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