DOCUMENT 375 AUGUST

1917

509

my

heart,

and

for

your very flattering

and favorable

opinion

of

the

mathematical consider-

ations in

my

latest

papers:

in

any case,

the main

credit

goes

to

you

for

opening up such

wide horizons in natural

philosophy

these

new

fields

of

research.

Now to

our

amicable

controversy.

As I believe

I

also indicated in

a

note I wrote

a

few

months

ago

to

my colleague

Grossmann,[3] I

understand

very

well

your

reluctance to

occu-

py

yourself

with the

not

very

fruitful

solution

represented

by

the

equations[4]

(1)

rik

+

Aik =

0

(i,k

=

0,1,2,3)

(Tik energy

tensor,

Aik

gravitational

tensor).

I

acknowledge

the

importance

of

your objec-

tion that

in this

way

the

energy principle completely

loses its heuristic

value,

in

that

it does

not

a priori

exclude

any

(or

almost

any) physical process

because it would suffice to

modify

the

ds2

in the

appropriate way.

You

point

out that in

abandoning (1),

or

rather

their

interpretation,

the

energy

contribut-

ed

by

the field

can

be

understood

as something

dependent

on

the form

of

ds2,

analogous

to

what

is done

concerning

the

concept

of

field

strength.

If

one

writes the

equations

of

mo-

tion in the form

(2)

d2x¡

ds2

dxjdxk

ds ds

and carries out the

necessary verification,

the

analogy

between

the

right-hand

side

(which

defines

neither

a

covariant

system nor a

contravariant

one)

and the

ordinary

concept

of

force is made

explicit;

in your

view,

your

tav

(which

do

not constitute

a tensor)

should be

dealt with in the

same way.

I

have

no objections

to

your

view;

on

the

contrary,

I

am

inclined

to

assume

that it

is sound,

as

is

always

the

case

with the intuition

of

a genius.

But

I would

need to

see,

in

appropriately explicated step-by-step reasoning,

how,

starting

from

(2),

one

actually

arrives at the

ordinary

concept

of

force

(or

at least how

one

should

go

about

it).

I shall

give

the matter

more

thought

when

circumstance

(or inspiration)

is

favorable,

but

it is from

you

in the first

place

that

I

expect a

solution.

As I

am

for

now

in this state

of

cautious

reserve,

I would like to defend

my

tensor

Aik,

at

least

with

respect

to its

logical

soundness.

Thus, I point

out that

no

contradiction such

as

you

believe to

find,

exists in the

example

of

a

pendulum clock,[5]

considered in two different

systems

K and K',

of

which

the

first is

stationary (in

the Newtonian

sense

of

the

word)

and

the

second

moves

with constant acceleration. You

say:

a)

with respect to

K,

the energy tensor

is

zero,

because

the

guv

are

constant;

b) but this

is

not the case with respect to

K';

on the contrary, the physical process shows a

transformation

of

energy into heat.

c) given the invariant

character of

the

vanishing

of

a

tensor, the simultaneous occurrence

of

a) and b) implies that the premises are flawed.

I object

to

a),

because

we can very

well

argue

that

the

guv

are

constant outside

of

pon-

derable

bodies but not inside

your

pendulum

clock.

Concerning

the final

point

of

your

letter

(response

4),

it is not linked

to

the

particular

form

of

your

tav,

if

I

understand

correctly,

but holds

just as

well for

my Aik.

In

fact,

it

seems

to

me

that

one can

also obtain from

(1)

the behavior at

°°,

by

making use

of

the fact

that

the