DOC.
411
JUNE
1912 311
411.
From Paul Ehrenfest
[Kanuka,
29
June
1912][1]
Dear
Mr.
Einstein:
Thank
you
so
much for
your
kind
letter![2]
I
needed
it
badly!
Let
me now
try
to
explain
the theorem about
which I
spoke
in
my
last two
letters.[3] Unfortunately,
I cannot
formulate
it
briefly
if
misunderstandings
are
to be avoided.
o
First
I
confine
myself
to
the
case
of
a
two-dimensional world-hence
I
operate
with
world lines
in
the
x,
y,
t-space.
(Extension
to
the
x,
y,
z,
t-space
will
come
only
later
on,
below!)
Suppose
a
two-dimensional
laboratory
moves
in
some
nonuniform
way
before
the
eyes
of
God. Some field
of
curved world lines in the
x, y,
t
space
records
this
motion the
way
God
sees
it.
My
problem is
this:
To
seek the
most
general
field
of
world
lines
that
satisfies
the
two
optical requirements
A
and
B
that I
am
about
to
formulate.
Requirement
A:
Suppose
that
at time
t1
from
point
A
of the
laboratory
a
light ray
is
sent out
that
traverses
points
B, C,
D,
E,
F
of
the
laboratory.
We
require:
if at
any
other
time,
t2,
a
light signal
is
again
sent
out from
laboratory
point
A
that
passes through
point
B,
it shall
again
pass through
points
C, D,
E,
F
on
its
journey,
and
this shall
be the
case no
matter
which
points A
and B
of the
laboratory
have
been
chosen.
["Conservativeness"
of the
path
of
the
ray][4]
Requirement
B: Suppose
that
at
time t1,
from
point
A
traverses
points
B C
D
E F of the
laboratory.
We
require:
if
at
any
other
time
t1' a
light signal
is sent,
conversely,
from
laboratory point
F
to
A,
it
shall
now
traverse
the series of
laboratory
points
in
the
reverse
order
F,
E,
D,
C,
B,
A.
And
this
too
shall
hold
again
for
an
arbitrary
choice
of the
laboratory
points
A
and F.
["Reversibility"
of the
path
of the
ray]
Intermezzo: Is there
any
sense
in
working
on
this
problem?
I believe
that there
is
only
one
person
who
can
decide
on
this:
you.
But
I
will set
forth the
reasons
why
I
believe
that
it
makes
sense.
You would
surely
be
pleased
if
you
had
the
following
theorem:
an
arbitrary
finite
stationary gravitational
field
can
be
conceived
of
as a
laboratory
that has been
accelerating
but
is
now
transformed
to rest
and
is
free
of
gravitational
fields.
I
know
of
three
papers
on
gravitation
by
you[5]
(In
your
letter
you
speak
of
a
"latest paper"-is
this
perhaps
a
fourth
one?!)[6]
And
I believe to have
correctly
understood that
you
do not
assert
the
equivalence
of
gravitation-free
-
accelerating
=
stationary
-
gravitation-endowed laboratory
for
finite
regions
of
space
but
only
for
infinitely
small
regions
of
space.-[7]