232
DOC.
235 JULY
1916
235. To
Willem
de
Sitter
[Berlin,]
15 July 1916
Dear
Colleague,
Many
thanks
for
your long
letter.
I
agree
with
your
calculation.
You
are
quite
right,
of
course,
that
my specialization
of
the coordinate
system
by
the
condition V-g
=
1
is not
a
complete one,
so
boundary
conditions would
not suffice to
make
the mathematical
problem
of
the determination
of the
guv's
unique.[1]
After
all,
substitutions
with functional
determinant
1
exist
that
leave
the
boundary
region
untransformed.
It
would be
very
nice if
the
[coordinate]
system
could be
specialized
further
in
a
natural
way,
if
only
in
the interest
of
better
comparability
of
found solutions.
But
I have not been able to find
anything
of
the
sort.
The
conditions added
by
me
in
the
case
of
the
mass-point
overdetermine
the
problem
without,
however,
contradicting
one
another. The
three
conditions
gi4
=
0
do not
yet
suffice.[2] For,
a
purely
spatial
transformation
can
still be
performed
with
subst.
determinant
1,
which
destroys
the
point
symmetry.
It
is
not
good
if in
my
letter
I
called
the
V-g
system
“Galilean.”[3]
Only
a
space
in which all
the
guv's
are
constant
can
be called
that. But there
it
is
not
just
the
“space”
that
is
“Galilean”
but the
“space”
together
with
the
frame
of
reference,
which
makes
the
guv's
into
constants.
Nevertheless,
these
are
only
questions
of definition
about
which
one
does not have
to
rack
one’s
brains much.
What
you say
there about
“true” and
“apparent”
is correct
in
principle.
What
I
mean
in
my
addendum
is
the
following.[4]
When
I
find
some
process
or
other,
e.g.,
a
wave
process,
as a
solution to
the
differential
equations,
two
possibilities
exist.
Either
such
wave
processes exist,
no
matter how I
may
have chosen
the
reference
system,
or
such kinds of
wave
processes
do not exist when
[I]
choose
the coordinate
system
in
a
particular
manner.
If the
latter
is
the
case,
I
can
then
denote the
relevant
process (because
it
can
be “transformed
away”),
in
a
certain
sense
as an
“unreal”
process.
“Unreal”
then
simply
means
“can be
transformed
away.”
But it
is better,
of
course,
to avoid such
words,
which
give
rise to
unclarity.
One
can say:
the
coordinate choice
according
to
the
condition V-g
=
1
is
simple
or
advantageous
to
the
extent
that
with
this
choice
only
waves
of
the
3rd
type[5]
occur. (For
the
calculation, however, your
coordinate choice
is
preferable.)
Best
regards, yours,
A.
Einstein.