504

ELECTRODYNAMICS

OF

MOVING

MEDIA

force.

Assuming

the

presence

of

elastically

bound

charges

in dielectrics, and

of

free

charges

in

conductors,

the electron

theory

aims to derive

the

macroscopic

field

equations

for various material

media, as

well

as

their constitutive

relations,

by suitably averaging

fields,

charges,

and currents

over macroscopic regions

of

each

medium. Lorentz

was

able

to

use

such

microscopic

models

of

matter to

explain a

number

of

electrical, magnetic,

and

optical phenomena

in

material

media.[3]

Hertz's

electrodynamics

of

moving

media

obeys

the

Galileian

relativity

principle,

and

hence is

able to account for

the failure

of

attempts

to detect the motion

of

the earth

by

means

of

optical experiments.

But it

failed

to

explain

other

optical

phenomena,

and

was

soon rejected.[4]

Emil

Cohn

postulated

another set

of

phenomenological equations

that

remedies the defects

of Hertz's

theory

and still

is

able

to

account for the failure

of

attempts

to detect the motion

of

the

earth.[5]

By

1899 Einstein

was a

firm adherent

of

atomism for both matter and

electricity,

and

expressed

himself

in

favor

of

the basic

concepts

of

the electron

theory a

number of

times

thereafter.[6] In his first

paper on

the

theory

of

relativity

he showed that the basic

equations

of Lorentz's

electron

theory are

consistent with relativistic kinematics

if

the

transformation

properties

of

the

quantities entering

the

equations are properly

defined. But he did not

address the

problem

of

formulating a

relativistic

electrodynamics

of

moving

media.

In 1908,

Hermann Minkowski turned

to

this

problem.

He had

recently

discovered

a

four-dimensional

geometrical

reformulation

of

the

theory

of

relativity,

in which Lorentz

transformations

are

interpreted

as

rotations

in

a space

with three real and

one imaginary

coordinate.[7]

He

utilized the four-dimensional formalism to facilitate

investigation

of

the

invariance

of

various

equations

under the Lorentz

group.

In

particular,

he found the elec-

trodynamical

equations

for

a moving

medium

that

follow,

with the

use

of

the

relativity

principle,

from the form

of

the

equations

for

a

medium

at rest.[8] Minkowski showed that

Lorentz's

macroscopic equations

for

moving

media do

not

agree

with the

relativistic

equa-

tions.[9]

He

was working on a

derivation

of

the relativistic

equations

from the electron

theory

at the time

of

his death

in 1909.[10]

Einstein

and Laub

wrote their two

papers

in

1908 as a

response

to

Minkowski's

work.

[3]

See Lorentz

1904c,

§

IV,

"Elektroma-

gnetische Vorgänge

in

ponderablen

Körpern."

[4]

For

a

discussion

of Hertz's

theory

and its

rejection, see

the editorial

note,

"Einstein

on

the

Theory

of

Relativity,"

§

II,

p.

255.

[5]

See Hirosige

1966

for

a

discussion

of

Hertz's

and

Cohn's

theories.

[6]

See Vol.

1,

the editorial

notes,

"Einstein

on

Thermal, Electrical,

and Radiation Phenom-

ena,"

pp.

235-237, and

"Einstein

on

the Elec-

trodynamics

of

Moving

Bodies,"

pp.

223-225.

[7]

His first lecture

on

the

subject (Minkowski

1907b)

was

not

published

until 1915. His first

publication on

the four-dimensional

approach

was

Minkowski 1908. In

a

letter

of

9 October

1907, Minkowski informed Einstein that Ein-

stein

1905r

(Doc. 23)

was

to be discussed in

a

Göttingen

seminar

(see Pyenson 1985,

p.

83),

and

requested

an offprint.

For discussions

of

Minkowski's

work

on special relativity, see

Galison 1979 and

Pyenson

1977.

[8]

See Minkowski 1909.

[9]

See Minkowski

1908,

§

9. In

§

10

Min-

kowski showed

that,

up

to

terms of first order in

the

velocity,

Cohn's

equations

agree

with his

own.

[10]

His work

was completed by

Max Born and

published as

Minkowski 1910.