EARLY

WORK ON

QUANTUM

HYPOTHESIS 143

the selective

absorption

of

radiation.[59]

Perhaps inspired by

Planck's

work,

in

1901

Ein-

stein wondered whether

the internal kinetic

energy

of

solids and

liquids

could be

conceived

of

as

"the

energy

of

electric

resonators"

("elektrische

Resonatorenenergie").

If

it

could,

then the

"specific

heat and

absorption spectrum

of

bodies

must

then be

related"

("[e]s

müßten dann

spezifische

Wärme und

Absorptionsspektrum

der

Körper

zusammenhän-

gen").[60]

He tried to

connect

this model with deviations from the

Dulong-Petit

rule.[61]

In 1907 Einstein avoided the

implications

of

the

equipartition

theorem for the

specific

heats

of

solids

as

he had avoided them for radiation

theory, by introducing energy quanta.

From the

average energy

of

a quantized

oscillator,

Einstein derived

an expression

for

the

specific

heat

of

a

monatomic solid

as a

function

of

ßt/v. The

expression approaches zero

with the

temperature,

and

approaches

the

Dulong-Petit

value at

high

temperatures.

Con-

sidering

the

simplified

nature

of

the

model,

the

expression

is in

fairly good agreement

with

Weber's

data

on

diamond.

A connection could be made with

absorption

results from

Drude's

optical dispersion

theory.[62]

Drude showed that the infrared

optical eigenfrequencies

of

a

solid

are

due to

vibrations

of

the lattice

ions,

while the

electrons

are responsible

for the ultraviolet

eigen-

frequencies.

At

room

temperature,

the

value

of Einstein's

expression

for

specific

heat

effectively

vanishes

at

a

frequency

well within the infrared

region

for most

solids,

and

increases to the

Dulong-Petit

value for

even

smaller

frequencies.

Einstein concluded that

only

the lattice ions and atoms contribute to the

specific

heats

of

solids. Moreover,

if

a

solid

displays

infrared

absorption

resonances,

the

temperature dependence

of

its

specific

heat

can

be determined from these resonant

frequencies.[63]

In 1910 Nernst and his assistant Frederick A. Lindemann obtained

general agreement

between

Einstein's

predictions

and observations

of

the variation with

temperature

of

the

specific

heat

of

a

number

of

solids.[64]

In

1911

Nernst

reported

the first confirmation

of

the

quantum hypothesis

outside the field

of

radiation:

"That

the observations in

their

totality

provide a

brilliant confirmation

of

the

quantum

theory

of

Planck and Einstein

is

obvious"

("Daß

in ihrer Gesamtheit die

Beobachtungen

eine

glänzende Bestätigung

der

Quanten-

theorie

von

Planck und Einstein

erbringen, liegt

auf

der

Hand").[65]

1875, 1887).

Einstein

1907a

(Doc. 38),

p.

189,

cites

Weber's

results

for

diamond,

taking

them

from tables in

Landolt and

Börnstein 1905.

[59]

For

a

discussion

of

his earlier interest in

such

a

connection,

see

Vol.

1,

the editorial

note,

"Einstein

on Thermal, Electrical,

and Radiation

Phenomena,"

pp.

235-237.

[60]

Einstein to Mileva

Maric,

23 March

1901

(Vol.

1,

Doc.

93).

[61]

See Einstein to Mileva

Maric, 23

March

1901

and 27 March

1901 (Vol.

1,

Docs. 93 and

94).

[62]

See

Drude

1904a, 1904b. For

a

discussion

of Einstein's earlier

interest in

Drude's

electron

theory

of

metals,

see

Vol.

1,

the

editorial

note,

"Einstein

on Thermal, Electrical,

and Radiation

Phenomena,"

pp.

235-237.

[63]

Einstein later noted

that,

if

the lattice

at-

oms

of

the solid

are

not ionized,

they

will

not

be

optically

active

(see

Einstein 1907d

[Doc. 42]).

[64]

See

Nernst

1911a, 1911b,

1911c. Nernst

personally

informed Einstein

of

the confirmation

(see

Einstein to Jakob

Laub, 16

March

1910,

and Einstein to Arnold

Sommerfeld,

July

1910).

Einstein also informed Sommerfeld

(see

ibid.)

of

a

recent confirmation

of

the

predicted

infrared

absorption

maximum for diamond.

[65]

Nernst

1911c,

p.

310. For further

discus–