DOC.
470
FEBRUARY
1918
485
cases (for
both
coordinate
choices);
only
the
boundary
conditions
(for
the
spatial
boundaries
of
the
considered
system) are
different.
Now
you
will
say:
In
one
case (Galilean
coordinate
choice),
guv
=
-1
0
0 0
0 1
0
0
0 0
1
0
0 0 0
1
at
the
boundary,
in
the
other
case,
they
are
certain
functions in which not
even
the
equivalence
of
all
the
directions in
space
is
observed
(a mere
axial
symmetry);
there
the first
system
does
indeed
appear preferred
in
principle.
I
say,
though:
I
do
not
believe
that
the
boundary
conditions
(guu=
1,
guv =
0)
apply
in
principle.
If this
were
the
case, my
entire
theory
would have to be
rejected.
Since
a
theory, generally
invari-
ant
with
regard
to
the
differential
equations (regarding
arbitrary subst.)
but
not
generally
invariant with
regard
to the
boundary conditions, is
a
monstrosity.[5]
The
usefulness
of
the
boundary
conditions
(guv
=
1
or
0)
is
only
based
on
the
circumstance
that the
parts
of
the
world
we are
considering
are
sufficiently
small.
A sufficiently
small
part
of
a
continuously
curved
manifold
can
always be
treated
as
flat.
The
gravitating
individual
masses,
the
fields of
which
we are
examining,
then
appear as
local
sources
of
perturbation
curvature
in the
otherwise flat
manifold. Belief in
the
Euclidean nature
of
the
world
corresponds fully
with
the
belief of
antiquity
in
the
basically
flat
shape
of the Earth’s
surface;
in order to
be able to adhere to
this
belief, autonomous,
nonrelativistic
boundary
conditions
for
infinity
must be
introduced,
and
on
top of
this,
this
infinite world
must
be
considered
essentially
as
empty
so
that
it
is not
curved
by
its
own
matter!
If
the
boundary
conditions
(guv =
1
or
0)
fall
away,
then
all essential
grounds
for
the
preference
of
one
specific
choice
regarding
the
coordinate
system’s
rotational
state also fall
away.
This becomes
completely
clear when
the
world
is
viewed
as
(spatially) closed;[6]
for then
spatial
boundary
conditions
are
eliminated,
so
that
for
any
choice
of
coordinates the events
of
the
world
as a
whole
are
determined
entirely by
the differential
equations alone.
To
your
remark about
the electron
I
just comment
that the transformation
to
an
electron
constantly at
rest would indeed be
a
formal
simplification
for
some
problems.
The
simplification
is less
great, though,
than
in
the
case
of
pure
translation
(in
the absence
of
a
gravitational
field)
because
of
the
nonsta-
tionary gravitational fields
which
are
generally present.
As
an
example
to
the
contrary,
however,
I
mention the
Earth-Moon
system,
the
mechanics
of
which
is
represented
naturally
only
when the non-Galilean
system
is
introduced,
where
the
origin
constantly
occurs
in
the
center
of
gravity
of
both
masses.
The
excep-
tionality
of
the
ordinary
th.
of rel. lies
in
that
the Euclidean nature
is
retained