DOC
411
JUNE
1912 315
A.
The
Conservativeness
Requirement (Cons.
Req.).
In
a
laboratory
at
rest with
a
station.
gravitational field,
the
following
shall hold:
If
at
some
point
of time there
was
a light ray
that traversed the
points
A,B,
.....
G of
the
laboratory,
then
A,B
....
shall
always
remain
a
possible light
path.
This
requirement
is
certainly nonrelinquishable.
B. The
Reversibility
Requirement
(Revers. Req.)
If
in
a
station-gravitat.-laboratory
at
rest
the series
of
points
A, B, C,
...
G
is
a
possible light
path,
then
G, F,
...
C, B,
A shall also be
a possible light
path.
This
requirement is
perhaps
relinquishable
C.
The
Requirement
of the Existence
of
a
Wall-clock Time
(d@-req.).
In
a
station.-gravitat. laboratory
at rest it should be
possible
to
establish
a
wall-clock
time
Đ
that
satisfies
the
following
requirement with
respect
to two
laboratory points
M
and
N: if two consecutive
light impulses pass
through point
M
as
well
as
through point N,
so
that, for
example, they pass
through point
M
at the local wall-clock times
M
and &M'
and
through point
N
at
the
new
local wall-clock times
ŪN
and
0N',
then
we
shall have
(S)N
(Ģ)
= E)
(h)
N M M
(this
shall hold
at all times
and
for
any
arbitrary[16]
pair
of
points
MN
in
the
laboratory)
For the
special case
of
an
oo
small time interval
we
shall
thus
have
(dŪ)N
=
(d%)M.
Do
you
consider this
requirement relinquishable?
Given this state
of
affairs it
is
surely
not
uninteresting
to
try
to
solve
the
following
problem:
The "macro-problem":
What
is
the
most
general
laboratory
motion
that
is
macro-
equivalent
with
a
stationary gravitational field:
Remarks:
1.
First
we
want to
confine ourselves
to
macro-equivalence
with
respect
to
experiments involving geometrical optics
and
to
velocity-of-light
determinations.
Once the
most general
class
of motions that
satisfies this
optical macro-equiv.
req.
has been
established, it
becomes much easier
to
pick
out
the
subclass
that
is
also
macro-equivalent
with
a
stationary gravitational
field with
respect
to
dynamic,
electromagnetic, thermody-
namic,
etc.
experiments
as
well.
2.
A few
requirements
that
can
be
posed with
respect
to
the
optic
phenomena in
a
stationary gravitational
field
must
be enumerated beforehand. Some
of
these
requirements
are
likely
to
be
absolutely
nonrelinquishable.
But
others
can
perhaps
be
relinquished
"in
an
emergency" (see
e.g.,
the
"Reversibil.
Req."). I
will
therefore
set
them
down
one
by
one,
and
will
simply
show
what
are
the solutions obtained
for
the "macro
problem"[17]
when
one
starts out from
one
or
the other
group
of
requirements.
One
can
then decide
afterwards
which
of these
requirements
one
wishes to
drop.
o