240
ON
THE
INERTIA
OF
ENERGY
It
seems
to
me
to
be
in the
nature
of
things
that other
authors
might
have already
elucidated part of
what
I
am
going to say. However, bearing
in
mind
that the
problems
under
consideration
are
being
treated here
from
a
new
standpoint, I
felt that
I
should
be
permitted
to forgo
a
survey
of the liter-
ature
(which
would
have been
very
troublesome for
me),
especially
since there
is
good
reason
to
hope
that this
gap
will
be
filled
by
other authors,
as
it
was
kindly
done
by
Mr.
Planck
and Mr. Kaufmann
for
my
first
paper
on
the
principle of
relativity.
§1.
On
the
kinetic
energy
of
a
rigid
body
in
uniform
translation
subject to
external
forces
We
consider
a
rigid
body
that is
moving
in
uniform
translation (velocity
v)
in the direction
of
the
increasing
x-coordinate of
a
coordinate
system
(x,y,z) that
is
assumed
to
be
at rest.
If
external forces
do not act
upon
it, then,
according to
the
theory of
relativity,
its kinetic
energy
K0
is
given
by
the
equation1
h
=
fiV2
1
-
1
1
"
(v),
where
u
denotes its
mass
(in the conventional
sense) and
V
the velocity of
light
in
vacuum.
We
now
want to show
that
according
to
the
theory
of relativ-
ity this
expression
does
not
hold
any
longer
if the
body
is acted
upon by
external forces that balance
each
other.
To
be
able
to
deal with
this
case,
we
must
assume
that these
are
electrodynamic
forces.
We
therefore
imagine
that the
body
is rigidly electrified
(with
continuously
distributed electri-
city),
and
that
an
electromagnetic
field
of
force is
acting
upon
it.
We
imagine
that the electric
density
is
always very
low
and
the field
strong,
so
that the forces
corresponding to
the interactions
between
the
body's
electric
masses can
be
neglected
compared
with the forces the external field
exerts
on
[4]
[5]
1A.
Einstein,
Ann.
d.
Phys. 17
(1905):
917ff.