DOC.
222 MAY 1916 215
222. From David Hilbert
Göttingen, 27
May
1916
Dear
Colleague,
First
of
all, many
thanks
for
your friendly
letter
of
last
March,[1]
to which
I
had
been
wanting
to
respond
for
so
long
now.
“Friendly”
also in
the literal
sense; although,
I
hope
we are going
to
discuss this “Freundlich” affair
soon
in
person.[2]
At
Easter
I
was
in
Lugano
for
4
weeks
and
gorged myself
there
on
meat
and
whipped cream,
etc. Schwarzschild’s
death
certainly
is terrible[3]
and
is
being painfully
felt
even
by people
who
everywhere
have become
so
heartless.
Now
as
regards
this semester’s
Göttingen physics lectures,
von
Smoluchowskias
has
now
been
confirmedwill
lecture
on
the
days
1921
June
on
diffusion and
coagulation
theory of colloid
particles,[4]
and
Szigmondy
will
perform experiments
on
it at
the
same
time.[5]
Furthermore,
Mie
has
agreed
to
come
here
to
present
a
talk
on
his
electrodynamics.
The time
for
that
is
not
yet
settled, however; I
am
thinking
of
the last
week in
the
semester.[6]
My
wife
is
already very
much
looking
forward
to
receiving you
in
our
home
again on
these
occasions;[7]
she
is
still
very
struck
by your modesty
but
will
nevertheless
attempt
not to
put
you
to
too
severe a
test: If
owing
to
grocery
assortment
we
have
nothing
to
eat,
we
shall
all
go
together
to
the
hotel
or on
excursions to
neighboring
villages.[8]
Finally,
I shall
immediately respond to your
postcard of
today,[9]
which also
pleased
me
very
much:
P
is nothing
more
than the
always generally
invariant
polar
process.[10]
Proof
is
thus.[11]
If
J(guvgouv...qs,
...)
is
an invariant,
then
obviously
J(guv
+
Kpuv,
gouv
+
kpouv,
...qs
+
Kps)
is
also,
where
k
is
a
constant and
puv
to
guv
a
cogradient,
and
ps
to
qs.[12]
Consequently every
coefficient
in
the
power expansion
in
k
is
indeed
an
invariant.
However,
the
coefficient of
k1
is
P
=
Pg
+
Pq.[13]
But this
is
not
connected,
as
you assume,
with
the
theorem
that
dH/dgkluv
is
a
tensor.
Rather the latter
follows
directly
from
the
manner
in which
the
derivatives
of
the
guv,s
transform
themselves;
this
always happens
in such
a way
that
upon
transformation the
nth
guv
derivatives
just
combine with derivatives
to
the
n

1ththus
with those of lower
order.[14]
And from this
you
can see,
of
course,
that
an
invariant’s differential
quotients
to
the
highest
guv
derivatives
occurring
in them must
always
be
tensors.[15]
My
energy
law
is
probably
related to
yours;
I have
already
assigned
this
question
to Miss
Noether.[16] As
concerns
your objection, however, you
must
consider
that
in
the
boundary
case
guv
=
0,
1
the
vectors
al,bl
do not vanish
by
any
means,[17] as
K
is
linear in the
gokuv's
and
is
differentiated
according
to these
quantities.[18]
For
brevity’s
sake
I
send
you
the
enclosed
slip by
Miss
Noether.