DOC.

25

SOLVAY

DISCUSSION REMARKS

391

Doc.

25

Discussion Remarks

Following

Lectures

Delivered

at

First

Solvay

Congress

[30

October-3 November

1911]

III.

LORENTZ

Lorentz's lecture

(Lorentz 1912)

discusses several

ways

of

studying

the

applicability

of the

law

of the

equipartition

of

energy

to

heat

radiation,

one

of

which

is

related

to

the

work

by

Einstein and

Hopf

(see

Einstein

and

Hopf 1910b

[Doc.

8]).

Following

this

approach,

which

was

outlined

by

Einstein in

1909

(see

Einstein 1909b

[Vol. 2,

Doc.

56],

p.

190),

Lorentz

assumes a

frictionlike force

acting

on an

electron

moving

in

the

radiation

field,

and he inserts

the

velocity change

in

the

time

r

due

to

this force into

an expression

for

the

fluctuations

of

the

velocity

of the

electron

(see

Lorentz

1912,

pp. 35-39).

From his

expression

for these

fluctuations,

he

attempts

to

determine

the

mean energy

of

the

electron

but

obtains

unsatisfactory

results. Einstein's first

comment refers

to

an objection

raised

by

Planck

against

the

separability

of

oscillatory

and linear motion

assumed

by

Lorentz

(see

Lorentz

et

al.

1912,

pp. 46-47,

and Lorentz

et

al.

1914,

pp. 39-40),

and his second

comment refers

to two

alternative

proposals

to

Lorentz's

procedure, one suggested by

Planck in his discussion

remark,

the other

by Langevin (see

Lorentz

et

al.

1912, pp. 42-44,

and Lorentz

et

al.

1914, pp. 36-37).

Contrary

to Lorentz,

Planck and

Langevin

in

their

respective

comments

describe the motion

of the

electron

by means

of

ordinary

differential

equations

instead

of

an expression

for fluctuations.

No. 22

(Lorentz

et

al.

1914, p.

40;

Lorentz

et

al.

1912, p. 47)

The smaller the radiation

density,

the

more completely can

the

oscillatory

motion

of

the electron that

is

caused

by

the

momentary

influence

of the radiation

be

separated

from its

translational motion.

No.

25

(Lorentz

et

al.

1914,

p. 40;

Lorentz

et

al.

1912,

pp. 47-48).

The last

sentence

in

the

following

text

reads

in

the

published

version:

"For

this

reason

neither

the

consideration

of

Mr.

Langevin

nor

that

of

Mr.

Planck

solves the

problem,

in

my opinion."

The consideration differential

equation

neglects

those

terms

by

virtue of

which

the

mean

translational

motion

of

the

electron

(independent

of

the

momentary

radiation

field)

can change. Mathematically,

this manifests

itself

in

the

circumstance

that

an

additive

constant in

v

remains

undetermined.

For

this

reason

the consideration does

not solve

the

problem

in

my opinion.

IV.

PLANCK

In his lecture Planck examined various

ways

of

accounting

for

the

spectral

distribution

of

black-body

radiation.

In

one approach,

which

corresponds

to

his earlier derivation

of

his

formula for

black-body

radiation

by

methods

of

statistical

physics,

he determined

the

probability

of

a

given macroscopic state by counting

the

combinatorial

possibilities

for

realizing

this

state

in

terms

of

microscopic configurations (Boltzmann's "complexions"); see

Planck

1914, pp.

86-87.

In his first

comment

on

Planck's

lecture,

Einstein summarized

the

critique

of this

approach,

which

he

had earlier

presented

in Einstein 1909b

(Vol. 2,

Doc.

56), pp.

187-188. In line with his