DOC. 47 JANUARY
1915 59
47. To Hendrik A. Lorentz
Berlin,
13
Wittelsbacher
St.,
23 January 1915
Highly
esteemed and dear
Colleague,
I have
long
been
eagerly awaiting your
detailed
letter,[1]
the
existence of which
de
Haas revealed to
me
after
his arrival from
Holland.[2] I
thank
you very
much for
having
spent
so
much time and effort
on
it. Before
I
answer
the
individual
points,
however,
I must
tell
you
that
in
the
course
of
our
collaboration
I
came
to
cherish
and
respect
your
son-in-law
exceedingly.
To
our
great delight
the
experiment
on magnetism
has
turned
out
positively.
Now de
Haas has devised
an even
nicer
investigative procedure
in which
the
use
of
resonance
can
even
be
dispensed
with.
With
it
the
reason
for
why
the
magnetic
axis and
the rotational
axis of
the Earth
nearly
coincide has
now
been
found.[3]
If
anyone
had
to relive
exactly
the
same
struggles
here in
the
considerations
on general
relativity,
I’d
ardently
wish
that
it be
you.
But
I
see
from the
first
part
of
your
letter that
this has
not
yet happened completely.
Had
I
committed
the
errors
you
rebuke
me
for
regarding
the
vanishing
of
the
Axv’s,
then
I
would
deserve to have
ink, pen,
and
paper
taken
away
from
me once
and for
all!
In
§12
the
Axv’s
refer to
a
coordinate
transformation
with
Axv’s
(&
deriva-
tives) vanishing
at
the boundaries.[4] As
you
know,
in
this
§
it
was
intended to
show
that
acceptance
of
such
transformations
prohibits
a
complete
mathematical
formulation
of
the
laws
of
gravitational fields.
From
§13
onward
the
Axv’s
relate
to
the
justified
transformations
for which
the
Axv’s along
with their
derivatives
do not vanish
at
the
regional
boundaries.[5]
Equations
65-65b
apply
to arbitrary
infinitesimal
(constant)
transformations.
Now,
when
I
say
about
(65b):
“It vanishes
if
the
Au
and
dAxu/dxv
terms
vanish,”
it
was
not
meant
to
mean
that this
would be
so
in
the
case
of
“justified”
trans-
formations;
for
the
latter,
this
had rather
to
be considered
a
priori
as
out of
the
question
according
to
§12.
When
on
the
second
half of
page
1070 I
examine
the transformations
K-K'-K",
etc.,
with definite border
coordinates,
under
no
condition
are
these
transformations
justified
ones.
This becomes
clear,
of
course,
from
the
fact
that
the observation
serves
to select from
among
these
systems only
one as
justified, namely,
the
one
with
an
extreme
J.
If
K
is
this
system,
then K
is
justified,
K',
K"
etc., however, are
not
justified. Therefore,
the transformation
K-K'
is
not
a
justified
one.
In the
reflections
of
§14,
which form
the
crux
of
the
whole
problem,
the coordinate
transformation
is
to be conceived of in
such
a
way
that the
Axu"
and
dAxu/dxv
terms do not vanish at
the
boundaries;
rather,
the
coordinate
system changes
(infinitesimally) over
the
entire
expanse
of
the
four–