DOCS.
180,
181
JANUARY
1916 175
letter-paper
coordinate
system
is
only
a
contrivance.
Always
the
same
points
are
illuminated
on
the
plate.
If
you perform
the distortion
of
the
tracing
paper only
within the
finite realm and in such
a way
that the
image
of
the
star,
the
aperture,
and the
plate
remain unshifted
without
damaging
the
constancy,
then
you
obtain
the
special
case
your question
refers
to.
The
essence
is:
As
long
as
the
drawing paper,
i.e.,
“the
space,”
is
unreal,
both
diagrams
do not differ at
all.
“Coincidences”
are
what
count, e.g.,
whether
the
plate
points
are
hit
by
the
light or
not.
Thus the distinction between
your
solutions
A
and
B
is
merely
a
difference in
presentation
with
physical congruency.
This
will
surely
become evident to
you upon
closer
contemplation.
If
the
equations
of
the
physics
were
not
generally covariant, you
would also
be able
to
make
the
above
consideration;
however,
relative to
the
letter-paper
system,
the
same
laws would not be
valid in the second
diagram
as
in the
first.
To this
extent
then,
both
of
them would not be
equivalent.
This
distinction
falls
away,
however,
with
general
covariance.
I also note
that
I
have
purposefully
left out the
fourth
(time)
coordinate,
which
is
insignificant
in
principle,
however.
Cordial
greetings
to
you
and
everyone, yours,
Einstein.
181. To Karl
Schwarzschild
[Berlin,]
9
January 1916
Highly
esteemed
Colleague,
I
examined
your paper
with
great
interest.[1] I would
not
have
expected
that
the
exact solution
to
the
problem
could be formulated
so
simply.
The mathe-
matical
treatment
of
the
subject
appeals
to
me
exceedingly.
Next
Thursday I
am
going
to deliver
the
paper
before the
Academy
with
a
few
words of
explanation.[2]
Meanwhile,
I
received
another letter
from
you yesterday evening,
which
I
would also
like
to
answer
right
away.
1)
The
theory is
fully developed,
as
far
as
the
fundamental formulas
are
concerned,
so no
other
difficulties remain in
the
treatment
of
the
individual
problems
aside
from
the
computational
ones,
which
are,
however,
inordinately large.
But
you
will gather
from
the
following
reflection
that
no
notable modification
is
made for
the
perturbation problem.
The modifications
that the
theory yields
are
of
a
relative order of
magnitude
determined
by
kM/r.
If
M
is
taken
as
the
solar
mass,
then
this
quantity is
barely
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