248
DOCS.
255,
256
SEPTEMBER
1916
By
differentiating
(2)
according
to
time,
_
dJ dJ
^
dJ
td dt
^
dqv
^".
results,
or
dJ
^
.
dJ
1h+h
=
0
(4)
H
=
-
L,
This
is
the
Hamilton-Jacobi differential
equation,
where
H
is
initially expressed
as
a
function of
the
qv’s
and
pv's
and
then the
pv’s are
substituted
by
dJ/dqv
according
to
(3a).-
Naturally,
the Jacobian transformation
is
by
no means yet
proven
with this.
But for
this the
formal,
less transparent
proof
offered
by Appell
suffices
for
me.[2]
What
I
was
missing
was
a
natural
way
to
arrive
at equations
(3a)
and
(3b)
from
the
Lagrange equations.
Wouldn’t
you
like
to reflect
a
bit
more
on
the
problem
of
closed time
lines?[3]
Here
lies
the
core
of
the
as yet
unresolved portion
of
the
space-time problem.
Best
regards, yours very truly,
A.
Einstein.
P.S.
Naturally,
I
do not
imagine
that
these trivialities
are
in
any way original
or
new.
These
things just
give me
the
sense
of
being
versed in
the
subject.
256. To Paul Ehrenfest
[Berlin,
6 September
1916]
Dear
Ehrenfest,
You have
no
idea how difficult
it
is to
venture out
nowadays. Yet,
after
Lorentz’s kind
help,[1]
I will
do
my
utmost to be with
you
all
as soon as
possible.
First, I
must
obtain
an
original
of
my
certificate of
citizenship,
located in
Zurich;[2]
then
a
long
chain of
other
still obscure obstacles awaits
me.
So
don’t be
surprised
if
many more delays occur.
I’m
happy
beyond
words
to
be
seeing
you
all
again.
Also
scientifically,
I
have
something
nice to show
you.[3]
Cordial
greetings
to
you
and
yours,
to
Nordstrom, Lorentz,
and de
Sitter,
yours,
Einstein.