DOC.
45
249
If
one
does
not ask
about
the
kinetic
energy
in
particular, but
simply
about
the
energy
e
of
the
moving mass
point, then
e
=
k
+
const.
While
it is
most
convenient
to set
the
arbitrary
constant
in
this
equation equal
to
zero
in
classical
mechanics,
the
simplest expression
for
e
in relativistic
mechanics
is obtained
by
choosing
the
zero
point such
that the
energy
e0
for
the
stationary
mass
point equals
uV2.1
One
then obtains
e
=
pY-2
1
j1
"
(j)
7
We
will henceforth adhere
to
this choice
of
the
zero
point
of the
energy.
We now
introduce
again
the
two
coordinate
systems
(x,y,z) and
(E,n,C)
that
are
always
moving
relative
to each
other.
Let
a
mass
point
u
move
relative
to
(E,n,C)
with
a
velocity
w
in
a
direction that
forms
the
angle
p
with the positive
£-axis. The
energy e
of
the
mass
point relative
to
the
system
(x,y,z)
can
easily
be
determined
using
the relations derived in
§5
(loc.
cit.).
One
obtains
pV2
1
,
vw cos
p
1
+ -fl-
t
-
(fa
If several
mass
points
are
present
that
have
different
masses,
velocities,
and
directions of motions,
we
obtain for their total
energy E
the
expression
E
=
1
1
-
(r/)
7
i
"P
1
O
"
(?)
+
V
-
(t)
7
i
j
(IW
cos
tp
1
-
(f)
Until
now we
have
not
stipulated
anything about the state
of
motion
of the
system
(e,n,c)
relative
to
the
moving masses. We
can
and
will
now
stipulate
1One
should
note
that the
simplifying
stipulation
uV2 = e0
is also the
expression
of the
principle of
the
equivalence
of
mass
and
energy,
and
that
in
the
case
of
the electrified
body
e0
is
nothing
other than its electro-
static
energy.
[11]
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