146 EARLY WORK ON QUANTUM
HYPOTHESIS
several
considerations,
from which it follows for
me
that not
only
the mechanics
of
molecules,
but also Maxwell-Lorentz
electrodynamics
cannot be
brought
into
harmony
with the
[Planck]
radiation formula.
einige Betrachtungen, aus
denen für mich
hervorgeht,
dass nicht
nur
die Mole-
kularmechanik
sondern auch die
Maxwell-Lorentz'sche
Elektrodynamik
mit
der
Strahlungsformel
nicht in
Einklang gebracht
werden
kann.[84]
After
replying
in turn to Ritz and
Jeans,[85]
Einstein
stated,
more clearly
than he had
pre-
viously
done
so,
what he
regarded as
the deviations from
proper
statistical foundations in
Planck's
derivation
of
the radiation
law.[86]
The
major
novelties
of
the
paper,
however,
are
two
arguments
for the existence
of
light quanta
based
upon
the
analysis
of
fluctuations in
black-body
radiation. As noted in section
II,
Einstein did not
apply
his
canonical
fluctua-
tion formula,
perhaps
to forestall doubts about the
applicability
of
this
formula
to radia-
tion.[87]
Instead,
he
applied an equivalent
formula based
on
Boltzmann's
principle,
a prin-
ciple
he held
to be
universally
valid. In addition to
energy fluctuations,
Einstein calculated
fluctuations
in the radiation
pressure
by
studying
the Brownian motion
of
a
small, two–
sided
mirror
in
a
radiation-filled
cavity.[88]
In
both
instances,
Planck's
law
yields
expres-
sions for the fluctuations that
are
the
sum
of
two
terms,
which
"behave
like fluctuations
(errors)
which arise from
causes independent
of
one
another"
("sich
verhalten
wie
Schwankungen
(Fehler),
welche voneinander
unabhängigen
Ursachen
entspringen").[89]
One
of
the
terms,
which dominates at low
frequencies,
Einstein
interpreted as
due to
the
interference
of
independent,
random
waves;
the
other,
which dominates at
high frequen-
cies,
he
interpreted as
due to
"complexes
of
energy
hv
of
small extension,
moving
inde-
pendently
of
one
another"
("von
einander
unabhängig beweglichen, wenig
ausgedehnten
Komplexen von
der
Energie
hv").[90]
It
is
not
enough
to
assume
that
the emission and
absorption
of
light
take
place
via
energy quanta;
the structure
of
the radiation
itself
shows
evidence
of
such
quanta. Although light quanta
cannot
be
deduced from
Planck's
law,
he
concluded,
"one
can
indeed assert that the
quantum theory
offers
...
the
simplest
inter-
pretation" ("[m]an
kann aber wohl
behaupten,
daß die
Quantentheorie
die
einfachste
Interpretation
.
.
.
liefert")
of
this
law.[91]
1909.
Presumably
the
"question"
("Sache")
to
which he refers is
the
"Strahlungsproblem"
in
the title
of
the
paper.
[84]
Einstein to Hendrik
Lorentz,
30 March
1909.
[85]
See
Einstein
1909b
(Doc. 56), pp.
185-
187.
Einstein's
response
to
Ritz occasioned
a re-
joinder
by
Ritz,
Ritz
1909,
and
a
joint
statement
of their
disagreement,
Ritz
and
Einstein
1909
(Doc.
57).
[86]
See
Einstein
1909b
(Doc. 56),
pp.
187-
188.
[87]
Einstein raised the
question
of
the
appli-
cability
of
statistical mechanics
to
thermal radia-
tion in
Einstein
1909b
(Doc. 56),
p.
186. Ein-
stein
and
Hopf
1910a, 1910b
dispose
of
such
doubts.
[88]
Einstein later stated that in 1905 he knew
Maxwell's
theory
leads
to
an
incorrect
expres-
sion
for
the fluctuations
of
the radiation
pressure
on a
mirror
(see
Einstein to Max
von Laue,
17
January
1952).
[89]
Einstein 1909b
(Doc. 56),
p.
190.
[90]
Einstein
1909b
(Doc. 56),
p.
190.
[91]
Einstein
1909b
(Doc. 56),
p.
191.