294
DOC. 393 MAY
1912
393.
From Paul Ehrenfest
[Rybinsk,
14
May
1912][1]
Highly
esteemed,
dear
Mr.
Einstein:
My
wife
and
I have
traveled
up
and down
the
Volga
for almost
10
days.[2]
At the
southernmost
point
of
our
trip (Samara)
I received
the
news
that
a
"scientific"
postcard
from
you[3]
is
waiting
for
me
in
St. Petersburg. I
don't
know
what
it contains,
but
am
already
very
curious.-The
following
letter
is
intended
more as a
greeting
from
the
trip-and
not
as some
kind
of
important
communication! It will be
long mainly
because
we
have to wait
here
in the
waiting room
for
a
train
for several
hours.[4]-It
is
not
even
necessary
for
you
to
read
it-it
is
only
necessary
for
me
to
write it
so as
to
bring
order
to
a
long
train of
thought.
-
o -
Problem:
To determine the
most
general
world-line field
that
is equivalent to
a
stationary
gravitational
field.
Solution:
If,
for
the
sake of
simplicity,
we
restrict
ourselves to
a
three-dimensional
"world"-space
x,
y, t,
then
this
most
general
world-line field must have
the
following
differential
form:
dx
=
ßt
-
yy
+
p
,
dy
=
yx
+
at
+
q
dt
ay
-
ßx
+
r
' dt
ay
-
ßx
+
r
Remark:
a,
ß,
y,
p,
q,
r
arbitrary
constants.
If
one
sets
a
=
y
=
p
=
q
=
r
=
0 and ß
=
1, one
has
dx-
=
t-
,
dy
=
0
thus,
hyperbolic
motion
as
(1st special
case.)[5]
dt
x
dt
2d
special
case:
p
=
q
=
0, a
=
ß
=
0, y
=
r
=
1
-
=
-y
dy-
=
x
thus, uniform
rotation
dt dt