DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY 49
kq
= q
d
dt
1
X
mC
d
N
mq2 mqq
HI
dt•
IJ^J
'
J
V
c
J
A
c
d_
dt
mq
+
mc
7
1
or
kq
=
d_
dt1
mc
1

7
...
(27a)
The
expression
within the brackets
on
the
right plays
the role of the
energy
E of the
moving
mass
point.
This
expression
E
=
mcl
. . .
(28)
N
i
q
c2
grows
to
infinity
when
q
approaches
the value
c;
thus,
it
would
require an
infinite
expenditure
of
energy
to
impart
the
velocity
c
to
the
body.
In order
to
see
that for
small velocities this
expression
turns
into that form Newton's
mechanics,
we
expand
the denominator in
powers
of
q2/c2
and obtain
E
=
mc2
+
m/2q2
+
...
. . .
(28')
The second
term
on
the
righthand
side is
the familiar
expression
for kinetic
energy
in classical mechanics. But what does the
first,
qindependent
term
signify?
To be
sure,
this does
not have,
strictly speaking, any legitimacy
here;
for
we
have
arbitrarily
omitted
an
additive
constant
in
(28).
But
on
the
other
hand,
a glance
at
(28)
shows
that the
term mc2 is
inseparably
linked
to
the second
term
of
the
expansion,
m/2q2.2
One is therefore
already
inclined
at
this
point
to
grant
a
real
significance
to
this
term
mc2,
to
view it
as
the
expression
for the
energy
of the
point
at rest.
According
to
this
conception,
we
would have
to
view
a body
with inertial
mass m as an energy
store
of
magnitude
mc2
("restenergy"
of the
body).
But
we can
change
the
restenergy
of
a
body, e.g., by
supplying
heat
to it.
Thus,
if
mc2
is
always
to
be
equal
to
the
rest–
energy
of the
body,
then the inertial
mass m
of
the
body
must
also
change during
this
warming,
with the
change amounting
to
AE/c2,
if AE denotes the
energy
increase
[p. 39]
produced by, e.g., warming.
We will show in
the next
§
that this latter
conse–