DOC. 47 JANUARY

1915 59

47. To Hendrik A. Lorentz

Berlin,

13

Wittelsbacher

St.,

23 January 1915

Highly

esteemed and dear

Colleague,

I have

long

been

eagerly awaiting your

detailed

letter,[1]

the

existence of which

de

Haas revealed to

me

after

his arrival from

Holland.[2] I

thank

you very

much for

having

spent

so

much time and effort

on

it. Before

I

answer

the

individual

points,

however,

I must

tell

you

that

in

the

course

of

our

collaboration

I

came

to

cherish

and

respect

your

son-in-law

exceedingly.

To

our

great delight

the

experiment

on magnetism

has

turned

out

positively.

Now de

Haas has devised

an even

nicer

investigative procedure

in which

the

use

of

resonance

can

even

be

dispensed

with.

With

it

the

reason

for

why

the

magnetic

axis and

the rotational

axis of

the Earth

nearly

coincide has

now

been

found.[3]

If

anyone

had

to relive

exactly

the

same

struggles

here in

the

considerations

on general

relativity,

I’d

ardently

wish

that

it be

you.

But

I

see

from the

first

part

of

your

letter that

this has

not

yet happened completely.

Had

I

committed

the

errors

you

rebuke

me

for

regarding

the

vanishing

of

the

Axv’s,

then

I

would

deserve to have

ink, pen,

and

paper

taken

away

from

me once

and for

all!

In

§12

the

Axv’s

refer to

a

coordinate

transformation

with

Axv’s

(&

deriva-

tives) vanishing

at

the boundaries.[4] As

you

know,

in

this

§

it

was

intended to

show

that

acceptance

of

such

transformations

prohibits

a

complete

mathematical

formulation

of

the

laws

of

gravitational fields.

From

§13

onward

the

Axv’s

relate

to

the

justified

transformations

for which

the

Axv’s along

with their

derivatives

do not vanish

at

the

regional

boundaries.[5]

Equations

65-65b

apply

to arbitrary

infinitesimal

(constant)

transformations.

Now,

when

I

say

about

(65b):

“It vanishes

if

the

Au

and

dAxu/dxv

terms

vanish,”

it

was

not

meant

to

mean

that this

would be

so

in

the

case

of

“justified”

trans-

formations;

for

the

latter,

this

had rather

to

be considered

a

priori

as

out of

the

question

according

to

§12.

When

on

the

second

half of

page

1070 I

examine

the transformations

K-K'-K",

etc.,

with definite border

coordinates,

under

no

condition

are

these

transformations

justified

ones.

This becomes

clear,

of

course,

from

the

fact

that

the observation

serves

to select from

among

these

systems only

one as

justified, namely,

the

one

with

an

extreme

J.

If

K

is

this

system,

then K

is

justified,

K',

K"

etc., however, are

not

justified. Therefore,

the transformation

K-K'

is

not

a

justified

one.

In the

reflections

of

§14,

which form

the

crux

of

the

whole

problem,

the coordinate

transformation

is

to be conceived of in

such

a

way

that the

Axu"

and

dAxu/dxv

terms do not vanish at

the

boundaries;

rather,

the

coordinate

system changes

(infinitesimally) over

the

entire

expanse

of

the

four–