198

DOC.

17

PROBLEM

OF

GRAVITATION

Doc.

17

On the Present State of the Problem of Gravitation

by

A.

Einstein

[Physikalische Zeitschrift

14

(1913):

1249-1262]

[1]

§1.

General Remarks

on

the Formulation

of the

Problem

The first

area

of

physical phenomena

where

a

successful theoretical elucidation

was

achieved

was

that of the

general

attraction of

masses.

The laws of inertia and of the

motions of celestial bodies

were

reduced

by

Newton to

a simple

law of motion

of

the

mass

point

and

to

a

law

of

interaction

of

two

gravitating mass points.

These laws

have

proved

to

hold

so

exactly that,

from

an

empirical standpoint,

there is

no

decisive

reason

for

doubting

their

strict

validity. If,

nevertheless,

scarcely

a

physicist might

be

found

today

who believes in the strict

validity

of

these

laws,

then this is

to

be

attributed

to

the

transforming

influence

of

the

development

of

our

knowledge

of

electromagnetic

processes during

the last few decades.

For before

Maxwell,

electromagnetic processes

were

traced back

to

elementary

laws that

were

fashioned

as

closely

as

possible

on

the

pattern

of

Newton's force

law.

According

to these

laws,

electrical

masses,

magnetic masses,

current

elements, etc.,

are

supposed

to exert

on

each other

actions-at-a-distance that

require

no

time for their

propagation through space.

Then Hertz

showed

25 years

ago by

means

of

his

brilliant

experimental

investigation

of

the

propagation

of electrical force that electrical effects

[2]

require

time for their

propagation.

In

this

way

he

helped

in the

victory

of

Maxwell's

theory,

which

replaced

the unmediated

action-at-a-distance

by partial

differential

equations.

After the

untenability

of the

theory

of action-at-a-distance had thus been

demonstrated in the

area

of

electrodynamics,

confidence in the

correctness

of

Newton's action-at-a-distance

theory

of

gravitation was

also

shaken. The conviction

had

to force itself

through

that Newton's law of

gravitation

does

not

embrace

gravitational phenomena

in their

totality any more

than Coulomb's law of electrostat-

ics and

magnetostatics

embraces the

totality

of

electromagnetic phenomena.

The fact

that Newton's law

previously

sufficed for

calculating

the motions of the

celestial

bodies is

to

be attributed

to

the fact that the velocities and accelerations of those

motions

are

small. In

fact,

it

is

easy

to demonstrate that celestial bodies whose

motions

were

determined

by

electrical forces

stemming

from electrical

charges

situated

on

the celestial bodies would

not unveil Maxwell's laws

of

electrodynamics

to

us

if the velocities and accelerations of those celestial bodies

were

of the

same

order of

magnitude

as

in the motions

of

the celestial bodies with which

we are

familiar. One

would be able

to

describe those motions with

great accuracy

on

the

[3]