

in

Einstein

to

Heinrich

Zangger,

before

29

February

1912

[Vol. 5,

Doc.

366]).

[10]"Lichtgeschwindigkeit

und

Statik

des Gravitationsfeldes"(Einstein

1912c

[Doc. 3]).

[11]A

denotes

the

Laplacian operator,

p

the

density

of

matter, and

k

the

gravitational

constant.