DOC.
8 ANALYSIS
OF A RESONATOR'S MOTION
221
(mv%o =
For
what
follows,
it
is
expedient
to
distinguish
two kinds
of
dynamical
effects
through
which
the radiation
field influences
the
oscillator,
namely
1.
The
resistive force
K,
with which
the radiation
pressure opposes
the rectilinear
motion of the
oscillator.
Neglecting
the
terms
of the order of
magnitude
of
(v/c)2
(c
=
velocity
of
light),
this
is proportional
to
the
velocity
v,
and
we can
therefore
write:
K
=

Pv.
If
we
further
assume
that the
velocity v
does not
change
markedly during
time
t,
then the
momentum
deriving
from
this
force
=

Pvt.
2.
The fluctuations
A
of the
electromagnetic
momentum
that arise
in
the
disordered radiation
field
owing
to
the motion of the electric
masses.
These
can
be
positive
just
as
well
as negative,
and
are
independentin first approximationof
the
circumstance
that the oscillator
is
in
motion.
These
momenta
superpose
themselves
on
the
momentum
(mv)t=0
during
time
t,
and
our
equation
becomes
(1)
(mv)l=0
=
(mv(=0
+
A

Pvxf.
By
increasing
the
mass m,
we can
always
bring
it
about that the
term
multiplied
by
t2,
which
appears on
the
righthand
side
of
equation
(1),
can
be
neglected.
Further,
the
term
multiplied
by vS"
vanishes
because
v
and
A
can
become
positive
or
negative
quite
independently
of each other.
If,
in
addition,
we
replace mv2
by
the
temperature
0
using
the
equation
known from
the
theory
of
gases
mv2
=
_eR
N
(R
=
the absolute
gas
constant,
N
=
Loschmidt's
number),
then
equation
(1) assumes
the form
(2)
x5
= 2^p6t.
Thus, we
only
have to find
A2
and
P
(or
K)
by
means
of
electromagnetic arguments,
and
equation
(2)
will
yield
the radiation
law.
§2.
Calculation of
the
Force
K.2
To
calculate
the
force with which
the radiation
opposes
a moving oscillator, we
calculate
first
the
force
on an
oscillator
at rest,
and
then transform
this force
by
means
of the
formulas
that
follow from
the
theory
of
relativity.
Let the oscillator
with
proper frequency
v0
freely
oscillate in
the zdirection of
an
orthogonal
coordinate
system
x,
y,
z.
If
£
and ^ denote the electric and the
magnetic
2
Cf. M.
Abraham, Ann. d.
Phys.
14
(1904):
273
ff.
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