DOCS.

226,

227

JUNE

1916 223

irregular

motion.

However,

this fundamental

difference

between uniform

and

irregular

[motion]

does

not

find direct

expression

in

the ether

notion;

it rather

attempts to

prove

constantly

uniform

motion.

With

affectionate

greetings

and best wishes for

your

wife’s

health,[11]

yours,

A.

Einstein.

227. To

Willem

de

Sitter

[Berlin,]

22

June

1916

Highly

esteemed

Colleague,

Your letter

pleased me very

much and

inspired me

tremendously.[1]

For

I

found

that the

gravitation

equations

in first-order

approximation

can

be solved

exactly by

means

of

retarded

potentials,

if the condition for

the

coordinate choice

V-g

=

1

is abandoned.[2]

Your solution for

the

mass-point

is

then

the

result

upon specialization

to

this

case.[3] Obviously

your

solution differs from

my

old

one[4] merely

in

the

choice of

coordinate

system,

but

not

intrinsically.

As

it

is, one

could

think that

the coordinate

choice

V-g

=

1

was

not at

all

natural.

However,

I

have found

a

very interesting physical justification

for

the

latter.

I

denote

the

V-g

system

as

K,

the

generalized

de

Sitter

system[5] as

K'.

We

now inquire

about

plane gravitational

waves.[6]

In

system

K'

I

find

3 types

of

waves,

of

which

only one

is

connected to

energy

transportation,

however. In

system

K,

by

contrast,

only

this

energy-carrying

type

is

present.

What

does this mean? This

means

that

the first two

types

of

waves

obtained

with

K'

do

not

exist in

reality

but

are

simulated

by

the coordinate

system’s

wavelike

motions

against

Galilean

space.[7]

The (V-g

=

1)

=

system

thus

excludes

undulatorily

moving

reference

systems,

which simulate

energyless

gravitational

waves.

System

K'

is

nonetheless useful for

the

integration

of

the

field

equations

in first-order

approximation.

I

am

curious

about

your

Moon

paper[8]

and

am

anyway delighted

that

you

like

the

general theory

of

relativity

so

much.

Cordial

regards,

yours very truly,

A. Einstein.