DOC.
56
369
where
p
again
denotes
the
radiation
density
at frequency
v,
and
f
the
surface
area
of the mirror.
By
substituting
the values
obtained for
v2
and
P,
we
get
RT
Nc
dvf.
If
we
transform this
expression using
Planck's radiation
formula,
we
obtain
The
close connection between
this relation
and
the
one
derived in the
last section for the
energy
fluctuation
(e2)
is
immediately
obvious,1
and
exactly
analogous
considerations
can
be applied
to
it.
Again, according to
the
current theory,
the
expression
would
be
reduced
to
the
second
term
(fluc-
tuation
due to
interference). If the first
term
alone
were
present,
the
fluctuations
of
the radiation
pressure
could
be
completely explained
by
the
assumption
that the
radiation consists
of
independently
moving,
not too
extended
complexes
of
energy
hv.
In
this
case,
too,
the formula
says
that in
accordance with Planck's formula
the effects of the
two
causes
of fluctuation
mentioned
act
like fluctuations (errors)
arising from
mutually independent
causes
(additivity
of
the
terms of which
the
square
of the fluctuation is
composed).
8. In
my
opinion,
the last
two
considerations
conclusively
show
that
the constitution of radiation
must
be
different
from
what
we
currently
believe. It is
true
that,
as
the excellent
agreement
of
theory
and
experiment
in
optics has
proved,
our
current theory
correctly yields the time
averages,
which
alone
can
be
directly
observed, but it
necessarily
leads
to laws
on
thermal properties of radiation that
prove
to
be incompatible
with
experience
if
one
maintains the
entropy-probability
relation.
The discrepancy
between
the
phenomena
and
the
theory
is the
more
prominent
the
larger
v
and
the
smaller
p.
At
small
p
the
temporal
fluctuations
of the radiation
energy
of
1That
relation
can
be written in
the
form
(assuming
R/Nk
=
1)
lipti
+
vdv
r
\\hpv
+
h
Ü
duf
.
[48]
[49]