654

DOC.

626

SEPTEMBER

1918

626. To Hermann

Weyl

Berlin, 27 September

1918

Dear

Colleague,

I

was

just

busy

with

your

new paper[1]

when

your

letter

arrived.[2]

It

is

a

pleasure beyond

words for

me

to

read

your scrupulously

thought-out

things.

The

division

into the three

theoretical

themes

is

very

effective

and

clear.[3]

However,

the

point

of

sacrificing congruency

while

keeping similarity

does not

seem

to work

so

naturally

for

me.[4]

You

know,

of

course,

how I conceive

the relation

to

reality;

nothing

has

changed

in this

regard.[5]

I know how much easier

it

is

to convince

people

than

to find

truths,

especially

for

someone

who

is

such

an

incredible master

of

exposition

as

you

are.

But

ultimately,

far be

it

from

me

to be

presumptuous;

I

can

be mistaken

here,

as

I

have been countless times before. In

a

couple

of

years

it

will

be obvious whose

eyes saw more

clearly.

And

I

know

precisely

that the

only

goal

either

of

us

has

is to

see

the truth.

From

what

you

wrote

me,

I

was

very impressed by

the

fact

that the statics

comes

out

right,

and this

with

a

A

still at

one’s

disposal,

also

that

an

energy

equation,

EdIki/dxk

=

0,

results.[6]

This does indeed

mean more

to

me

than the

results

I already

knew

about

previously.

I

am

looking

forward

to

the

opportu-

nity

of

studying

this

more

closely.

The

expression

Rguvdxudxv

for

the

measured

length[7]

is,

in

my opinion,

by no means

acceptable, however,

when

the

curvature

invariant

is

taken

for

R,

because R

is

very dependent

on

the

mass

density.

A

very

small

change

in the

measurement

path

would have

a

very

pronounced

influence

on

the

integral

of

the

square

root

of this

quantity.[8]

Furthermore, although

it

is

correct

that

you

did

not

assert

anywhere

that

your geodesic

line

was

the

path

of

an uncharged

point-mass,[9]

nonetheless

this

does

appear necessary

to

me

without

extra

proof.

For

the

only

type

of world line

preferred

in

reality must

surely

cor-

respond

to

the

world line

preferred by

the

theory;

I at

least

cannot

think

of

any

other

arrangement.

If

this

is

so,

however,

we

encounter

a

contradiction with

your

theory

with the

energy principle,

in

the

following

manner.

The

vector potential

p1p2p3

would act

as

a

moving

force

upon

a

static

point;

a

permanent magnet

generates

closed lines

dx1

:

dx2

:

dx3

=

p1

:

p2

:

p3.[10]

Of

course,

I

know

very

well

that the

state of

the

theory,

as

I

have

set

it

up,

is

not

a

satisfactory

one, disregarding

the

fact

that

matter remains

unexplained.

The unrelated

juxtapositioning

of

the

gravitation

terms, electromagnetic

terms,

and

A-terms

is

undeniably a

product of

resignation.

I

share

your

firm conviction

that this must and

will

be otherwise.

I just

do

not

believe

that the

route

you

have embarked

on

is

the

right one,

as

finely

thought-out

as

it

is.

In

the

end,

the

answer

must include

that the

action densities do

not

have

to

be stuck

together