468

DOC.

460

FEBRUARY

1918

p

means

the

density

of

the stellar

matter

(conceived

as

evenly distributed)

in

the

world,

compared

to

the

density

of

liquid

water.

(2)nR,

the

length

in

natural

measure

of

the

geodesically

measured circumfer-

ence

of

the

world[4]

(i.e.,

measured with

the

cm

scale

(= 15

531.-

wavel[ength]

of

the

Cd

line))

That this

is

the

meaning

of

p

and R

according

to

my papers

is

easily

drawn from

my

considerations. The

crux

of

the

matter is

that

R

must not

be conceived

as

a

“coordinate

length”

but

as a

length

in

“natural

measure,”

and

thus

is

defined,

just

as p,

independently

of

the

coordinate

choice.-[5]

What

divides

us

most of

all is ultimately

the

circumstance

that

you

do

not

take the

standpoint I

call relativistic:

the

behavior

(continuation

of the

tempo[ral]

course

of

states)

of

every single physical body

is

such

that

it

is

uniquely

deter-

mined

by

its

own

state and

by

those of all

the other

bodies

(this

statement

must,

of

course,

be

interpreted

without

instantaneous action

at

a

distance). Only

the

observable

objects of

our

physical

world

are

to

be

understood

here

as

“natural

bodies.” The

varying

behaviors of

S1

and

S2

(in my pamphlet)[6]

must be

ex-

plained

in

that the

state of motion

of

the

remaining

world of bodies relative to

S1

is

different from

the

one

relative to

S2.

Any

other

interpretation is

not relativistic.

(Mach

has

already recognized

this

very

clearly.)

Now,

if

you

do not share

this

relativistic

point of

view,

then I

do

not

un-

derstand

in the least

why you

assign any significance

to

the

general

covariance

requirement.[7]

Either the

hypothesis

that

in

physics only

relative motions exist

is

taken

seriously,

i.e.,

that

only

relative motion

appears

as

efficacious in laws of

nature,

or

absolute

space

is

introduced

as an

independent

element in

the

causal

construction;

a

compromise point

of

view

between

these

two

does

not

exist.

In

justification

of

the

“Cosmological

Considerations,”

the

following:[8]

What

happens

at

infinity

is

all

the

same

to

me as

well. Nevertheless, I must

know

whether

what

I interpret

as

the

relativity

principle can

be

thought through

with-

out

encountering

contradictions.[9] For

this,

it

is

necessary

that the

gravitational

field

be

determined

entirely by

matter[10]

which, however,

is not true

for

the

quasi-Euclidean

world. The

latter rather

has

the

following

properties:

1)

The

mean

density (in

natural

measure)

of

matter

inside

a

spherical

surface

must

go

to

zero

with

the

spherical

surface’s radius.

(That

is,

the

world

is

essentially empty

and

has

a center.)