48 DOC.
1
MANUSCRIPT ON SPECIAL
RELATIVITY
one
obtains first
m
dq
dt
=
st
...(26).
i
-a.
/
If
one
considers the fact that
dq
dt
1
_
1
d_
dt
N
1
and
that,
according
to
a
remark in
§2,
the
right-hand
side of
(26)
is to
be viewed
as
the force
tx
that
acts
on
the
material
point, (26)
assumes
the form
d_
dt
mq
N
1
-
1
=
I
Thus,
if
the law of momentum
is to
be maintained in the
theory
of
relativity,
then the
expression
inside the
curly
brackets
must
be viewed
as
the
momentum
of the material
point.
From this
we
draw the
general
conclusion that
mq-
is
equal
to
the
N
1
momentum
vector
of
an arbitrarily moving
material
point
in
any arbitrary
motion.
Thus,
if
the law
of
momentum is to
be maintained in the
theory
of
relativity
and
if
the
foundation
of
Lorentz's
electrodynamics
is
to
be
retained,
then the
vector
equation
of the motion
of
the material
point
under the influence
of
the
arbitrary
force f
must
read
d
dt
mq
1
q
= ft
...(27)
If
the
only
force
acting on
the material
point
is of
electrodynamical
character,
then
one
has
to
set
k
=
e{e+
-c'K
}
It
can
easily
be shown that
(27)
also satisfies the
energy
law,
if
fn
is
retained
as
the
expression
for the work
done
on
the material
point per
unit time. For
one
obtains
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