XlVi

INTRODUCTION

TO

VOLUME

8

Einstein’s

challenge triggered

a

correspondence

with Michael

Polányi, starting

in December 1914. In

an

earlier

proof

of

the

heat theorem

Polányi

had tried

to

show

thermodynamically

that

at

absolute

zero

reversible isothermic

changes are

isen-

tropic-an alternative formulation

of

the heat theorem. A

crucial

ingredient

in the

proof

was

the

vanishing

of

the

specific

heat at absolute

zero,

for

which both theo-

retical and

experimental

indications existed.

Polányi’s

proof is

based

on a thought-

experiment,

in which the

temperature

of

a system

is

systematically

lowered

by

a

succession

of

adiabatic

expansions

and isothermal

compressions.

He claims

that

as

one comes

closer

and closer to

absolute

zero,

the isothermal

compressions

would

eventually

become

isentropic.

Einstein directed his

criticism

at this

claim, pointing

out

that the

proof

is

only

valid

if

it takes

infinitely many steps

to

reach absolute

zero.

If,

on

the

contrary, a

finite

number

of

steps

suffices,

the

proof

fails. Einstein

also

gives a counterexample,

worked

out

in various

ways,

to show that

systems

might

exist

for

which isothermal

compressions

at

zero

temperature

would not be

isentropic.

In

response

to Einstein’s fundamental

criticism,

Polányi

tried

to

modify

his

proof,

but at the end he had to

admit

that it had

at

best

a

limited

validity.

Another

correspondent

who

was

concerned with the

validity

of

the

heat theorem

was

Einstein’s

former

collaborator,

Otto Stern. He had also

published a

thermody-

namic

proof

of

the theorem.

From

his

proof

it

followed that the

entropy

of

mixed

crystals

or

solid solutions

vanishes at

absolute

zero,

if

these

systems

have

a

single

microstate with

an

energy

lower than that of

all

others. In

an

exchange

in the

spring

of

1916,

Einstein

stressed

once again

his conviction

that

the heat theorem could

only

be valid

for

single crystals.

The

discussion then

focused

on

the

question

whether

mixed

crystals

could exist at absolute

zero, and,

if

so,

what their

entropy

would be. Both

parties put

forward

clever

and instructive

arguments

and models to

support

them. The debate ends in

a

stalemate,

with

neither of

the

correspondents

prepared

to

give up

his

point

of

view.

These

two

exchanges on

the heat

theorem

are

not

just interesting

because

of

the

importance

of

the

issues involved.

They are

also

typical

in

showing

Einstein’s

con-

cern

with

fundamental

physical questions

and his

talent of

getting

directly

to the

heart

of

the

matter, illustrating

his

arguments

with

simple

but

illuminating

analo-

gies

or

models and

always aiming

at

conceptual

clarification.

VI

Most

of Einstein’s

scientific

activity during

the

years

covered

by

this volume

was

focused

on

the

development

of

the

general

theory

of

relativity.

In the fall

of

1913,

when Einstein

presented

his lecture

on

the

current state

of

the

problem

of

gravita-

tion in

Vienna,[15]

the

early

version

of

his

theory,

the so-called “Entwurf”

theory,[16]