xxiv INTRODUCTION TO VOLUME
6
the
other-stimulated-induced
by
the radiation
field
and
with
probability
proportional
to
the radiation
density.
Third, at
equilibrium
the
atoms
are
dis-
tributed
among
their internal
states according
to
the Boltzmann distribution
law.
From these
assumptions
Planck's law follows in
a
simple
way.
Einstein
was
very pleased
with his
derivation,
which
he
characterized in
a
letter
to
Besso: "An
amazingly simple
derivation of Planck's
formula, I
should like
to
say
the
derivation."[37]
As
a
bonus from his derivation Einstein found that the
energy
difference between
two
internal
energy
states
of the
atom
had
to
be
equal to
hv,
with
v
the
frequency
of
the
radiation absorbed
or
emitted in
tran-
sitions between these
two
states,
thus
confirming
one
of the
postulates
of
Niels Bohr's
theory
of
spectra.
In
Einstein
1916n
(Doc. 38)
the derivation of
the
first
paper
is
repeated
and
augmented by a
discussion of
the
momentum
transfer that
accompanies
emis-
sion and
absorption processes.
Einstein
points
out
that in addition
to energy,
momentum is
transferred between
atom
and
field
if
the radiation
exchanged
is directed;
if
energy
is
radiated in the form of
spherical
waves,
there
is
no
momentum
transfer. He then makes the
fundamental and nonclassical
as-
sumption
that
an
amount
of
momentum
hv/c is transferred
in all instances of
emission
or
absorption
of
radiation
by
atoms
in
a
radiation field. He
explores
the
quantitative consequences
of
this
assumption, using a technique
that he
had
already successfully applied
to
quantum phenomena on
various earlier
occasions: the
technique
of
calculating
fluctuations,
in this
case
the
momen-
tum
fluctuations
experienced by a particle
moving
in
a
radiation
field.[38]
For
the actual calculation
Einstein draws
on
methods
developed
earlier in his
joint
work with
Ludwig
Hopf.[39]
The
final
result
is
an
equilibrium
condition
for
a
system
of
atoms
and radiation which takes the form of
an
equation
for
the radiation
density.
It is
satisfied
by
Planck's law but
not by
the
Rayleigh-
Jeans radiation
law.
This
is
interpreted
as a
strong
confirmation
that all radi-
ation emitted
by
atoms,
induced
as
well
as
spontaneous,
is
indeed directed:
"There
is
no
radiation in
spherical
waves."[40]
This
very important
conclusion
constitutes
a
major step
toward
the
photon
concept.
As Einstein
put
it:
"With
this,
the existence of
light quanta
is
practically
assured."[41]
[37]"Eine
verblüffend
einfache
Ableitung
der Planck'schen
Formel,
ich möchte
sagen
die
Ableitung."
Einstein
to
Michele
Besso,
11
August
1916.
[38]In
1909
Einstein had calculated
the
momentum
fluctuations of
a
mirror
in
a
radiation
field
(see
Einstein 1909b and Einstein
1909c
[Vol. 2,
Docs. 56 and
60]).
See
Klein 1964 for
a
discussion of Einstein's earlier
use
of fluctuation methods in
quantum theory.
[39]See
Einstein and
Hopf
1910b
(Vol. 3,
Doc.
8).
[40]"Ausstrahlung
in
Kugelwellen gibt
es
nicht." Einstein 1916n
(Doc. 38),
p.
61.
[41]"Damit
sind die
Lichtquanten
so
gut
wie
gesichert."
Einstein
to
Michele Besso, 6
Sep-
tember 1916.