12 DOC.

5

APRIL

1914

5.

To

Joseph

Petzoldt

[Berlin,]

16[14]

April 1914[1]

Highly

esteemed

Colleague,[2]

I

read

your

comments

on

relativity

theory

in

the

Zeitschr. für

posit.

Philoso-

phie

with much

pleasure.[3]

From

it

I

see

with astonishment

that

you

are

closer

to

me

in

your

understanding

of

the

subject,

as

well

as

with

regard to

the

sources

from which

you

draw

your

scientific

convictions,

than

my

true

colleagues

in

the

field, even as

far

as

they

are

unconditional

supporters

of

relativity

theory.[4]

Af-

ter

great

exertion I have

now

succeeded in

establishing proof

that the

gravitation

equations

formed

last

year

have

a very high degree

of covariance with acceleration

transformations.[5]

Seen from the

physical

standpoint,

rotation

and acceleration

prove

to

be

entirely

relative;[6]

there

is

no

distinction

between

a

“real” gravita-

tional

field

and

an

“apparent”

gravitational field

produced through

the

accelera-

tion of

the

reference

system.

In

both

fields

the

same

field

equations

of

gravitation

apply.-

The

only

point

in

regard

to

which

I

do

not

agree

with

your

representations

is

the

matter of

the

moving

clock

(38).[7]

Relativity theory

allows

the strict

con-

clusion

that

a

clock U'

moving uniformly

and in

a

straight

line relative to

the

“justified”

reference

system

K travels

slower

(seen

from

K)

than

identically

con-

structed

clocks

U

at rest in

K

with which

we measure

the time

in

K.

We

know

nothing though

about

how

U'

proceeds

relative

to

K

while

U' is

in accelerated

motion.

But the

traveling speed

of U' relative

to

K

can

only

be influenced

finitely

by

a

finite acceleration.

Thus,

if

we

allow U'

to

describe

a

closed

path

relative

to

K in such

a way

that U''s

acceleration times

disappear

against

U''s

times while

moving

in

a

straight

line

(all

seen

relative

to K),

we can

then

disregard

the

influ-

ence

of acceleration

times

on

the

angles

traveled

by

the

hands

of

clock U'.

Then

we

must

conclude that

the

hands of

U'

advance

slower

while

traveling along a

closed

polygon[al path]

than

the hands of

an

identically designed

clock

that

was

constantly at

rest relative to

K.

On closer consideration of

this

case, doubtlessly

you

also

will

have to

come

to this result.

I would be

very pleased

if

we were

to

see

each

other

one

day

soon so

that

we

can

discuss

this

question

of

common

interest

to

us

both.

With

regards, your colleague

Einstein

Kais. Wilh.

Inst.

of

Phys. Chemistry.

Dahlem.