DOC.
532 MAY 1918 551
always
is, as
your
researches in
particular
have
demonstrated
so brilliantly,
to
point
out
new
paths for research. The
purely
mathematical,
manner
of
thinking
without
following
principles
can never
lead to
this;
the
guiding
stars
for
this
are
precisely
these
principles
of scientific
logic,
principles
whose
ultimate
basis
is
the
postulate of
a
real,
objectively existing world,
without
which
there
could be
no
empirical
science
at
all. These
principles
guide
the
physicist,
be
it
consciously
or unconsciously.[13]
And
you
discovered all
the
wonderful
consequences
of
your
theory,
which
point I
also
particularly
emphasized
in
my
Göttingen
lectures,[14]
precisely
because
you
did not adhere
consistently
to
the
purely
mathematical
point of
view of “Hilbert’s
world,”
but rather
thought
as a
physicist.[15]
Imagine
for
a
moment
that
one
wanted
to support
very consistently
the
view
that
there
were no
gravitational
fields,
just
non-Minkowskian
spatial
domains!
Perhaps
one
can
attack
many problems mathematically
in this
way,
but
one
would
never
arrive
at
the
predictions
of the
bending
of
light rays,
the alteration
of atomic
frequencies
within
a
gravitational
field,
and
so
on,
because
for
it
thinking
in
physical
terms
is
necessary.
A
problem, now,
which
initially
will
not.
affect the
mathematician
at
all
but
which
seems
to
me
to be of
the
greatest importance
to
the theoretical
physicist
is
the
question
of
a
natural
coordinate
system
altogether
determinable
according
to
generally
valid rules and
permitting
the
description
of
the
phenomena
with
the
greatest
possible simplicity,
in
which,
for
example, “apparent”
waves
and
similar monstrosities
are
excluded in
principle,
in which
the
field
of
a
sphere
has
spherical symmetry,
and in which
the
principle
of
relativity
for constant
velocities
applies.
I believe
we
do share
the
same
opinion
in
that the
question
of
this
preferred
natural
coordinate
system
has
both
sense
and
purpose.
But
in
this
preferred
coordinate
system,
like
it
or
not,
the Earth
will
rotate
around
its axis.
From Schwarzschild’s
paper[16]
I
noticed with
very
particular
interest that also
in
the
case
of
spherically shaped symmetry
the
additionally
inserted condition
\/-g
= 1
is not
quite
sufficient. In his solution Schwarzschild
obtains
two
other
arbitrary integration
constants,
one
of
which,
a,
is
determined
by
the central
body’s mass;
the
other, however,
which he
calls
p,
remains
entirely
arbitrary.
Schwarzschild did determine
p,
though, by
the
condition
that the
discontinuity
in
the
solution
occurs
at
the
origin
of
the
coordinate
system. Nevertheless,
he
was
apparently
led to
this
just
out
of
reverence
for
the old Newtonian
potential
m-r
since
it
is altogether
incomprehensible why
the
discontinuity
cannot
lie
anywhere
else
within
the interior
of
the
gravitational
central
body.
Thus
despite
p
=
a3
being
laid down
quite arbitrarily,
Schwarzschild
says on
p.
195
at
the
bottom
that, in order
to
obtain the strict
solution to
Mercury’s
orbit,
(r3
+
a3)1/3
must
be
inserted
into
the
solution indicated
by you
in
place
of R.
To
what
extent