260

DOC.

272 NOVEMBER

1916

272. From

Willem

de

Sitter

Leyden,

1

November

1916

Dear Mr.

Einstein,

I

am sending you

today

a

separate

offprint

of

a

little

popular

exposition

of

the

general

theory of relativity which

I

have

published

in

an

English

astronomical

journal.[1]

I

have been

thinking

much

about the

relativity

of

inertia

and

about

distant

masses,[2]

and

the

longer

I

think about

it,

the

more

troubling

your

hypothesis

becomes for

me.[3] I

mean

the

hypothesis

that

(a)

at

infinity

the

gij's are

such

that

the

Minkowski

cones

become

planes

(i.e.,

three-dimensional flat

spaces),

and

that

(b)

far

beyond

all known

material

bodies,

as-yet-unknown masses

exist which

produce

the

effect

that,

in

regions

of

space

and time

we

know

about,

the

special

theory

of

relativity is

valid in

the

absence of

mass,

thus

that the

Minkowski

cones

have

a

finite

aperture. First,

a

question.

As I

understand the

hypothesis,

not

only

does it

predict

that the

gij's

degenerate

in

the

way

mentioned for infinite values

of the

space

variables

x1 x2

x3,

but

also

for

infinite values of

the

time variables

x4.

Is

this

correct,

or

do

the

gij's remain

Galilean-or

approximately

Galilean-for

x4

=

oo

but

x1, x2,

x3

finite? If

I

am

right,

the

hypothesis

would

thus

make

the

universe finite

not

only

in

space

but

also in time.

We

know

nothing

about

the

infinitely

distant

past

and

about the

infinitely

distant

future-therefore,

no

observations

can

tell

us

that there

has

always

been

a

universe and

that there

always

will

be

a

universe.

It

is not

the

finiteness,

in

principle,

in

space

and

time

which

bothers

me,

but

the

conviction

that the

boundary,

the

“envelope,”

will

always

remain

hypothetical

and

will

never

be observed.

Now

we can

say:

the

sources

of inertia

lie

beyond

the

Milky

Way,

but

when

our

grandchildren

make

an

invention

that

enlarges

the

known world in

the

same

proportion

that

it

was

enlarged

300

years ago

through

the

invention of

the

telescope,

then the

envelope

will

simply

have

to

shift

farther

outwards

again.

From

this

I conclude

that

the

envelope

is

not

a

physical reality.

If

the

hypothesis

is

accepted,

one

would first want

to

get

a

[crude]

idea

of

where these

distant

masses are

and of what

they

are

composed; second,

how

the

inertia

comes

over

here from there. An

artificial

mechanism will be

invented. The

coordinate

system

with reference to

which

the

envelope

and

this

mechanism

are

at rest

will

also be defined.

Although

the

principle

of

relativity will

still hold

formally, effectively, we

shall have

the

old absolute

space

with the ether

back.

And

another

thing

as

well.

At

infinity, only

transformations

in which

t'

is

just

a

function of t

are permissible,[4]

hence,

no

Lorentz transformations,

for

ex.

Thus in

the

finite

realm,

no

exact Lorentz

transformations

may

be

performed

either, only

one

that,

as

far

as our

universe

extends,

coincides

very precisely

with