296
DOC.
394 MAY
1912
point
O
for the
resting light,
point
O"
for the
moving light
(Doppler
effect!),
because
we
must
not
forget
that
in
this time
the
centers
of
the
induced
spherical
waves
have
traversed
the
distance
v
·
R/C
behind the
grating
to
the
points
A", B",
C",
D"!
I
hope
that
you
will
admit that
I
am
right.-I
have
considered
in
truly
quite general
terms
the
proposition
that I
set
down
without
proof
in
my
note.[6]
I would be
very
grateful
if
you
would
tell
me
quite
briefly
whether the
proposition
I
recently wrote
down for
you
on a
postcard (about
the
most
general
world-line field
that
corresponds to
a
stationary
gravitational
field)[7]
is
of
any
interest
to
you.
If
so,
then
I
would like to
give
you a
clean
exposition
of the
thing.
At the
moment
I'm
only
taking
the
liberty
of
sketching
my
train of
thought to
you.
If the
gravitational field,
and thus also
the
light velocity
field,
is to
come
out
stationary,
then the
following
is
to be
demanded,
first and
foremost,
of the
"wall-clock
time"
Đ:
If
an
observer
sitting
at point
Ģ,77
of
the
laboratory
sends out
a
light signal
after
every
dĐ
seconds,
then
every
other observer
must
get
these
same
time
intervals
dĐ
between
consecutive
light signals
on
his wall clock.
Do
you acknowledge
this
"dO
demand"?!!
Now I take the world
lines
of the
laboratory points
in
the
heavenly x,y,t-space
and
observe the
cones
pair
that
corresponds
to
two
consecutive
dŪ
impulses
sent out
by an
observer
A.
They
intersect
the world line
of observer
B
at
two
points.
I
assume
that
I already
know
the
wall-
clock time
Đ
(for
the
given course
of the
world
lines)
as a
function
of
x,
y,
t
Đ
=
Ū(x,y,t)
then
I
demand that the
same
dĐ be
punched
out
by
the above-mentioned
cone
pair
on
the
world
lines
BB,
CC,
DD
of
all
possible
observers.
Sup-
dx dy
pose
that
and
are
given as functions
of
dt dt
__
=
A
(x,y,t)
dy
=
B(x,y,t)
dt
and
that
the
following
abbreviations
are
used
x,
y,
t