EARLY WORK ON QUANTUM HYPOTHESIS 139
of
the
system.[36]
If
the
entropy
of
a system
is
given as a
function
of
its
macroscopic
state
variables,
then
Boltzmann's
principle,
in
the form
W
=
exp(S/k), can
be used
to
calculate
the
probability
of
a
state,
and hence
of
the fluctuations
of
any
state variable. In 1909
Einstein used this method to calculate the fluctuations
in
the
energy
of
black-body
radia-
tion
in
a given region
of
space.[37]
The stochastic
method,
used in the
same
paper
to cal-
culate fluctuations in the
pressure
of
radiation, is
based
on
his work
on
Brownian motion.
Pressure
fluctuations maintain the Brownian motion
of
a
small mirror
moving
through
the
radiation
field,
in the face
of
the
retarding
force exerted
on
the mirror
by
the
average
radiation
pressure.[38]
The results
of
these two fluctuation calculations
are
discussed
in the
next section.
Einstein's
work
on relativity
also contributed to the
development
of
his views
on
the
nature
of
light. By eliminating
the
concept
of
the ether and
showing
that
a
flux
of radiant
energy
transfers inertial
mass,
the
theory
of
relativity
demonstrated that
light no longer
need be treated
as a
disturbance
in
a hypothetical
medium,
but could be
regarded as com-
posed
of
independent
structures,
to which
mass
is
attributed.[39]
III
Among
Einstein's
papers on
the
quantum hypothesis,
the 1905
paper
is
unique
in
arguing
for the notion
of
light
quanta
without
using
either the formal
apparatus
of
his statistical
papers
or
Planck's
law.[40]
As noted in the
previous
section,
Einstein demonstrated
that
only
the
limiting
form
of Planck's
formula
for small values
of
v/T
is
consistent
with the
accepted
foundations
of
statistical mechanics and
electrodynamics.
At the
other
extreme,
at which
Wien's
distribution law
holds,
"the
theoretical foundations
we
have utilized
.
. .
fail
. . .
completely"
("die
von uns
benutzten theoretischen
Grundlagen
. . .
versagen
. . .
vollständig").[41]
As he
explained
later that
year,
this failure
"seems
to
me
to have
its basis
in
a
fundamental
incompleteness
of
our physical
concepts"
("scheint
mir
in
einer
elementaren Unvollkommenheit
unserer physikalischen Anschauungen
ihren Grund
zu
ha–
[36]
The method
is
first discussed
in
Einstein
1907b
(Doc. 39).
[37]
See Einstein 1909b
(Doc. 56),
pp.
188-
189. The
equation
for the
energy
fluctuations
that results from
Boltzmann's
principle
is
equiv-
alent
to
one
that Einstein derived earlier from the
canonical distribution in Einstein 1904
(Doc. 5),
pp.
359-360,
as a simple thermodynamic argu-
ment shows. Einstein
evidently preferred a
for-
mula not
dependent on
the canonical distribution
for the
application
to
black-body
radiation.
[38]
See
Einstein
1909b
(Doc. 56),
pp.
189-
190,
and Einstein 1909c
(Doc.
60),
pp.
497-
498. For
a
discussion
of
the stochastic
method,
see
the editorial
note,
"Einstein
on
Brownian
Motion,"
pp.
213-215.
[39]
The conclusions
are implicit
in
some
of
Einstein's
earlier
papers
but
are
first made
ex-
plicit
in Einstein 1909c
(Doc. 60).
For discus-
sion
of
the elimination
of
the
ether
and the iner-
tia
of
energy,
see
the editorial
note,
"Einstein
on
the
Theory
of
Relativity,"
pp.
253-274.
[40]
A
year
later Einstein
explained
that ini-
tially
he had
regarded
Planck's
theory as
form-
ing
"in
a
certain
sense an
antithesis" ("in
ge-
wisser
Beziehung
ein
Gegenstück") to
his
own
work
(Einstein
1906d
[Doc. 34], p. 199).
While
"Gegenstück"
can
also
mean
"complement,"
the
context
in which
it is
used here
suggests
"antithesis."
[41]
Einstein
1905i
(Doc. 14),
p.
137.