EINSTEIN

AND

STERN ON ZERO-POINT

ENERGY

271

puzzled physicists

since the end of

the

nineteenth

century,

was

the

contribution of

the

rotational motion of molecules

to

the

specific

heat of

gases. Applying

the

quantum

hypothesis

to this

problem

was

therefore

a

natural

step,

but

the

problem

of the

quan-

tization of the rotational motion of

gas

molecules

proved

to be

a

major conceptual

stumbling

block.[5]

By

the end of

1910

Einstein had found

a

method for

determining

the

specific

heat of

a

diatomic molecule

on

the basis of Planck's radiation formula.

"The

matter is

quite simple,"

he wrote to

a

collaborator,

"but of

course

somewhat

problematic."[6]

While Einstein

apparently

hesitated

to

publish

his result,

Nernst

in 1911

postulated

a

simple quantum

formula for the rotational motion of

a

molecule

and

attempted

an

explanation

of the

specific

heat of diatomic

gases

at low

temperatures.[7]

He

also

encouraged

measurements

of

the

specific

heat of

hydrogen,

because

quantum

effects

on

the rotational motion should

in this

case

be

observable

even

at

higher temperatures.

Measurements

were

performed

by

Arnold Eucken

in

Nernst's

laboratory

in

Berlin,[8]

but Eucken's

results,

published

in

1912,

could neither

be

explained

by

Nernst's

simple

formula

nor by

the

equally simple

but

more

consistent

approach

that Einstein had

first

advanced

in 1910

and then

presented

at

the

Solvay Congress

in

1911.[9]

III

When Einstein learned about Eucken's results

in

early

1912,[10]

he

made several

attempts

to

explain

them

theoretically.[11]

He

then abandoned

the

problem during

the

first

intensive

phase

of

his

collaboration with Marcel Grossmann

on

the

theory

of

gravitation

and

only

returned

to it in late

1912.[12]

The result

was

Einstein and Stern

1913

(Doc.

11).

As the

authors

point

out in

the

first

section of their

paper,

a gas

of

rotating

diatomic molecules

is ideal

for

testing

Planck's

assumption

of

a

zero-point

energy,

because for such

a

system

a

zero-point

term

should reveal itself

in

the

specific

heat.

Combining

Einstein's earlier

approach

to

the

quantization

of rotational motion

with Planck's

new

formula,

Einstein

and

Stern found

a

striking agreement

with

Eucken's results

on

hydrogen.

Einstein

may

have discussed

some

of these ideas

with Otto

Stern

already

in

the

summer

of 1912.

Stern,

a

recent graduate

in

chemistry,

had

joined

Einstein

in

Prague

[5]For

historical

discussion,

see,

e.g.,

Kuhn

1978,

pp.

219-220.

[6]"Die Sache

ist

recht

einfach,

aber

natürlich

etwas

problematisch"

(Einstein to

Ludwig

Hopf, 27

December

1910

[Vol. 5,

Doc. 239]).

[7]See

Nernst

1911, §5,

and

Nernst and Lindemann

1911.

[8]See

Eucken

1912.

[9]See

Einstein 1914a

(Vol. 3,

Doc.

26), §4.

[10]See

Arnold Eucken

to Einstein, 23

January

1912

(Vol. 5,

Doc.

340).

[11]See

Einstein

to

Heinrich

Zangger,

27

January

1912

(Vol.

5,

Doc.

344), and

Einstein

to

Heinrich

Zangger,

20

May

1912

(Vol.

5,

Doc.

398).

[12]See

Einstein

to

Paul

Ehrenfest,

20-24 December

1912

(Vol.

5, Doc. 425).