272

EINSTEIN AND

STERN

ON

ZERO-POINT ENERGY

after

obtaining

his

doctorate

in the

spring

of

1912

and later followed

him to Zurich.[13]

From

a

later recollection

by

Stern

it is

clear that

his

principal

contribution

was

the

derivation, in the

second

part

of

the

joint paper,

of Planck's radiation

law using

the

zero-point

term.[14] According to

Stern's

recollection,

Einstein had

suggested

to

him

that

this

result

might

be

achieved

by

modifying

a

derivation of

the

classical

Rayleigh-

Jeans

law

that Einstein and

Hopf

had

developed

earlier.[15]

Stern

performed

the

cal-

culation but found that

he

needed

a

zero-point

term

of

hv

instead of Planck's

hv/2.

Einstein asked

him to

redo

the

calculation

and

eventually

did it

himself

as

well,

each

time with the

same

result.

Although

the

particular

value for

the

zero-point energy

found

by

Einstein and

Stern

was

not

confirmed

by

Eucken's

measurements,

their

derivation showed that

one

could also obtain Planck's radiation

law

without

the

assumption

of

a discontinuity.

Successful

as

Einstein

and Stern's

explanation

of

the

temperature

dependence

of

the

specific

heat of

hydrogen

seemed

to be,

it

was

marred

by

a

number of

problematic

assumptions.

In

order

to

simplify

their

calculation,

they

assumed that

all molecules

rotate

with

the

same

speed.

What

is

more,

their

very use

of Planck's formula

with

a

zero-point

term

was

questionable,

since the

derivations of

this formula-by

Planck

as

well

as

by

Einstein and

Stern-refer

to resonators

whose

energy

is

independent

of

their

frequency,

and

not

to rotators. It

was

therefore natural that various other

avenues

to the

quantization

of diatomic molecules

were

pursued.

Einstein and Lorentz had

discussed

one

such

approach already

in

1911.[16]

Lorentz

presented

it at the first

Solvay

Congress, arguing

that

the

quantum hypothesis

should

be

applied directly

to

restrict

the

possible energy

values,

and

hence

the

possible frequencies

of

a single

rotator.

Einstein

suggested addressing

the

problem

of

the

relation between

energy

and fre-

quency

by

introducing

what

were

later

to be

called "adiabatic

invariants."[17]

The

paper

by

Einstein

and Stern

aroused

widespread

interest and stimulated theo-

retical

as

well

as

experimental

research.[18]

Pierre Weiss drew Einstein's attention

to

measurements

by

Pierre

Curie

on

the

paramagnetic susceptibility

of

oxygen as

evi-

dence for

the

existence of

a

zero-point

energy.[19]

But

in the fall

of

1913

Einstein

[13]Stern

received

his

doctorate

in

physical chemistry

from

the

University

of Breslau. For

a

contemporary comment

by

Einstein

on

his

collaboration

with Stern,

see

his

Gutachten

zu

dem

Habilitationsgesuch

des

Herrn

Dr. O. Stern,

15 July

1913 (see

Vol.

5,

Doc.

452).

For later

recollections

by

Stern,

see

the

typescript

of

Res

Jost's

interviews with

Stern, 25

November and

2

December

1961,

SzZE Mediathek.

[14]See

typescript

of

Res

Jost's interviews with

Stern,

25

November and

2

December

1961,

SzZE

Mediathek,

pp.

6-7. See also

Segre 1973,

pp.

216-217.

[15]See

Einstein and

Hopf

1910b (Vol. 3,

Doc.

8).

[16]See,

also for

the

following,

Einstein

et

al.

1914a

(Vol. 3,

Doc.

27),

pp.

362-364.

[17]In

1913

Ehrenfest

independently

developed

the

approach

earlier considered

by

Lorentz

and

Einstein, and

also dealt

with the question

of

the

statistical distribution of rotational

fre-

quencies

(see Ehrenfest

1913, 1914).

For historical

discussions,

see

Klein,

M.

1970,

pp.

264-

273,

and Needell

1980, pp.

256-259.

[18]See

Eucken

1914,

pp.

400-405.

[19]See

the note

added

in

proof

to

Einstein and Stern

1913

(Doc. 11).

See

also

Klein, M.

1966 for

a

discussion of other

experiments

that seemed

to

support

the

existence of

zero-point

energy.