464 DOC.
456
FEBRUARY
1918
transformability is
taken without
closer
reflection;
for
I
believe
that it
actually
has
already
caused
quite
some
confusion.
It
even seems as
though, at
one
place
in
your
Annalen
essay,
in
the
introduction,
where
you
discuss two
spheres
rotating
relative to
each
other,[14] you yourself
lost
sight
of home-baked
logic,
blinded
by
the mathematical
spell
of
the
general
transformability
of
the fundamental
phys-
ical
equations. For,
as a
matter
of
fact,
it
is
possible
to
declare
both coordinate
systems
S1
and
S2 as
completely equivalent only
when
a
world
permeated
by
an
arbitrarily
construed
gravitational field
in accordance with
physical
laws not
caused
by
matter
is
considered
as equally
admissible
as a
world whose
space-time
scheme
is inherently
homogeneous
and in which
only
gravitational
fields caused
by
matter
occur.
At
least,
I
cannot
see any
other
possibility
and
am
incapable
of
regarding
both
these schemes
as
equivalent.
If
one
wants to declare
S1
and
S2
as
equivalent,
then
one
must also
admit that the
snaking
rod
in
my example
is
logically equivalent
to
a rigid
straight
rod. The
same error
in
logic
is
made,
in
principle, except
that
in
the
example
I
have chosen
it
manifests itself
a
bit
more
drastically.
For
the time
being, incidentally,
I
do not
yet
want
to assert
definitely
whether
the
projection
of
the
so-called “Hilbert
world”[15]
into
the
smooth
space-time
scheme
(which
I
assume
as
flat,
whereas
you
prefer
to
attribute
a
curvature
to
it)
is
simply
feasible
by
the method
described in
my
third
lecture. For
it
seems
to
me
that
fitting
the
world
points
into
the
space-time
scheme would have to
occur
according
to
very specific logical
and
methodological
rules
or
at
the
very
least that,
among
several
possibly logically
admissible
methods,
a
best method
must
exist.
I
consider
it
necessary
first
to
consider
according
to
which
principles
experimental
physics
would
actually proceed
in
measuring lengths
and times
in
gravitational
fields,
and in
making
the
necessary
corrections to
the
directly
ob-
tained
measurement results in accordance
with
your
theory
of
gravitation.
It
is
only
then that
one can see
which
projection
must
be used
to
assign
the
points
of
“Hilbert’s world” to
the
“physical
world.”
I
named
the
simple
vertical
projection
as an
example
of
just
one
possibility,
without
intending
to
propose
that
it
is
the
right
one.[16]
Once
the
railways
are
better accessible to civilians
again,[17]
I
hope
to be able
to
speak
with
you someday.
But
perhaps
with
this letter
I
shall have succeeded
in
clarifying
the
situation
a
bit
in advance.
I
would be
very pleased
if
you
found
the
time
to
reply
to
it,
so
that
I
could
attempt
to familiarize
myself
a
little with
your
mode of
thought
(which
really
is
quite
different
from
mine).
With best
regards,
yours
truly,
G.
Mie.