232

DOC.

235 JULY

1916

235. To

Willem

de

Sitter

[Berlin,]

15 July 1916

Dear

Colleague,

Many

thanks

for

your long

letter.

I

agree

with

your

calculation.

You

are

quite

right,

of

course,

that

my specialization

of

the coordinate

system

by

the

condition V-g

=

1

is not

a

complete one,

so

boundary

conditions would

not suffice to

make

the mathematical

problem

of

the determination

of the

guv's

unique.[1]

After

all,

substitutions

with functional

determinant

1

exist

that

leave

the

boundary

region

untransformed.

It

would be

very

nice if

the

[coordinate]

system

could be

specialized

further

in

a

natural

way,

if

only

in

the interest

of

better

comparability

of

found solutions.

But

I have not been able to find

anything

of

the

sort.

The

conditions added

by

me

in

the

case

of

the

mass-point

overdetermine

the

problem

without,

however,

contradicting

one

another. The

three

conditions

gi4

=

0

do not

yet

suffice.[2] For,

a

purely

spatial

transformation

can

still be

performed

with

subst.

determinant

1,

which

destroys

the

point

symmetry.

It

is

not

good

if in

my

letter

I

called

the

V-g

system

“Galilean.”[3]

Only

a

space

in which all

the

guv's

are

constant

can

be called

that. But there

it

is

not

just

the

“space”

that

is

“Galilean”

but the

“space”

together

with

the

frame

of

reference,

which

makes

the

guv's

into

constants.

Nevertheless,

these

are

only

questions

of definition

about

which

one

does not have

to

rack

one’s

brains much.

What

you say

there about

“true” and

“apparent”

is correct

in

principle.

What

I

mean

in

my

addendum

is

the

following.[4]

When

I

find

some

process

or

other,

e.g.,

a

wave

process,

as a

solution to

the

differential

equations,

two

possibilities

exist.

Either

such

wave

processes exist,

no

matter how I

may

have chosen

the

reference

system,

or

such kinds of

wave

processes

do not exist when

[I]

choose

the coordinate

system

in

a

particular

manner.

If the

latter

is

the

case,

I

can

then

denote the

relevant

process (because

it

can

be “transformed

away”),

in

a

certain

sense

as an

“unreal”

process.

“Unreal”

then

simply

means

“can be

transformed

away.”

But it

is better,

of

course,

to avoid such

words,

which

give

rise to

unclarity.

One

can say:

the

coordinate choice

according

to

the

condition V-g

=

1

is

simple

or

advantageous

to

the

extent

that

with

this

choice

only

waves

of

the

3rd

type[5]

occur. (For

the

calculation, however, your

coordinate choice

is

preferable.)

Best

regards, yours,

A.

Einstein.