DOC.
56
367
is
the greater the
smaller
the
energy
n0,
and
that the
magnitude
of this
percent
fluctuation yielded
by
the first
term
is
independent of
the size
of
the
space
v over
which
the radiation is distributed;
I mention
this in order
to show
how
fundamentally
different
the actual statistical
properties
of
radiation
are
from
those
to be expected
on
the basis of
our
current theory,
which
is based
on
linear,
homogeneous
differential
equations. [41]
7.
In the
foregoing
we
have
calculated the fluctuations of the
energy
distribution in order
to
obtain
information
on
the
nature
of thermal radia-
tion.
In what
follows
we
shall
briefly
show
how
one
can
obtain
analogous
results
by
calculating
the fluctuations of the radiation
pressure,
due to
fluctuations
of
the
momentum.
[42]
Let
a
cavity surrounded
on
all sides
by
matter
of absolute
temperature
T
contain
a
mirror that
can
move
freely in
the direction
perpendicular
to
its
normal1.
If
we imagine
it
to be
moving
with
a
certain
velocity from
the
outset,
then,
due
to
this
motion,
more
radiation will
be
reflected
at
its
front than
at
its
back;
hence, the radiation
pressure
acting
on
the front will
be
greater
than that
acting
on
the
back.
Thus, due to
its
motion
relative
to
the
cavity
radiation, the mirror will
be
acted
upon by a
force
comparable
to
friction,
which
little
by
little
would
have
to
consume
the
momentum
if
there
did
not
exist
a cause
of
motion
exactly
compensating on
the
average
for the
momentum
lost
through
the above-mentioned
frictional force.
To
the irregular
fluctuations of the
energy
of
a
radiation
space
studied
above,
there
also
correspond
irregular fluctuations
of
the
momentum,
or
irregular fluctuations
of the
pressure
forces exerted
by
the
radiation
on
the
mirror,
which would
have
to
set the
mirror
in motion
even
if it
had
originally
been at
rest. The
mean speed
of the
motion of
the mirror
has
then
to be
determined
from the
entropy-probability
relation,
and
the
law
of the
above-mentioned
frictional
forces
from
the radiation
law,
which is assumed
to
be
known.
From
these
two
results
one
then calculates the effect of the
pressure
fluctuations,
which
in
turn makes
it possible
to draw
conclusions
concerning
the
constitution
of
the
radiation
or-more
precisely-concerning
the
elementary processes
of
the
reflection of
the
radiation
from
the mirror.
1The
motions of
the mirror considered here
are
completely analogous to
the
so-called
Brownian motion of
suspended
particles.