576 DOC.
556
JUNE
1918
556. To
Felix Klein
[Berlin,
before
3
June
1918][1]
Highly
esteemed
Colleague,
I
shall first
answer your
second
letter.[2]
If
radiation
exists in
a system
in the
form of
electromagnetic
waves,
then the
Uvo’s
do not vanish
at
the
boundary
to
such
an
extent
that the
surface
integral[3]
ƒ
{Ul
cos nx
+
Ul cos
ny
+
I73 cos
nz)dS
extending
over
a
remote surface would
approach
zero
if
the
surface moved into
infinity.
In
this
case,
one
cannot
say[4]
that
one
has
an
isolated
system
in
my
sense
of
the
term.
I
restrict
myself
in
the
paper
to such
cases
where
(with a
suitable
choice of
coordinates) an
isolated
system
can
be identified.
This
agrees
completely
with the
history
of
the
energy concept;
if
approximately “isolated”
systems
did not
exist,
this
concept
could not have
emerged.
The fact that
Ja,
despite
the
asymmetrical way
in which it
is
formed,
can
be
a
four vector
(for
linear
transformations),[5] depends
on
the
following:
If
the
Tuv’s
are
tensor
components,
then the
integrals[6]
ƒ
Ta4dXldx2dx3dx4
= ^4ct4
or
ƒ
ƒ
Ta4dVdx4,
also
are
or,
if
one
integrates
over a
piece
of
an
isolated
system’s
“world
strand”
[Weltfaden],[7]
Aa4
=
A
x4J(T.
Since
this
is
a
tensor
component,
and
Ax4 a
vector
component,
it
suggests
itself
that
Ja
would be
a
four vector.