DOC.

19

JULY

1914 31

19. To

Paul

Ehrenfest

[Berlin,]

8 July

[1914][1]

Dear

Ehrenfest,

Despite

all

the

assurances lately,

it

is

now

unfortunately

impossible

for

me

to

take the

trip

with

you.[2]

One

of

these

days my

mother must endure

a

serious

operation

(cancer)[3]

which has

upset

all

my plans.

But

even

if

it does

not

work

out

this

year:

I

hope

to

go

with all of

you on my

next

walking

excursion.

The

hydrogen

affair

is

very interesting.

It

seems

to

prove finally

that

quanta

without

zero

point

energy

do not conform with

experience.[4]

The

specific

heat

of

heavily compressed gases

also clamors for

zero

point

energy.

But

now we

must

try

it

with

quanta

and

zero

p[oint]

energy:[5]

w=(o+1)e-eo/kTEo=h2/32/n4J(o+1/2)2

E

=

Kr2¿{lgf

+

1e"S}'

The

expressions only differ,

of

course,

by

the

1/2

in

(o+1/2)2

in

Eo.

Would

you

not want to consider

this

case

as

well?

If it

also did

not

conform

with

experience,

it would

get

the

adiabatic

theorem in

trouble

and

surely

also

quantum theory

in

general.

If

you do,

write

me

how

the

matter

stands.-

I

have

considered Nernst’s theorem at

length

and find

that

it should be valid

if

all

solid

phases

at absolute

zero are

unmixed

(chemical individuals)

and

are

crystallized

in

space

lattices.[6]

It

is

simply

S=KlgZ,

where Z is

the

number of

possible

realizations of

the

thermodynamic state.

In

unmixed

space lattices, only

atoms

of

the

same

type

can

be

exchanged

without

leaving

the

thermodynamically

defined

state.

If the

system nv

has

v-type

atoms,

it

is

then

simply

z=II(nv!)

But

if mixed

crystals occur,

then Z

is

larger,

because states allowed

by

the

exchange

of dissimilar atoms result.

With

cordial

greetings

to

you, your

wife,

and

your

little

ones, yours,

Einstein.

Amicable

greetings

also to

your

aunt.