140 EARLY WORK ON QUANTUM HYPOTHESIS
ben").[42]
In order to
suggest
what
new concepts might
be
needed,
he
focused
on
the
problematic
Wien
region.
Using
Wien's
law,[43]
Einstein showed that the
expression
for the volume
dependence
of
the
entropy
of
radiation at
a given frequency
is
similar
in
form to that
of
the
entropy
of
an
ideal
gas.
He concluded that
"monochromatic
radiation
of
low
density (within
the
range
of
validity
of
Wien's radiation
formula)
behaves
thermodynamically as
though
it
consisted
of
quanta
of
energy,
which
are independent
of
one
another,
and
of
magnitude
Rßv/N"
("[m]onochromatische
Strahlung von geringer
Dichte
(innerhalb
des
Gültigkeits-
bereiches der Wienschen
Strahlungsformel)
verhält sich in
wärmetheoretischer
Beziehung
so,
wie
wenn
sie
aus
voneinander
unabhängigen Energiequanten von
der
Größe
RBv/N
bestünde").[44]
Einstein
opened
the
paper by pointing
out the
"fundamental
formal dis-
tinction"
("tiefgreifender
formaler Unterschied") between current theories
of
matter,
in
which the
energy
of
a body
is
represented as a sum over a
finite number
of
degrees
of
freedom, and
Maxwell's
theory,
in which the
energy
is
a
continuous
spatial
function hav-
ing
an
infinite number
of
degrees
of
freedom. He
suggested
that the
inability
of Maxwell's
theory
to
give an adequate
account
of
radiation
might
be remedied
by a theory
in
which
radiant
energy
is
distributed
discontinuously
in
space.[45]
Einstein
formulated "the
light
quantum hypothesis"
("die
Lichtquantenhypothese")[46]
that
the
energy
of
a light ray
emitted from
a point
[is]
not
continuously
distributed
over an ever increasing space,
but consists of
a
finite number
of
energy
quanta
which
are
localized
at
points
in
space,
which
move
without
dividing,
and which
can only
be
produced
and absorbed
as
complete
units.
bei
Ausbreitung
eines
von
einem Punkte
ausgehenden
Lichtstrahles
[ist]
die
Energie
nicht kontinuierlich
auf
größer
und
größer
werdende Räume verteilt,
sondern
es
besteht dieselbe
aus
einer endlichen Zahl
von
in
Raumpunkten
lokalisierten
Energiequanten,
welche sich
bewegen,
ohne sich
zu
teilen und
nur
als Ganze absorbiert und
erzeugt
werden
können.[47]
As noted in the
previous
section,
Einstein first asserted that
Planck's derivation
implic-
itly assumes
quantization
of
the
energies
of
charged
oscillators in his second
paper
on
[42]
Einstein 1906b
(Doc. 32),
p.
375.
[43]
See Wien 1896.
[44]
Einstein
1905i
(Doc. 14),
p.
143.
Rß/N is
equivalent
to
Planck's
h.
Except
in
reviewing
Planck
1906c
(see
Einstein
1906f
[Doc.
37]),
Einstein did not
use h
before Einstein 1909b
(Doc. 56).
In 1901, Einstein had
pointed
out
a
parallelism
between
the
kinetic
energy
of
mole-
cules and the thermal
energy spectrum
(see
Ein-
stein to Mileva
Maric,
30
April
1901 [Vol.
1,
Doc.
102]).
[45]
See Einstein 1905i
(Doc. 14),
pp.
132-
133. Einstein reiterated that radiation in
a
finite
region
of
space
should be described
by a
finite
number of
degrees
of
freedom in Einstein 1907h
(Doc. 45),
p.
372. For further discussion
of
this
point,
see
McCormmach 1970b. For
an analysis
of
Einstein 1905i
(Doc. 14), see
Klein 1963b.
[46]
Einstein
1906d
(Doc.
34),
p.
203.
[47]
Einstein
1905i
(Doc.
14),
p.
133. Four
years
later
Einstein
stated the
light-quantum hy-
pothesis more
cautiously,
as
the
assumption
"that
emission and
absorption
of
radiation
only
take
place
in
quanta
of
this
magnitude
of
energy
[hv]" ("daß Emission und
Absorption
von
Strahlung überhaupt nur
in
Quanten
von
dieser
Energiegröße
stattfinde")
(Einstein
1909c
[Doc.
60],
p.
495).