472

DOC.

463 FEBRUARY

1918

463. From Rudolf

Förster

Essen,

6

Kunigunda

St.,

16 February 1918

Esteemed

Professor,

I

thank

you kindly

for

your

nice

letter

of 17

January.[1]

Again

I

could not make

up my

mind to

answer

it

immediately,

since

very

many

questions I hoped to

clarify

were

passing

through

my

head.

Now

that the

full extent of

the

mathematical

difficulties has become evident

to

me, however,

I

cannot

postpone

it

any

longer.

Your

objections

to

the

expositions

in

my

earlier

letter[2] apparently

are

based

on

misunderstandings

for

which, owing

to

my

so

frugal

choice of

words,

I

myself

am

at fault.

1)

B12,34

=

B13,24 = B14,23 =

0

should

not

be

a

satisfactory

condition

but

only a necessary one

which allows

ds2 to

be

changed

into the

orthogonal

form.

2)

I

derived

directly

from

the transformation

formulas

my generalization

of

the

Riemann

tensor

Buv,Po

to

the

case

of

an

asymmetric

fundamental

tensor,

without

resorting

to

splitting

it into

a

symmetric

and

an

antisymmetric

component.

The

occurrence

of

the

connected

symmetric

contravariant

tensor suv

automatically

results

as a

requirement.

3)

If

guv

is

reduced in

the

specified

manner

to

suv

+

auv

and forms

the

guv's (or

suv's

or auv’s)

from

the determinant

of

the

guv's

(or

suv’s,

or auv)'s,

then under

no

circumstance

is

guv

= suv

=

auv.

Rather,

guv

- smv

depends

not

only

on

the

six

tensor

of the

auv's,

but

also

on

all the

suv’s

besides in

a

quite

complicated

way.

It

is

thus

not

correct

that

in

my

tentatively

suggested electromagnetic

field

equations

the

symmetric

and

antisymmetric components

separate like oil and

water.

This

separation

occurs,

in the form

I

have

used, only

in

the

2nd Maxwell

equation;

in

the

first

one,

the

guv's

enter

completely.

I

had

unfortunately

omitted

to

emphasize

this

explicitly.

4)

My

considerations

on

“gravitational

fields

that

are

derived

from

a

potential”

have of themselves

nothing

to do with those

on

the

asymmetric

fundamental

tensor; indeed,

they

are

in conflict with them to

a

certain extent. Whereas

the

introduction

of

the

asymmetric

tensor is

a

generalization,

that

of

the

potential

is

a

specialization.

Your

objection

that the

field

energy depends essentially

on

the

first derivatives

of

the

guv's

does

admittedly

apply

to

my

auv’s

but

not to

my

potential.[3]

I

have

abandoned

asymmetric

guv

again

for

another

reason

besides,

which

I

want to

go

into

now.

In

a

note

to

appear shortly

in

the

Astronomischen Nachrichten

under the

pseudonym Rudolf Bach,[4]

I

conduct

probability

considerations

on

the

attractive