DOCS.
284,
285
DECEMBER
1916
273
284. To
Constantin Carathéodory
Berlin, Sunday.
[10
December
1916][1]
Dear
Colleague,
I
find
your
derivation wonderful. At
first,
a
small
slip
of
the
pen,
to be found
on
the
second
page,
caused
me
difficulties. But
now
I
understand
everything.
You
ought
to
publish
the
theory
in this form in
the
Annalen der
Physik,
since
physicists usually
know
nothing of
this
subject,
as was
the
case
with
me as
well.
With
my letter,[2]
I
must
appear
to
you
like
a
Berliner who has
just
discovered
the
local Grunewald woods and asks whether
people
have
ever
been
in
it
yet.[3]
If
you
would
like
to take
the
trouble to
explain
the
canonical
transformations
as well,
you
will
find
a
grateful
and careful listener. If
you
solve
the
problem
of
the
closed
time
lines,[4]
though,
I
shall
place myself
before
you
with hands folded
in
reverence..... Behind this
is
something worthy
of
the
sweat
of
the best
of
us.
Best
regards, yours,
A. Einstein.
285.
From
Constantin Carathéodory
Göttingen, 31
Friedländer
La.,
16
December
1916
Dear
Colleague,
The main
point
in
the
theory
of canonical substitutions
can,
in
my opinion,
be
most
simply
derived
as
follows.[1]
If
[
L(xk; xk;
t)dt
(1)
is
the
Hamiltonian
integral
and
we
set
yk
=
Lik
H(xk,
yk,
t)
=
-L
+
Yj
Ukik (k
=
1,
..
.,
n),
(2)
then the
differential
equations
of mechanics read
xk
=
dH
dyk
yk =
dH
dxk
(k
=
1,...,
n).
(3)
•
•
*.®2n)
yk
-
2/fc(oU
•
• •
&2ni
t)
Thus
Xk
-
Xk(cx
i
(4)