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INTRODUCTION
TO VOLUME
2
in his work
on
Brownian motion combine statistical
physical concepts
he
had
re-
cently investigated
with
concepts
from the
theory
of
diffusion familiar to him from
his work
on
molecular
forces.[21]
As
a consequence,
he not
only gave
the first
satisfactory explanation
of
Brownian motion
as a
stochastic
process,
but
also de-
veloped
a new
method for the determination
of
molecular dimensions,
based
on
related
techniques,
and
completed
a
doctoral dissertation
on
this
topic.[22]
Einstein
emphasized
that
the existence and
properties
of
stochastic fluctuations
represented
a
critical
test
of
the
kinetic
theory
of
heat,
which
was
still
challenged
by
a
number
of
scientists.
His theoretical studies
helped
to
stimulate much
experimental
work
by
Perrin and others
that
effectively
served
to
put
such doubts to
rest.
Initially,
Einstein believed
black-body
radiation to be the
only system
for which
energy
fluctuations
are
empirically significant.
In 1904 he
applied
the
thermody-
namic
approach developed
for mechanical
systems
to the
energy
fluctuations
of
"a
radiation-filled
space"
("ein
Strahlungsraum"),
with
encouraging
results.[23]
The
following year,
Einstein returned
to
the
problem
of
black-body
radiation,
us-
ing thermodynamic
methods combined with
Boltzmann's
principle
to show that,
in the
high
v/T
limit,
the
entropy
of
radiation
varies with its
volume
in
the
same
way
as
does the
entropy
of
a system
of
particles.
Such considerations led
him
to
formulate the heuristic
viewpoint
that radiant
energy,
like matter and
electricity,
is
quantized.[24]
In 1907 he extended the
quantum hypothesis
to the vibrational
energy
of
solids.
He
was
thus able to
explain a long-standing anomaly
in the
theory
of
specific
heats
of
solids,
which had led to serious doubts about the kinetic
theory
of
heat.
Begin-
ning
about
1911,
with the first
experimental
confirmations
of
Einstein's
theory
of
specific
heats,
this work
played an important
role in
persuading many
physicists
of
the basic
significance
of
the
quantum
hypothesis.[25]
In 1909 he
applied
both of
his methods for
treating
fluctuations in
an investigation
of
black-body
radiation
based
on
Planck's
law. He used
a thermodynamic approach,
based
on
the inver-
sion
of Boltzmann's
principle,
to
investigate energy
fluctuations;
and
a
stochastic
approach, examining
the Brownian motion
of
a
small mirror in
equilibrium
with
the radiation, to
investigate pressure
fluctuations. As noted
above,
the
results of
[21]
See the
editorial
notes,
"Einstein
on
Brownian Motion,"
pp.
206-222, and "Ein-
stein
on
the Nature
of
Molecular Forces,"
pp.
3-8.
[22] See the
editorial note,
"Einstein's
Disser-
tation
on
the
Determination
of
Molecular Di-
mensions,"
pp.
170-182.
[23]
See
Einstein
1904
(Doc. 5), pp.
360-362.
This
success
of
methods
developed
for
systems
with
a
finite number
of
degrees
of
freedom when
applied
to radiation
may
have
encouraged
Ein-
stein
to
treat radiation
itself
as
such
a
system (see
Einstein
1905i
[Doc. 14], pp.
132-133).
[24]
See the editorial note,
"Einstein's
Early
Work
on
the Quantum Hypothesis,"
pp.
134-
148.
[25]
For
a
discussion
of
the
important
role
of
the
quantum theory
of
specific heats,
see
Klein
1965,
and Kuhn
1978,
pp.
210-220.