218

DOC. 36 REVIEW OF LORENTZ

Doc. 36

Review

of H. A.

Lorentz,

Statistical

Theories

in

Thermodynamics:

Five Lectures

...

[p. 375]

[1]

Whoever has

studied mathematical theories has had the

following, embarrassing

experience:

he verifies

every step

in

a

deduction with

diligence

and

eagerness,

and

at the

end

of his efforts he understands

nothing.

He did not

get

the

guiding

idea of

the whole

concept

because the author

himself

suppressed it,

either from

an

incapacity

to

phrase

it

concisely, or worse,

from

an

almost comical

coquettishness-as

the

insightful

would say-which

was especially popular

in the

past.

This evil

can only

be

overcome by

unrestrained

openness

of the

author,

who should not

shy away

from

familiarizing

the reader

even

with his

incomplete guiding

ideas

if

they

have furthered

[p. 376]

his

own

work. There is

hardly

a

field in theoretical

physics

where this commandment

is

more

difficult to fulfill than

in

statistical mechanics.

Every knowledgeable

reader

[2]

will

agree

with

me

that

Gibbs,

in his

pioneering

book about this

very topic,

has

sinned

quite a

lot

against

this commandment.

Many

have read

it,

many

have verified

it-and

did not understand

it.

Lorentz tackled this evil in his first three lectures

by

displaying

the foundations

of

the

theory

in

a

stunningly simple

mathematical

form,

such that the

guiding

ideas

are

sharply

focused

upon.

In

doing

so,

he

puts

Boltzmann's

principle

at

the

forefront,

and

thoroughly

discusses the

question

of

how the

probability

W in

Boltzmann's

equation

S

=

Klg

W

is to be defined.

Thereby

he

uses

the definition "W

=

phase integral"

and demon-

strates that the definition which has been

suggested by

this

referee,

"W

=

frequency

of

occurrence as a

function

of

time,"

is

essentially

the

same.

The author

explains

on

this occasion what made him refrain from the

second, more descriptive definition;

and

[3]

I

specifically

want to direct the reader's attention

to

this

point.

The last

two

lectures deal

mainly

with the

theory

of Brownian

movement and

with fluctuations. The

last lecture is

a masterly application

of

this latter

theory

to

Planck's radiation

formula. As is well

known,

there

emerge

statistical

properties

of

radiation that cannot be

represented by

the undulation

theory.

The fact that these

relations found

H.

A. Lorentz's interest is

a special pleasure

to this reviewer.

Every

physicist can

learn from this

illuminating

booklet.

A.

Einstein,

Berlin-Charlottenburg