552 DOC. 56 THE RADIATION PROBLEM
[36]
In this
equation, n0
=
pvdv,
as
follows
from the definition
of
r\
on
p.
188. See
also
fn.
1
on p.
190.
[37]
The
equation
in
parentheses
should read
"ac/\
=
-
pdv".
[38]
Except
for the factor 1/8tt. The second
term
was
derived from
electromagnetic theory
in
Lorentz 1916.
[39]
See
Planck
1901b and
Planck
1906c,
pp.
162-163.
[40]
The first term
can
be obtained
directly
from
Einstein's
expression
for
e2
above
by using
the
expression
for
entropy corresponding
to
Wien's
law
given
in Einstein 1905i
(Doc. 14),
p.
139.
[41]
Einstein
wrote Hendrik
Lorentz,
30 March
1909:
"In
particular
the
argument given
in
sec-
tion
7
of
the
paper
convinces
me"
("Insbeson-
dere wirkt die unter
7. in der Arbeit
mitgeteilte
Überlegung
auf mich
überzeugend").
The
ar-
gument
given
is
closely
related to his
prior
work
on
Brownian motion,
especially
Einstein 1906b
(Doc. 32).
[42]
On
17 January
1952 Einstein
wrote to
Max
von
Laue:
"In
1905 I
already
knew for certain
that
it
[Maxwell's
theory]
leads
to
false fluctua-
tions
of
the radiation
pressure
and thus to
an
in-
correct Brownian
motion
of
a
mirror in
a
Planck
radiation
cavity"
("1905
wusste ich schon
sicher,
dass sie
zu
falschen
Schwankungen
des
Strahlungsdruckes
führt und damit
zu
einer
un-
richtigen
Brown'schen
Bewegung
eines
Spie-
gels
in einem
Planck'schen
Strahlungshohl-
raum").
[43]
The
parenthetical expression on
the
left–
hand side
of
this
equation_should
be
squared.
[44]
"A2"
should
be "A2".
[45]
The motion
of
the mirror
is
assumed
to
be
one-dimensional.
[46]
A calculation
of
P
is
given
in Einstein
and
Hopf
1910b. After
citing
Einstein 1909b
(Doc.
56),
the authors state:
"The
essentially new
ele-
ment in the
present paper
lies in the fact that the
momentum fluctuations
were,
for the first
time,
calculated exactly" ("Das
wesentlich Neue der
vorliegenden
Arbeit besteht
darin,
daß die Im-
pulsschwankungen
zum
erstenmal exakt
ausge-
rechnet wurden")
(Einstein
and
Hopf 1910b,
p.
1115).
[47]
A factor
of
1/m2
is
missing
from the
right–
hand side
of
this
equation.
[48]
The left-hand side
of
this
equation
should
be
"m2A2/t".
[49]
Planck criticized this
interpretation
of
the
first term in
Planck
1910. For
Einstein's
re-
sponse, see
"Antwort auf
Planks
Manuskript,"
ca. January
1910. In
addition,
Einstein
and
Hopf
1910b shows that the momentum fluctuations
derived from
Maxwell's
theory yield a
differen-
tial
equation
for the
energy density,
the
only so-
lution
of
which is the
Rayleigh-Jeans
law.
[50]
Laue and Planck held this view
(see
Max
Laue
to Einstein, 2
June
1906;
Max Planck
to
Einstein,
6
July
1907;
and
Planck's
comment in
Einstein
et
al.
1909c
[Doc. 61],
pp.
825-826).
[51]
See
Einstein
1905i
(Doc. 14).
[52]
For treatments
of
these
phenomena, see
Einstein
1905i
(Doc. 14),
pp.
144-147;
Laden-
burg 1907;
Stark
1908;
and
Lenard and Saeland
1909.
[53]
Stark 1908.
[54]
For the
predicted
exceptions,
see
Einstein
1905i
(Doc. 14), p.
145.
[55]
Direct
proportionality
between the inten-
sities
of
emitted
and absorbed
fluorescent
light
is
reported
in Knoblauch 1895. It
is
confirmed
in
Kowalski 1910.
[56]
Einstein
1909c
(Doc. 60),
p.
492, consid-
ers a
similar process, in which decelerated cath-
ode
rays generate X-rays.
[57]
Einstein 1905i
(Doc. 14).
See
p.
148.
[58]
Stark
reported
tests
of
this
relationship
in
Stark
1909b,
which
appeared shortly
after this
paper.
[59]
Einstein
1907a
(Doc. 38);
Einstein 1907d
(Doc. 42).
[60]
This
is
probably a
reference to
Jeans
1905d. Jeans does
not,
however,
use
the
con-
stant h,
nor
does he consider the ratio
e2/c.
[61]
Einstein
wrote
nearly
the
same
words
to
Hendrik
Lorentz,
30 March 1909. He then
con-
tinued:
"I
hope
that
you can
find the
correct
way,
if
you
find the
reasons given
in the
paper
for the
untenability
of
the
current foundations at
all
valid"
("Ich
hege nun
die
Hoffnung,
dass
Sie den
richtigen Weg
finden
könnten,
wenn
Sie
überhaupt
die
in der Arbeit
angegebenen
Gründe
für die
Haltlosigkeit
der
heutigen
Grundlagen
stichhaltig
finden").
[62]
"R/N"
should be
"N/R".
[63]
See Wien 1893. Einstein
wrote
Hendrik
Lorentz,
23
May
1909:
"It
seems
to
me
indeed
quite significant
that
one
arrives
by means
of
a
dimensional consideration
at
the Wien
displace-
ment
law and at the Planck determination
of
the
elementary quantum,
which is
certainly
correct
in order
of
magnitude"
("Aber die
Thatsache,
dass
man
durch die
Dimensionalbetrachtung