EINSTEIN

AND STERN ON

ZERO-POINT

ENERGY 273

retracted his results. Soon after the

publication

of the

paper,

he wrote

in

a

letter that

the theoretical

untenability

of

its

results had become

apparent

to

him

"with terrible

clarity."[20]

Without

going

into details,

Einstein

explained

in

a

discussion remark

at

the second

Solvay Congress

in

October

1913

that

in

pursuing

the

implications

of their

derivation of Planck's

formula, he

and Stern had encountered

contradictions,

and that

as a

result their

explanation

of

the

temperature dependence

of

the

specific

heat of

hydrogen

had lost

its foundation.[21] He

also criticized the notion of

a

zero-point

energy

from

an

experimental point

of

view,

finding

it

incompatible

in

particular

with

the

phenomenon

of

superconductivity.[22]

From these

as

well

as

from

other

arguments

Einstein concluded that the

zero-point energy

was

"dead

as a

doornail."[23]

Einstein then returned

to

an

approach

that had

occupied

him after

the first

Solvay

Congress.[24]

The calculation of the

mean

energy

of

a

rotating dipole

in

equilibrium

with

a

radiation

field,

in

analogy

to the

calculation for

a

resonator

performed

by

Einstein and

Hopf

in

1911,

had remained

an

open problem.

When Adriaan

Fokker,

a

former student of

Lorentz's,

came

to

Zurich

in

early

November

1913,[25]

this

was

apparently

the

first

problem

on

which

he

collaborated

with Einstein.[26]

Within

a

month

Fokker

came

to

the conclusion that the calculation of

the

mean

energy

of

a

rotating

dipole

in

equilibrium

with

a

radiation

field

governed

by

Planck's

law

could

not account

for Eucken's

measurements.[27]

Only

after

more

than

a

decade

did it turn out

that these

measurements

were

unsuitable

as a

test

of the

theory

of

the

quantization

of rotational

motion,

since

they

were

clouded

by

complexities

later

to be

described

in terms

of the

distinction between ortho-

and

parahydrogen.[28]

The notion of

a

zero-point energy,

however,

survived

its first

unsuccessful

application

to

the

problem

of

specific

heats

by

Einstein and

Stern,

and

eventually

reemerged as a rigorous consequence

of

quantum

mechanics.

[20]"mit

schrecklicher

Deutlichkeit"

(Einstein

to

Ludwig Hopf,

2

November

1913

[Vol. 5,

Doc.

480]). In

summer

semester 1913

Einstein discussed Eucken's results

in

his

course on

the

molecular

theory

of heat

(see

Appendix A).

According

to

the

notes

on

this

course

taken

by

his

student,

Walter

Dällenbach,

Einstein concluded the discussion with

the

remark: "God

only

knows

why

and

according

to

which law"

("Kein

Teufel weiss

warum

und nach welchem

Gesetz").

[21]See

Laue

et

al. 1921

(Doc. 19),

p.

127.

[22]See

Laue

et

al. 1921

(Doc. 19),

p.

124.

[23]"mausetot"

(Einstein

to

Paul

Ehrenfest,

before

7

November

1913

[Vol.

5,

Doc.

481]).

[24]See

Einstein

to

H. A. Lorentz, 23

November

1911

(Vol. 5,

Doc.

313).

[25]Fokker arrived

in

Zurich

on

7

November

1913

(see

Einstein

to

Elsa

Löwenthal, 7

Novem-

ber

1913

[Vol. 5,

Doc.

482]).

[26]See,

also for the

following,

A. D.

Fokker

to H. A. Lorentz,

4 December

1913 (Vol.

5,

Doc.

490).

See

Needell

1980,

pp.

263-268,

for

a

historical

account.

[27]For

the

publication

of Fokker's

results,

see

Fokker

1914.

[28]See

Dennison 1927

and,

for historical

comments,

Fowler and

Guggenheim 1949,

pp.

83-

93,

and Mehra and

Rechenberg 1982,

p.

148.