ELECTRODYNAMICS

OF MOVING MEDIA 507

again

defended the Einstein-Laub

expression

with the

help

of

a new

example.[32]

However,

the

expression was soon disputed

in

print.[33]

Controversy

continued

over

this

question,

as

well

as over

the

closely

related

question

of

the

correct

expression

for the stress-momen-

tum-energy

tensor

of

the

electromagnetic

field in

a

material

medium.[34]

In recent

years,

it has been

suggested

that these controversies

arose

from the

failure

to

recognize

that

only

the total force

acting

on

a macroscopic body

is

uniquely

defined. Its

division into two parts-an

electromagnetic (ponderomotive)

force exerted

by

the field

and

a

mechanical force exerted

by ponderable

matter-is

arbitrary

to

a large

extent.

Fur-

thermore, the division

of

the

electromagnetic

force

density

into

components acting respec-

tively on

charge

and conduction current

densities and

on polarization

and

magnetization

densities is also

not

unique.[35]

It

is

possible

to rewrite

Einstein's

and

Laub's

expression

for the total

electromagnetic

force

density

in such

a way

that it

is

consistent

with Min-

kowski's

expression

for the force

density

on a

conduction current

element.[36]

As noted

above,

Lorentz's

equations

for

moving

media differ from Minkowski's

rela-

tivistic

equations.

This

was

considered

puzzling,

since the

underlying equations

of

the

electron

theory,

from which Lorentz derived the

macroscopic

equations,

are

relativisti-

cally

invariant.

Dmitry

Mirimanoff,

a

Privatdozent

in Mathematics at the

University

of

Geneva,

attempted

to show that

Lorentz's

equations can

be

brought

into accord with the

principle

of

relativity by suitably redefining

the transformation

properties

of

some

of

the

field variables under Lorentz transformations.[37] Einstein 1909a

(Doc.

55)

shows

that

this

is

impossible.[38]

Einstein

apparently

had

some difficulty getting

this

paper

accepted by

the

Annalen. In

a

letter

of

19

January

1909,

Wien indicated that he

was once again

returning

the

paper

to

Einstein,

and asked for

a

somewhat

more

detailed

exposition.

Presumably,

Einstein's

revision

of

the

manuscript

satisfied

Wien,

since it

was accepted

three

days

later.

In the last

paragraph

of

his

paper,

Einstein drew attention to

an

electron-theoretical

derivation

of Minkowski's

equations by

Frank.[39]

This

paper

established, for

nonmagnetic

media,

that it

was

Lorentz's

failure to take the Lorentz contraction and time dilation

fully

into account which led to his derivation

of

nonrelativistic

equations.

[32]

See

Einstein

1910b.

[33] See, e.g.,

Gans 1911 and Grammel 1913.

[34]

See

Pauli

1921, pp.

662-668,

for

a

review

of

these discussions

up

to 1921

(see p.

216

of

Pauli

1958 for

a

note

added

to

the

English

edi-

tion).

See

De Groot and

Suttorp

1972,

chap. V,

§

7,

for

a

review that includes

subsequent con-

tributions.

[35] See, e.g.,

De

Groot and

Suttorp 1972,

chap.

V,

§

7,

and Pavlov 1978 for discussions

of

the

nonuniqueness

of

these divisions.

[36]

See, e.g.,

Pavlov

1978,

p.

172.

[37]

See Mirimanoff

1909.

[38]

A letter

of

12

February

1909 from Miri-

manoff

to

Einstein indicates that

they

had

pre-

viously corresponded

about

Mirimanoff's

paper.

[39]

See

Frank

1908. For

a

review

of

electron-

theoretical derivations

of Minkowski's

equa-

tions

up

to 1920,

see

Pauli

1921,

pp.

659-662.