316
DOC.
411
JUNE
1912
Some
requirements regarding
optical
phenomena
in
a
stationary gravitational
field.
Provisional
postulate:
Let each
individual
point
P
of
the
station.-gravitat.-laboratory
at rest
be
uniquely
characterized
by
three
numbers
X,
fx,
v
that
are
permanently
associated
with
it. (For
the
present,
A, /x,
v
do
not
yet
have
to
form
a
rectangular
coordinate
system!)
In addition,
the
time
of
any
event at
point
P
shall be
characterized
by
the time-number ü.-
I
now
enumerate
a
series of
requirements,
one or
the other of
which
you
will
perhaps
reject.
I.
Requirement
of the
Conservativeness
of the
Light Ray
Paths.
["Path-Conserv.
req."]:
If
at
some
point
of
time
there
was a
light ray
that
passed through points
A,
B,
C,
D,
E,
F,
G
of
the
laboratory,
then
A B C
D E F
G shall
always
remain
a
possible light
path.
II.
Requirement
of
the
Reversibility
of the
Light Rays ["Ray-Revers.
Req"]:
If
A
B C D
E
F
G
is
a
possible light path,
then
G
F E
D C B
A is
also
a possible light
path.
III.
Requirement
of the Stationariness
of
the
Velocity-of-Light
Value
[Light-Vel-Station-
req.
].
If several
light signals
S'
S"
S"'
....
pass
one
after another
through
both
points
P and
N of the
laboratory,
and if
M', N';
M",
üN";
üM"',
ftN"'
are
the
("wall")
times
at which
these
signals
pass through
M
and
N,
then
we
have
N'
-
M'
=
N"
-
M"
=
N"'
-
M"'
=
····
=
(1)
Inferences
from this:
IIIa. If
light
impulses
I', I",
I"'
...
start
out
from
M
at
(the
wall
times)
M',
M",
M"'
·· ?
and travel
to
laboratory point
N
and from
there
immediately
back
(reflected),
so
that
they
return
to
M
at
the wall-clock times (M'),
($M"),
(öM"'),
···
,
then
we
have[18]
(M')
-
M'
=
(M")
-
M"
=
......
=
(M-N-M)
(2)
IIIb. If
one, likewise,
sends
light rays
from
labor.
point
M to
another
point
P of
the
laboratory,
and
from
there
immediately
back to
M,
then
,
ir
Ä-A-M
I
(3)
tt
|
Mi
A/
.
N-M)
I
J.t.vir.t.'iv.v.v.v.'.v.t.v.v.v.v.vŦ ·
ŧ*ŧŧ
is
a
fixed
numerical ratio that
does not
depend
on
when
the
signals
are
sent from
M
to
N or
P
This proposition
is
very
important
to me at
a
later
point