DOC.

5

CONTRIBUTIONS TO QUANTUM THEORY

39

Published in

Deutsche

Physikalische Gesellschaft. Verhandlungen 16 (1914):

820-828. Lec-

ture

held

on

24

July 1914.

Published

30 August 1914.

[1]See

Nernst

1906 for the

first formulation of the heat

theorem and

Planck 1912a for

Planck's views

on

it.

[2]On many

earlier occasions Einstein had made extensive and

important

use

of Boltz-

mann's

principle (see, e.g.,

Einstein

1909b,

1909c

[Vol. 2,

Docs.

56 and

60]).

The discussion

in

this

paper

of

an

approach

that avoids its

use

stands

in

striking

contrast.

[3]In discussion remarks

at the

first

Solvay Congress

in 1911

as

well

as

at

the second

one

in

1913,

Einstein had

criticized

Walther Nernst's

thermodynamic proofs

of

his

heat theorem

(see,

respectively,

Nernst

et

al.

1912, p.

302,

or

Nernst

et

al.

1914,

p.

243

[Vol. 3,

Doc.

25,

sec.

VII];

and

Grüneisen

et

al.

1921,

pp.

293-298,

or

Vol.

4,

Doc.

22,

sec.

IV).

In

1912

Einstein

wrote

a

paper

criticizing Nernst,

which

he first

submitted

to

the

Physikalische Zeitschrift

but later

retracted.

See

Einstein

to Ludwig Hopf,

after

20 February 1912

(Vol. 5,

Doc. 364), note 6,

for

more

details and

references

to

Einstein's

contemporary

correspondence on

this topic.

[4]Einstein's

offer

was

taken

up

by

Michael

Polanyi,

which

led

to

an

exchange

of letters

between him

and

Einstein and

a

paper,

Polanyi

1915

(see

Einstein

to

Michael

Polanyi,

13

December

1914,

30

December

1914, 10

February

1915, 8

May

1915, 18

June

1915,

and

6 July

1915;

see

also

Polanyi

1915,

p.

351,

for mention of Einstein's

offer).

[5]The

inclusion of

the

last

term

makes

the

entropy

extensive.

See

also

Doc.

26, note

11,

for

further discussion of this

point.

[6]"Ev"

should

be

"EO."

[7]The plus sign

in the

second

term

on

the

left-hand side should be

a

minus

sign.

[8]This is

actually

a

refinement of Planck's formulation of Nernst's theorem

(see

the

Preface

of Planck

1913).

[9]"Eo"

in the exponential in

the third

expression

should be

"Eö."

[10]This

derivation

was

first

given

by

Einstein in Einstein 1907a.

[11]Bernoulli 1914.

See

also Einstein's earlier

negative

evaluation of Bernoulli's abilities

in

Einstein

to

Fritz

Fichter-Bernoulli,

17

January 1912

(Vol. 5,

Doc.

338),

and Einstein

to

Hein-

rich

Zangger, 20

May

1912

(Vol. 5,

Doc. 398).

Einstein

was

asked

his

opinion

of Bernoulli

in

connection with

the

latter's

candidacy

for

a

chair

at

the

University

of Basel.

His

advice

was

ignored,

and

Bernoulli

was

appointed

Extraordinary

Professor of

Physical Chemistry.

[12]See

Debye

1910,

1912.

[13]In

his revised

quantum

theory

of

1911

Planck

had

introduced

a

zero-point energy

(see

Planck

1911a,

1911b).

The

possible physical

consequences

discussed

by

Planck included the

speculation

that random

"quantum

emission"

might

somehow

account

for

radioactivity

(see

Planck

1911a,

p.

148).

See

also Einstein's

comments

on

the

connection between

diamagnetism

and

the

existence of

a

zero-point energy

in

his

papers

on

Ampere's

molecular

currents

(see,

e.g.,

Einstein and

De

Haas 1915a

[Doc. 13], p. 153); see

also Vol.

4,

the

editorial

note,

"Ein-

stein and Stern

on

Zero-Point

Energy,"

pp.

270-273,

for Einstein's earlier interest

in

zero-

point energy.

[14]"3)"

should

be "1a)."

[15]In

his later

papers

on

the

quantum

theory

of

radiation,

Einstein

1916j

(Doc.

34)

and

Ein-

stein 1916n

(Doc. 38),

Einstein

carefully

allowed for the

possible degeneracy

of

energy states.

[16]See Debye

1912 and

especially

Debye

1910.

James

Jeans,

following

Lord

Rayleigh,

had

treated

the

radiation

in

an

enclosure

as a

physical system to

which

one

could

apply

statistical

mechanics

(see Rayleigh

1900

and

Jeans

1905a, 1905b,

1905c).

[17]"3b)"

should

be

"1b)."

[18]See

Ehrenfest 1913. Although

Ehrenfest

did

not publish

a

general

treatment

of

the

adia-

batic

theorem until

1916 (Ehrenfest

1916),

he

certainly

discussed

the

topic

earlier with Ein-

stein.

In Ehrenfest

1916,

Ehrenfest

even

ascribes the

name

"adiabatic

hypothesis" to

Einstein.

[19]This

conclusion

was

later criticized

by

Ehrenfest. For Einstein's admission three

years

later that

he

was

wrong, and

for

a

modified

argument

to prove

the

general validity

of

equation

4a),

see

Einstein

to

Paul

Ehrenfest,

12

November

1917.