352

DOCS.

469,

470

AUGUST

1913

469. To

Heike

Kamerlingh

Onnes

Hofstr.

116,

Zurich

[16

August 1913]

Dear

Colleague,

Having

returned

from

my

trip,[1]

I

would be

delighted to

visit

you

one

of these

days.

Please

specify

a

day,

hour,

and

place

convenient

to

you.

With

kindest

regards

from

my family

to

yours,

yours very truly,

A.

Einstein

470. To

Hendrik

A.

Lorentz

Zurich, 16 August

[1913][1]

Dear and esteemed

Prof.

Lorentz:

I must

add

a

few

things

to

the

scientific

part

of

my

letter.[2]

You have

broached

the

question

of whether

one

is

justified

in

assuming

that the

stress-energy

tensor

is

always

symmetric;[3]

Minkowski,

e.g.,

used

a non-symmetric

tensor.[4]

I believe with

Laue that

in

this

instance

Minkowski

was

mistaken.[5]

The

equivalence

of the inertial

mass

and

the

energy,

which

is certainly

correct-at

least for

closed systems-can

be

expressed

most

simply by

Xt

=

Tx.[6]

In the

customary theory

of

relativity

one

will

therefore

certainly

persist

in

viewing

the

tensor

as symmetric.

Hence

it

is

also most

natural

to

assume

in

our

case[7]

that the covariant and contravariant

stress-energy

tensors

are symmetric.

Furthermore,

yesterday

I

found

out to

my greatest delight

that the doubts

regarding

the

gravitation theory,

which

I expressed

in

my

last

letter

as

well

as

in

the

paper,

are

not

appropriate.

The solution of

the matter

seems

to

me

to

be

as

follows:

The

expression

for

the

energy principle

for matter

& gravitational

field

taken

together is

an

equation

of the

dF

form

(19),[8]

i.e.,

of the

form

^

Fuv-dxv-

=

0;

starting out

from this

assumption,

I

set

up

equations

(18).[9]

But

a

consideration of

the

general

differential

operators

of the

absolute

differential

calculus shows

that

an

equation

so

constructed

is

never

absolutely

covariant.

Thus,

by

postulating

the

existence

of

such

an equation, we

tacitly specialized

the

choice

of the reference

system.

We

restricted

ourselves to

the

use

of

such

reference

systems

with

respect to

which

the

law of momentum

and

energy

conservation holds in this form.

It

turns out

that

if

one

privileges

such

reference

systems,

then

only more

general

linear

transformations remain

as

the

only ones

that

are justified.[10]

Thus,

in

a

word:

By

postulating

the conservation

law,

one

arrives

at

a

highly

determined

choice

of

the

reference system

and

the admissible substitutions.