484 DOC.

470

FEBRUARY

1918

470. To

Gustav

Mie

[Berlin,]

22 February

1918

Dear

Colleague,

First

of

all,

to

what

I

called

the

“relativistic stance” in

my

last

letter.[1] I

maintain

that this

requires

the

following

interpretation

regarding

inertia. If L

is

the actual

path

of

a

certain

freely moving body

and L'

is

one

deviating

from it

with identical

initial

conditions,

the relativistic

point

of

view

requires

that the

actually

described

path

L be

preferred

over

the,

from

the

logical

point

of

view,

equally possible

paths

L',

on

the

basis of

a

real

cause,

which has

the

preference

of L

over

L'

as a

consequence. According

to

the theorem

you

recapitulated,

nothing

but the

(relative) positions

and states of motion of all

the

remaining

bodies

present

in

the

world

can

act

as

such

a

real

cause.

These

must

determine

entirely

and

uniquely

the inertial

behavior of

our mass.

Mathematically

this

means:

the

guv’s

must

be

determined

completely by

the

Tuv's-up to

the

4

arbitrary

functions,

of

course,

which

corre-

spond

to

the

free

choice

of

coordinates.[2]

This

requirement

is

not satisfied

by

Newton’s

theory,

but

also

just

as

little

by

mine

as

long

as

the world

is

conceived

as

quasi-Euclidean.

For

then the

guv's

are

predominantly fixed

by

nonrelativistic

boundary

conditions at

infinity.

Then

no

real

cause

exists for the

preference

of path L

over

certain other

L''s

(rectilinear

ones

against

non-Galilean

rigid

coordinate

bodies).

It

is

in

this

sense

that

I

said

that

Newton’s theory violates

the

causality requirement;

but

Schlick

is

right

when

he finds

fault with this

form of

expression.[3]

I

agree fully

with the

quote

from

Schlick[4]

but

not

with

the

use

you

make of it.

I

do not

deny

that the

description

of

the

world

proves

simpler

when

a

reference

system

is

introduced relative to which

the Earth

rotates in

a

specific

way.

But

I

do

contest

that the

corresponding

preference

of

one

coordinate

system

has essential

significance.

You

say,

in

one case

the

guv's

must be

assigned

particular properties

not

determined

by

the

matter

and

that,

on

the other

hand,

this

was

not

the

case

for

a

“natural

coordinate

choice.” If

you were

right

in

this, though,

I

would

regard

my standpoint, indeed, my

whole

theory altogether,

as

untenable.

But

let

us see

how

this

holds

up.

When

we

consider

the

solar

system or, perhaps,

the

Milky

Way,

in

any

case,

only

a

part

of

the

universe,

then the

differential laws

are

the

same

in

both