DOC.

23

PROPAGATION OF LIGHT

379

Doc.

23

On the Influence of Gravitation

on

the

Propagation

of

Light

by

A.

Einstein

[Annalen

der

Physik

35

(1911): 898-908]

In

a

paper published

three

years

ago,1

I

already

tried

to

answer

the

question

as

to

whether the

propagation

of

light

is

influenced

by gravitation.

I

now

return to this

topic

because

my

former

treatment

of the

subject

does

not

satisfy me, but, even more

importantly,

because

I have

now come

to

realize that

one

of the

most

important

consequences

of

that

analysis

is

accessible to

experimental

test.

In

particular,

it turns out

that,

according

to

the

theory

I

am going

to set forth,

rays

of

light passing near

the

sun

experience a

deflection

by

its

gravitational

field, so

that

a

fixed star

appearing

near

the

sun

displays

an apparent

increase of

its

angular

distance from

the

latter,

which amounts

to almost

one

second of

arc.

In the

course

of

carrying

through

the

analysis,

further results

regarding

gravitation

were

obtained.

However,

since

the

presentation

of

the

argument

in its

entirety

would

be

[2]

rather

difficult

to

follow,

I shall

present

in what follows

only a

few

quite elementary

considerations

on

the

basis

of

which

one

can

easily

orient

himself

regarding

the

assumptions

and the

line

of

reasoning

of the

theory.

Even if

their theoretical

basis

is

correct,

the

relationships

here derived

are

valid

only

in first

approximation.

§

1.

A

Hypothesis Concerning

the

Physical

Nature

of the

Gravitational Field

[3]

In

a homogeneous

gravitational

field

(acceleration

due

to

gravity,

y)

let there

be

a

coordinate

system

at rest

K,

which

is

oriented

in such

a

way

that the

lines

of

force

of

the

gravitational

field

run

in

the direction of the

negative

z-axis.

In

a space

free of

gravitational

fields,

let

there

be

another

coordinate

system

K' that

moves

with

a

uniform

acceleration

(acceleration y)

in

the direction of

its

positive

z-axis. So

as

not to

complicate

the

analysis unnecessarily,

we

will

disregard

the

theory

of

relativity

for the

time

being,

and

consider, instead,

the

two

systems according

to

conventional

kinematics,

and the motions

occurring

in

them

according

to

customary

mechanics.

Material

points

not

subjected

to

actions

of other

material

points

move

relative

to

K

as

well

as

relative

to

K'

according

to

the

equations

1

A.

Einstein,

Jahrb.

f.

Radioakt.

u.

Elektronik IV.4.

[1]