DOC. 411
JUNE
1912 317
IV.
Req.
of
the
Isotropy
of
the
Velocity
of
Light
in
the
Infin.
Small
[Isotropy-Req.].
One
formulates
this
requirement
in
that
one
states
that
among
all
of
the
imaginable
X, fi,
v
coordinate
systems
there
exists at
least
one
that shares
with
ft
the
following
properties
with
respect
to the
propagation
of
light,
which
I
am
going
to
explain
straightaway.
From
laboratory point
P0(X0,
/x0,
v0)
one
sends
out
a light impulse
in all
directions
at
the
moment
when
the
hand of
its wall-clock
indicates
ft0.
Now
one
considers the
ensemble of
all
those
laboratory points
whose wall clocks
were
caught
by our light
impulse as
their hands indicated
ft.
The
X,
jjl,
v
of
all
these
points
are
through
an
equation
F(v)
= S(A0,
|j.0,
v0;
ü0,
ü)
(4)
Adducing
the
veloc.-of-light
-
stationar.
req.
III
means
first
of
all
that
on
the
right-
hand side
ü and
ft0
occur
only
in
the
connection
ft
-
ft0.-
Hence the
equation
for
our light
shell
reads
F(v)
=
i|/(Ao,n0,
v0;
ft-öo)
(5)
o
Some
requirements
with
regard
to
optical
phenomena in
the
stationary gravitational
field.
Introductory
remark:
Let each
individual
point
P of the
station.-gravit.-laboratory
at rest
be
uniquely
characterized
by
three numbers
X,
/x,
v
that remain
permanently
associated
with
it. Furthermore,
each
event
at
point
P
should also be characterized
by
the
time
number
ft.
Only
later
on
will the
total arbitrariness
in the choice
of
this
system
of four
numbers
be
successively
reduced
by
some
requirements.
I
now
enumerate
a
series
of
requirements,
one or
another
of which
you
will
probably
reject.
I. Conservativeness
of
the
Light
Paths
["Path-Conserv.-Req"]:
If there
once
existed
a
light ray
that
passed through
the
lab.
points
A,
B, C,
....
F,
G,
then
A,
B,
....
F,
G shall
always
be
a possible light
path.
II.
Reversibility
of the
Light Rays
["Path-Revers.-Req."]:
If
A, B,
....
F,
G
is
a
possible light
path,
then
so
is
also
G,
F,
....
B,
A.
III. Stationariness of
the
Velocity-of-Light
Value
go
["oo-Station-Req:"]
If
a
light signal
passes through two-arbitrarily
chosen-laboratory
points
P0
·
X0
A*
o
v
0
A
and
P
V
and strikes them
when the
hand of
the wall clocks
at
these
two laboratory
points
are
at
positions
ft0
and
ft,
then
we
shall have
ft
-
ft0 =
F(X,fi, v;
A0,/i0, v0)
(1)
i.e.,
even
though
the
difference
in
the
positions
of the
hands
depends
on
the
positions
of
the
two laboratory points, it
should
show the
same
value
for
all consecutive
light signals.