EINSTEIN

AND

STERN

ON

ZERO-POINT ENERGY

I

The

paper by

Einstein and Otto

Stern,

Einstein and Stern

1913

(Doc. 11) presents

the

results of their

study

of

some

ways

in

which the

zero-point

energy,

introduced

two

years

earlier

by

Max Planck

in his

"second

quantum

theory," might

affect

physical

phenomena[1] They

offered

two

arguments

in

favor of

accepting zero-point

energy

as

real.[2]

Planck had deduced the existence of

an

extra term in

the

energy

of

an

oscillator

of

frequency

v

that absorbs

energy continuously

but emits

energy

only

in

integral

multiples

of

hv. The

spectral

distribution of

black-body

radiation

is

unaffected

by

the

extra

energy,

whose

magnitude

is

hv/2 for each

oscillator,

and is

independent

of

temperature.

Einstein and Stern showed that

a

theory,

an

approximate

one,

of

the

energy

of

rotating

molecules which

incorporates

the

zero-point energy agreed quite

well with

Arnold Eucken's

recent measurements

of the

specific

heat of

hydrogen gas

at low

temperatures.

The

same

approximate theory

but with the

zero-point energy

omitted

led

to

a specific

heat

versus

temperature curve qualitatively as

well

as

quantitatively

different from the

experimental

behavior.

Einstein

and

Stern also

gave a

new

derivation of the Planck

radiation distribution

law,

a

derivation based

on

the

assumption

of

a

zero-point

energy,

but

making

no

assumption

of

discontinuity

at all. In

spite

of the

apparent

success

of this

paper,

Ein-

stein

soon

lost confidence

in

the

concept

of

zero-point energy

and

publicly

stated that

he

no

longer

believed

in it at

the second

Solvay Congress

in

late October

1913.[3]

II

Following

the

publication

of Einstein's work

on

the

specific

heat of

solid bodies in

1907,[4]

the

quantum hypothesis

had become

an

important

instrument

for

solving prob-

lems related

to the

atomistic

conception

of

matter.

One of those

problems,

which had

[1]See

Planck

1911a, 1911b, 1912,

1914a.

See,

e.g.,

Einstein

to Wilhelm

Wien,

17 May

1912

(Vol. 5,

Doc.

395),

for

an expression

of Einstein's

skeptical

attitude toward

this

theory.

For

a

historical discussion of Planck's second

theory, see

Kuhn

1978, chap. 10,

and Needell

1980, chap.

4.

[2]For

historical

accounts

of the Einstein-Stern

paper,

see Klein,

M.

1970,

pp.

265-267, and

Needell

1980,

pp.

252-256. See Eucken

1914,

pp.

374

and

400-405,

for

a

contemporary per-

spective on

Einstein and Stern's work

on

zero-point energy.

[3]See

Einstein's discussion remark

following

Max

Laue's lecture

(Doc.

22).

See also

Ein-

stein to

Ludwig Hopf,

2

November

1913

(Vol.

5,

Doc.

480),

in which

he states

that the

unten-

ability

of

the

zero-point energy

became clear

to

him

soon

after

the publication

of Einstein and

Stern

1913

(Doc.

11).

[4]Einstein 1907a

(Vol.

2,

Doc.

38).