150

DOC. 30

FOUNDATION OF

GENERAL RELATIVITY

knowledge,

there

is

a

well-known

physical

fact

which favours

an

extension

of

the

theory

of relativity.

Let

K

be

a

Galilean

system

of reference, i.e.

a

system relatively

to which

(at

least

in

the

four-dimensional

region

under

consideration)

a

mass,

sufficiently

distant

from

other

masses,

is

moving

with uniform

motion

in

a

straight

line.

Let

K' be

a

second

system of

reference

which

is

moving relatively

to K

in

uniformly

accelerated

translation.

Then,

relatively

to

K',

a mass

sufficiently

distant

from

other

masses

would have

an

acceler-

ated motion such that its

acceleration and

direction of

acceleration

are

independent

of the

material

composition

and

physical

state of

the

mass.

Does

this

permit

an

observer at rest

relatively

to K' to

infer that he

is

on

a

"really"

accelerated

system

of

reference?

The

answer

is

in

the

negative;

for the

above-mentioned

relation

of

freely

movable

masses

to K'

may

be

interpreted

equally

well

in the

following

way.

The

system

of reference

K' is

unaccelerated,

but the

space-time

territory

in

question

is

under the

sway

of

a

gravitational

field,

which

generates

the

[8]

accelerated

motion

of

the

bodies

relatively

to K'.

This

view

is

made

possible

for

us

by

the

teaching

of

experience

as

to

the

existence

of

a

field

of

force,

namely,

the

gravitational

field,

which

possesses

the remarkable

property

of

imparting

the

same

acceleration to all bodies.*

The

mechanical

behaviour of bodies

relatively

to

K' is

the

same

as

presents

itself to

experience

in the

case

of

systems

which

we are

wont to

regard

as

"stationary"

or

as

"privileged."

Therefore,

from

the

physical

standpoint,

the

assumption

readily

suggests

itself

that the

systems

K and

K'

may

both

with

equal

right

be looked

upon

as

"stationary,"

that

is

to

say, they

have

an equal

title

as

systems

of reference for

the

physical description

of

phenomena.

It

will be

seen

from

these

reflexions

that in

pursuing

the

general

theory

of

relativity

we

shall be led to

a

theory

of

gravitation,

since

we are

able to

"produce"

a

gravitational

field

merely by changing

the

system

of co-ordinates.

It

will

also be obvious

that the

principle

of

the

constancy

of

the

velocity

of

light

in

vacuo

must be

modified,

since

we

easily

[9]

*

Eötvös has

proved experimentally

that

the

gravitational field

has this

property

in

great accuracy.