DOC.
14
HEURISTIC
VIEW OF
LIGHT
167
Published in Annalen
der
Physik 17 (1905):
132-148.
Dated
Bern, 17
March
1905,
received
18
March
1905,
published
9
June 1905.
[1]
For
a
discussion
of Einstein's
use
of
the
word "heuristisch," see Klein 1982b.
[2]
Boltzmann noted
a
distinction between
continuous and discrete
energy
distributions
in
Boltzmann 1896,
p.
5.
[3]
For
a survey favorably comparing
the
opti-
cal
predictions
of
electromagnetic theory
with
experiment, see
Wien
1909,
pp.
186-198.
[4]
"Schwarze
Strahlung"
("black radia-
tion")
is radiation emitted
by a perfectly
black
body,
i.e., with
absorptivity
of
1.
The
phrase
was common
at that time
(see, e.g.,
Graetz
1906,
p.
366).
[5]
For treatments
of
similar
phenomena, see
Einstein 1906d
(Doc. 34)
and Einstein 1907a
(Doc.
38).
[6]
See
Drude
1900a and 1900b. In
Drude's
theory
electrons
are
treated
as freely moving
charge
carriers, similiar
to
molecules in the ki-
netic
theory
of
gases.
For
a
discussion
of
Ein-
stein's
early
interest in the electron
theory
of
metals and its relation
to radiation
theory, see
Vol.
1,
the editorial
note,
"Einstein
on
Thermal,
Electrical,
and Radiation Phenomena,"
pp.
235-237.
[7]
In
Planck's
model,
Planck
1900a,
p.
70,
black-body
radiation
was
in
equilibrium
with
bound electron
"oscillators"
("Oszillatoren"),
but
not
with free electrons
and molecules.
[8]
Kirchhoff inferred that thermal radiation
at
equilibrium
in
a cavity
of
perfectly reflecting
walls
is equivalent
to
black radiation
of
the
same
temperature
(see
Kirchhoff 1860,
pp.
300-301).
The
equivalence
of
electromagnetic
radiation
in
thermal
equilibrium
with oscillators
to
black
ra-
diation
was
the basis
of Planck's
work
(see,
e.g.,
Planck
1900a,
pp.
69-70).
[9]
Einstein
was
troubled
earlier
by
Planck's
seeming neglect
of
resonators
of
all
frequencies
(see
Einstein to
Mileva
Maric, 10
April
1901
[Vol.
1,
Doc.
97]).
[10]
"Wirkliche Moleküle"
("real mole-
cules")
are presumably
those that
are
not disso-
ciated.
[11]
Planck
1900a.
[12]
Planck called this
assumption
"a
special
hypothesis" ("eine
besondere
Hypothese")
(Planck
1900a,
p.
71).
Such
"natural radiation"
("natürliche Strahlung")
was originally
defined
in
a
somewhat different
fashion from
Einstein's
in
Planck
1898,
pp.
467-469,
473;
Planck
1899,
pp.
451-453; and
Planck
1900a,
pp.
88-
91. In
particular,
Planck used
perfect
incoher-
ence
while Einstein
employs
"statistical
proba-
bilities"
below.
[13] x
should be
a.
[14]
This formula does not
appear
on
p.
99 of
Planck
1900a. It
can
be derived from
equations
on pp.
99 and 111. Planck first
published
it in
Planck
1900e,
p.
241.
[15]
In 1900
Rayleigh
obtained the
proportion-
ality
between T and
Ex,
the
energy per
vibration
mode,
by applying
the
equipartition
theorem to
the vibration
modes
of
matter-free
black-body
radiation
(see Rayleigh 1900).
His result
was
Ex
=
cT/\4, where
c
is
a
constant.
Expressions
equivalent
to
Einstein's
equation
were
obtained
in
1905
by Rayleigh
and Jeans without
the
use
of
material
resonators (see Rayleigh 1905a,
1905b,
and Jeans
1905a,
which
appeared
after
the
receipt
of Einstein's
paper).
[16]
Rubens
and
Kurlbaum
1901,
p.
666,
states
that
Rayleigh's
formula
"fails
in the
region
of
shorter
wavelengths.
It also shows considerable
systematic
deviations from
our
observations"
("in
dem Gebiet
kurzer
Wellenlängen versagt.
Auch
zeigt
sie
gegenüber unseren
Beobach-
tungen
erhebliche
systematische
Abweichun-
gen"),
but for
large
values
of \T
it
agrees fairly
well with
the
observed distribution. See also
Lummer
and
Pringsheim 1908,
p.
449.
[17] Rayleigh
apparently
noticed this
difficulty
in 1900
(Rayleigh 1900),
asserting
that the
equi-
partition
"doctrine"
yields
valid results
only
for
"the
graver
modes."
In
May
1905 he stated:
"According to [the
equation
for
EJ],
if it
were
applicable
to all
wave-lengths,
the total
energy
of
radiation
at
a given temperature
would be
in-
finite"
(Rayleigh
1905a,
p. 55).
[18]
Here
"Elementarquanta"
("elementary
quanta") refers to fundamental atomic
con-
stants.
In
Planck
1901b,
Planck determined the
mass
of
the
hydrogen
atom,
Loschmidt's
num-
ber
(N),
Boltzmann's
constant,
and the elemen-
tary
electric
charge.
[19]
Planck
1901a.
[20]
Planck's
formula
appears
in
Planck
1901a,
p.
561,
with the constants h and
k,
in-
stead
of
a
and
ß
(a
=
8nh/L3,
ß
=
h/k,
and
k
=
R/N).
Planck's
values for
h
and
k,
obtained in
Planck
1901a,
pp.
562-563,
yield
Einstein's
values for
a
and ß.
[21]
See
Planck
1901b, pp.
565-566, and
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