DOC.

21

THEORY OF RELATIVITY

261

From this

point

of

view,

there

is

no

substantial difference between

inertia and

gravitation;

for

it

depends

on

the coordinate

system,

i.e., on

the

point

of

view,

whether, at

a

certain

instant,

a

body

is

under the exclusive influence of inertia

or

under the combined influence of inertia and

gravitation.

Thus, widely

known

physical

facts lead

us

to

the

general relativity

principle, i.e.,

to

the

conception

that the laws of

nature

are

to

be formulated

in

such

a

way

that

they

hold with

respect

to

arbitrarily

moving

coordinate

systems.

[22]

The

Theory

of

the Gravitational

Field

From

what has been said

so

far,

one sees

immediately

that the

general relativity

principle

must

lead

to

a theory

of the

gravitational

field. For if

one

starts

out

from

the

gravitation-free

inertial

system

K and introduces

a

coordinate

system

K' that

moves

arbitrarily

with

respect

to

the

former, then,

with

respect

to

K',

there exists

a

precisely

known

gravitational

field,

and

one can

find the

general properties

of

gravitational

fields from the

general properties

of those

gravitational

fields

at

which

one

arrives in this

way.

However,

one

must

be careful

not to

assume

that,

conversely, every gravitational

field

can

be made

to vanish,

i.e.,

can

be turned into

a

gravitation-free region, by

means

of

a

suitable choice of the coordinate

system.

For

example,

it

is

impossible

to

make the

gravitational

field of the Earth vanish

by means

of

a

suitable choice of the

coordinate

system.

In

fact,

for

a

region

of

finite

extension this

is

only possible

with

gravitational

fields of

a very special

kind.

But for

an infinitely

small

region

the

coordinates

can

always

be chosen such that

no

gravitational

field will be

present

in

it.

With

respect

to

such

an

infinitely

small

region

one

may

then

assume

that the

special theory

of

relativity

is

valid. That

way

the

general theory

of

relativity

is

connected with the

special theory

of

relativity,

and the results of the latter

can

be

utilized for the former.

The

Bending

of

Light

Rays

A

simple argument

shows that

a

ray

of

light

that

propagates rectilinearly

and

uniformly

with

respect

to

the inertial

system

K

must

describe

a

curved

trajectory

with

respect

to

the coordinate

system

K'

that is

in

accelerated translational motion. From

this

we

conclude that

light rays are

bent

by

gravitational

fields,

which

means,

according

to

Huygens's principle,

that the

velocity

of

light

in

gravitational

fields

depends

on

the location. This

consequence

was

confirmed for the first time

on

the

occasion of the solar

eclipse

in 1919.

[23]