486

DOC.

470 FEBRUARY

1918

through

the

Lorentz

transformation;

the

importance

of

special

relativity

thus

ex-

tends

only

to

the

consideration

of

regions

that

are

small

enough

to

be

regarded

with

sufficient

precision

as

Euclidean

(Galilean).

From

the last

exposition

in

your

letter

I unfortunately

see,

as

in

many

other

instances

already,

that

my Academy paper

“Cosmol. Considerations”

is

being

totally

misunderstood.[7]

Apparently

I

did

not

express myself precisely enough.

The

equations

Guv

v

~

-g^T")

should be

exactly

valid

everywhere.

The

T44’s are

thus

supposed

to differ from

zero

only

in

the

interior

of

the

stars

but

vanish

everywhere

else.

If

I

imagine

the

universe divided into

regions

of

equal

size,

each of

which

contains

on

average

1,000

fixed

stars,

then

each

of

these

regions

will

contain

approximately

the

same

amount

of

mass.

I.e.,

I make

the

hypothesis

that

apart from

the

local concentration in

stars,

the matter

is

uniformly

distributed

on

the

large

scale.

This matter

I

replace,

for

the

sake of

convenience,

with

homogeneously

distributed

matter

of

the

same

mean

density.

In

this

way,

the

grav.

field’s

local structure

is admittedly

changed,

or

disturbed

compared

to

reality.

However,

the

metric

character

of

this

field

will

be

preserved

on

the

large scale,

so

I

am

correctly

informed

about the

geometric

nature of

the

universe

on

the

large scale. Thus,

in

this

consideration

I

abstract

totally

from

the

structure of

the

field

in

spaces

of

the

order of

magnitude

or

smaller

than the

distance

from

neighboring

fixed stars.-

Finally,

I note

that

Michelson’s

experiment

must

always

come

out

negatively

according

to

the

general

theory

as

well,

in the

case

where the mirror

structure

is

so

small and in such

a

state of

motion

that the

guv’s,

with

reference

to

the

structure

as a

coordinate

system,

are

constant

enough

in

the

relevant

space.-

Now I

believe

I

have addressed

everything you

mentioned in

your

letter.

I

think

we

shall

come

to

understand

each other’s

standpoint

by

this

means

of

“successive

approximation.”

With best

regards, yours truly,

A. Einstein.