DOC. 40 ON KOTTLER'S PAPER 237

Doc. 40

5.

On Friedlich Kottler's

Paper:

"On Einstein's

Equivalence Hypothesis

and Gravitation"1

by

A. Einstein

[p.

639]

Especially noteworthy among

the

papers

that take

a

critical look

at

the

general theory

of

relativity are

those

by

Kottler

because this

colleague

has

truly penetrated deeply

into

the

spirit

of

the

theory.

I

want

to

discuss here the most recent

of

his works.

[2]

Kottler claims

I

had abandoned in

my

later

papers

the

"principle

of

equivalence"

which I did introduce in order to

unify

the

concepts

of "inertial mass" and

"gravitational

mass." This

opinion

must be based

upon

the fact that

we

both do not

denote the

same thing as

"the

principle

of

equivalence";

because

in

my opinion my

theory

rests

exclusively upon

this

principle.

Therefore

I

repeat

the

following:

[3]

1.

The

Limiting

Case of

the Special Theory

of

Relativity.

Let

a

finite

space-time-

like domain be without

a

gravitational

field; i.e.,

let it be

possible

to

introduce

a

system

of reference K

("Galilean

system")

relative to which the

following

is

true

for

the domain. As

is

usually presupposed

in the

special theory

of

relativity,

let

the

coordinates be

directly

measurable in known

manner by means

of

a

unit

measuring

stick,

and the times

by

a

unit clock. Relative to this

system an

isolated material

point

shall

move uniformly

in

a straight

line,

just

as

it

was postulated by

Galileo.

2.

The

Principle

of

Equivalence. Starting

from the

limiting case

of

the

special

theory

of

relativity, one may

ask if in the domain under consideration

an

observer,

who is

uniformly

accelerated relative to

K,

must

necessarily

judge

his state

as [p.

640]

accelerated,

or

whether he has

an option

left-according

to the

(approximately)

known laws of nature-to

interpret

his state

as

"at rest."

Or,

to

phrase

it

more

precisely:

Do the laws

of

nature,

known to

us

in

some approximation,

allow

us

to

consider

a

reference

system

K'

as

being

at

rest

if

it is in uniform acceleration with

respect

to K?

Or,

somewhat

more

generally:

Can the

principle

of

relativity

be

extended such

as

to

encompass

reference

systems

that

are

in

(uniform)

accelerated

motion relative

to

one

another? The

answer

is:

insofar

as we really

know the laws

of

nature, nothing prevents us

from

considering a system

K'

as

at

rest,

provided

we

assume

a

gravitational

field

(homogeneous

in first

approximation)

relative

to

K'.

Because

in

a homogeneous gravitational

field, as

with

regard

to

our system

K',

all

bodies fall

with the

same

acceleration

independent

of

their

physical

nature. I call

"principle

of

equivalence"

the

assumption

that K'

can

be treated with all

rigor as

lAnn.

d.

Phys.

50

(1916),

p.

955.

[1]