DOCS.

658,

659

NOVEMBER

1918 697

658. To Arnold Berliner

[Berlin,

before

19

November

1918][1]

Dear Mr.

Berliner,

I

shall be

glad

to

give a

report

on

Nordstrom.[2] The

figures

are

incorrect.

I

shall sketch

the

correct

figures

with

the

request

that

they

be

incorporated

into

the

two columns in which

the

two

illustrations

of

the

clock

paradox are

described.[3]

Best

regards,

yours,

A.

Einstein.

659. From

Paul

Bernays

Göttingen,

43

Nikolausberger Way,

22

November

1918

Esteemed

Professor,

Thank

you very

much indeed for

your

kind

letter

in

answer!

In view of

my

too

imprecise

argumentation, I

hardly

deserved such

a

thorough

reply.[1]

I

am

answering your

letter

only

today

because

I

first wanted to allow

the

substance

of

your explanations

to

run

through

my

head for

a

while. These

con-

siderations

I

have been

engaging myself

in

were

not able to assist

me

with

a

certain

difficulty,

however,

with

regard

to

the

concept

of

the

rigid body,

and

I would

like

to

take the

liberty of

interrogating you

again on

this account.

It

involves

the

following:

As

far

as

I

understand

it,

a

body

can

count

as

rigid only

when

it

is

in “the

same” state of rest at

all

times,

given

a

suitable

division

of

space

and

time,

whereby

“the same”

means

that

every

establishable

property

of

the

body

that

can

be

expressed

as

invariant remains

unchanged. (Otherwise

I

would not know

how,

in

the

case

where

a

Euclidean

determination

of

mass

possibly

occurs

twice

at separate times,

a

return

to

the

same

state

should

be

guaranteed.)

Now,

the

invariantly expressible

determinations

of

a

Euclidean

body,

of

a

cube,

for

instance,

obviously

include not

only

the

angles

and

edge lengths

but

also

include,

for

ex.,

that

every

pair

of

points

of

an

interface

can

be

linked

together

with

a geodesic

line

lying completely

on

this surface

(where “geodesic”

relates

to

the

three-dimensional

space);

furthermore,

that

the

geodesic linkings

of

three

points

on

the

interface form

a

geodesic

triangle

with

the

angular

sum

7r.

Now,

it

seems

to

me

very doubtful, though,

that

for

any given

metric

field

the

division of

time

and

space

can

be executed in such

a way

that,

in

the

relevant