148 EARLY WORK ON

QUANTUM

HYPOTHESIS

that

light propagating through empty space

consists

of

electromagnetic

fields

behaving

as

"independent

structures"

("selbständige

Gebilde").[101] Moreover,

"according to this

theory

[of

relativity],

light

has the characteristic in

common

with

corpuscular

theory

of

transferring

inertial

mass

from the

emitting

to the

absorbing

body"

("hat nach

dieser

Theorie mit einer

Korpuskulartheorie

des Lichtes das Merkmal

gemeinsam,

träge

Masse

vom

emittierenden

zum

absorbierenden

Körper zu

übertragen").[102]

In view

of

the

pres-

ence

of

both

wave

and

corpuscular

terms in fluctuations

of

black-body

radiation

(see

sec-

tion

V),

he

argued

that

a new

"mathematical

theory

of radiation"

("mathematische

Theo-

rie

der

Strahlung") is needed,

which

"can

be considered

as a

sort

of

fusion

of

the

wave

and the

emission

theory

of

light" ("sich

als eine Art

Verschmelzung von

Undulations–

und Emissionstheorie des Lichtes auffassen

läßt").[103]

Einstein

1909b

(Doc. 56)

and Einstein 1909c

(Doc. 60), together

with

Einstein's

con-

temporary correspondence, report some

of

Einstein's

intense,

but unsuccessful,

efforts

to

find

an appropriate theory

that would

serve as

such

a

"fusion."[104]

Rather

than

maintain-

ing

his

earlier

inclination toward

a

corpuscular

theory,

Einstein

now suggested

that

per-

haps some

nonlinear modification

of

the Maxwell field

equations

would

yield

not

only

the

quantum

of

electric

charge e as a consequence,

rather than

an assumption

of

the

theory,

but also the

quantum

structure

of

radiation. He

suggested

that the

linear, homogeneous

optical wave equation

should be

replaced by a

nonlinear

or inhomogeneous wave

equation

containing e as a

coefficient.[105]

In

a lengthy

letter

to

Einstein,

Lorentz criticized

Einstein's

search for

a

modification

of

electrodynamics

that would

encompass

both electrons and

quanta,

remaining

unconvinced

of

the existence

of

independent

light

quanta.[106]

In his

reply,[107]

and in his

Salzburg

lec-

ture, Einstein described further

efforts

to

find

a

suitable modification.

By

the

time

of the

Salzburg meeting

he had

hit

upon an

idea

that

allowed

for

both

interference

and

individu-

ality:

in

analogy

to the electrostatic field

surrounding an electron, a light

quantum

could

be treated

as a

mathematical

singularity

surrounded

by an

extended

vector field,

all

of

the

energy

of

the field

being

concentrated in

such

singularities.[108]

He

suggested

that,

if

many

singularities

lie close

together,

their

fields

overlap

to

produce

the effect of

a

continuous

wave

field.

By

this

example

Einstein

attempted

to show that the

wave

and

quantum

aspects

of

radiation,

which he

firmly

believed to be inherent in

Planck's

law, are

not

necessarily

incompatible.

The

problem

of

finding

the correct relation between these two

aspects

of

radiation dominated his

subsequent

work

on

the

quantum hypothesis.

[101]

Ibid.,

p.

487.

[102]

Ibid.,

p.

490.

[103]

Ibid.,

pp.

499 and 483.

[104]

In addition

to

the

papers cited, see,

in

par-

ticular: Einstein to Arnold

Sommerfeld, 19

Jan-

uary

1910;

Hendrik Lorentz

to Einstein,

6

May

1909;

Einstein

to

Jakob

Laub, 19

May

1909;

Einstein to Hendrik

Lorentz,

23

May

1909;

Ein-

stein

to

Johannes

Stark, 31

July

1909;

Einstein

to

Michele Besso,

31

December 1909. For dis-

cussions

of Einstein's

efforts, see

McCormmach

1970a and Klein 1967.

[105]

See Einstein 1909b

(Doc. 56),

p.

192.

[106]

See Hendrik Lorentz

to Einstein,

6

May

1909.

[107]

See Einstein to Hendrik

Lorentz,

23

May

1909.

[108]

See

Einstein

1909c

(Doc. 60),

pp.

499-

500,

and

Einstein

et

al.

1909c

(Doc. 61).

A

year

later,

Lorentz still

expressed

doubts about

light

quanta,

primarily

because

of

the interference

of

very

weak radiation

(Lorentz 1910,

pp.

1249-

1250).