550 DOC.
532 MAY
1918
Recently
I
took
a
closer look
at
Schwarzschild’s
papers
on
the
gravitational
field
of
a sphere[6]
and have also read
your
essay
on
“Approximative
Integration”
of
1916.[7]
There
at
the
end
I
find
the
remark:
“Therefore,
although
in
this
analy-
sis
it
has
proved
convenient from
the
outset
not to
subject
the
coordinate
system
choice to
any
constraints,
... our
last
result does nevertheless show
that
there
is
profound physical
justification
for
a
coordinate choice
according
to
the condition
\-g
=
1.”[8]
This
is
entirely
the
same
point
of
view
that
I
take
in
my
Göttingen
lectures.[9]
To
be
more precise,
the
reason
leading you
to make
this remark
is
also almost
exactly
the
same one
I have
explained
with
the
slithering
rod.[10]
In
your analyses, you
came
upon
a
coordinate
system
in
which such
a
snaking
would
occur,
and
you reject
this
“undulatorily
oscillating
coordinate
system”
as
nonphysical.[11]
From
this
I
see
what
I
have
always suspected, namely,
that
our
views
are basically
in
far-reaching agreement;
I should
like
to
say: we
both
simply
think
essentially
in
physical
terms.
The
mathematical
manner
of
thinking
can
be
of
a
completely
different
kind;
I
find
that
mathematical talent and
physical
talent
are more
different from
one
another
anyway
than
what
is
usually
thought.
If
one
just
wants to
solve
the
problems mathematically,
the most
paradoxical
assump-
tions
may
be
employed
in order
to
facilitate
the
manipulation
of
the
calculations.
Mathematics
is
riddled with such
paradoxes,
of
course.
The scientific
logic
of
a
physicist
is
much
stricter
and
more
constrained.
To
give
a very elementary
ex-
ample
as an
illustration
of what
I
mean,
I point out
that
in
analytical mechanics,
time-dependent
forces
are
easily accepted.
The
physicist
must
take
exception
to
such
a
force;
he must first seek to
explain
it: he
encounters
a
problem
where for
the
purely
computational
mathematician
everything appears nicely
settled. Thus
the mathematician
can
also be
satisfied when Foucault’s pendulum
experiment
and the
phenomena
related
to
it
can
be
mastered
mathematically
with the
aid of
some
curious coordinate
system
in accordance with the
“general
theory
of relativ-
ity.”
The
physicist,
on
the other
hand,
can never
ascribe
the
same
legitimacy
to
a
coordinate
system,
in which
what
you
call
“apparent”
or
I
call “fictitious”
grav-
itational
phenomena
occur,
as
he
can
to
one
in which
only
“real”
gravitational
fields exist. As
soon as
you
say, now,
that
all coordinate
systems
are
equivalent
“in
principle,” you
are
assuming
the
mathematician’s
standpoint,
who
can
define
everything
as
he wants
“on
his
sovereign
authority.”[12]
By
contrast, if
one
says,
as
I
always do,
that
they
are
not
equivalent
in
principle,
then
one
is
speaking
as a
physicist
who
is
bound
by
stricter
principles
of scientific
logic.
Thus in
the
sentence
quoted
above,
you
also
speak
as a
true
physicist.
Allow
me
to
sketch
my opinion
on
this in somewhat
greater detail;
I
hope
I
do not bore
you
with
it.
It
is
precisely
these
principles
of
scientific
logic,
alien to
the
mathematician,
that
are
of most
importance
in
theoretical
physics.
For
obviously,
theoretical
physics
does not
merely
aim at
solving
mathematical
problems;
its
highest goal