EINSTEIN AND LAUB ON THE

ELECTRODYNAMICS

OF MOVING MEDIA

At the

beginning

of

this

century,

the

electrodynamics

of

moving

bodies,

as

usually

under-

stood,

included not

only

the

microscopic

electron

theory,

but also the

macroscopic theory

of

electromagnetic

and

optical phenomena

in

polarizable

and

magnetizable

material

media

in

motion. To

distinguish

between the two

topics,

the latter

is

referred to here

as

the

elec-

trodynamics

of

moving

media. In

1905

Einstein had

only applied

relativistic kinematics

to

Lorentz's

electron

theory.

In 1908 Minkowski offered the first solution

to

the

problem

of

formulating a

relativistic

electrodynamics

of

moving

media. Since

then,

the nature

of

the

proper

solution

to

this

problem

has been

a subject

of

considerable

controversy,

with

a

number

of

questions

still in

dispute.

Einstein, in

collaboration with Jakob

Laub,

discussed

the

topic

in two

papers,

Einstein

and

Laub 1908a

(Doc. 51),

1908b

(Doc. 52).

In the

first,

they

rederived

Minkowski's

relativistic field

equations

and

suggested an experimental

test

of

them. In the

second,

they disputed

his

expression

for the force exerted

by

the

magnetic

field

on a

volume element

of

a magnetic

medium.

They

also

published

two

corrections to

the

first

paper,

Einstein

and Laub

1908c

(Doc. 53),

1909

(Doc. 54).

In

Einstein

1909a

(Doc. 55),

Einstein commented

negatively

on an

attempt

to

show

that

Lorentz's

electro-

dynamics

of

moving media,

which

appears

to

be

a

nonrelativistic theory,

is

actually

in

accord

with

relativity.

Starting

with

Hertz, one

approach

to

the

electrodynamics

of

a (resting or moving) me-

dium

was simply

to

postulate

the

macroscopic

field

equations,

which

may

be

considered

to be

fundamental,

or

to be

ultimately

derivable from

some underlying

microscopic

model.[1] This

approach employs a pair

of

fields

(E

and

D) to

describe the electric state

of

the

medium,

another

pair

(B

and

H) to

characterize its

magnetic

state,

as

well

as charge

and current

density

functions

(the

latter

may

include conductive and convective

terms).

In

addition

to

Maxwell's

field

equations,

which take the

same

form

in

all

media,

constitutive

equations

must

be

specified

to characterize the relations between the field

quantities

in

a

particular

medium. An

expression

for the force exerted

by

the electric and

magnetic

fields

on a

volume element

of

the

medium,

then known

as

the

ponderomotive

force, must

also

be

specified.

Starting

with

Lorentz,

another

approach

to

the

macroscopic equations was

to

derive

them from

microscopic

models

of

the structure

of

material

media,

both dielectrics and

conductors.

Lorentz's

electron

theory,

the

most

influential such

program, postulates only

one

electric and

one magnetic

field vector

in

vacuum (ether),

and

charged

particles,

the

motions

of

which constitute convection currents.[2] Lorentz

also

specified an expression

for the

ponderomotive

force

on

a

moving charged particle,

which

is

now

called the Lorentz

[1]

For

a

review

of Hertz's

theory, as

well

as

other theories

of

electrodynamics

before

1905,

see

Hirosige 1966, which, however,

does

not

stress

the distinction between the

macroscopic

and

microscopic approaches.

[2]

See Lorentz

1904c, 1909b,

and 1915 for

contemporary

reviews of his work

on

the elec-

tron

theory.

For further discussion

of

Lorentz's

theory, see

the editorial

note,

"Einstein

on

the

Theory

of

Relativity,"

§

II,

pp.

256-257.