DOC.

51

329

Doc.

51

ON

THE FUNDAMENTAL ELECTROMAGNETIC

EQUATIONS

FOR

MOVING

BODIES

by

A.

Einstein

and

J.

Laub

[Annalen

der

Physik 26

(1908):

532-540]

In

a

recently

published

study1

Mr. Minkowski

has presented

the funda-

mental equations

for the

electromagnetic

processes

in

moving

bodies.

In view

of

the fact that this

study

makes

rather

great

demands

on

the reader in its

mathematical

aspects,

we

do

not

consider it

superfluous

to

derive here these

important equations

in

an

elementary

way,

which,

is,

by

the

way,

essentially

in

agreement

with that

of Minkowski.

§1.

Derivation

of

the

fundamental equations

for

moving

bodies

The route to

be

taken

is

as

follows:

We

introduce

two

coordinate

systems

K

and K',

both

of which

are

nonaccelerated but

in

relative

motion.

If

the

space

contains

matter at rest

relative

to

K', then the

laws of

the

electrodynamics

of

bodies

at rest,

described

by

the Maxwell-Hertz equations,

will hold with

respect to

K'. If

we

transform these

equations to

the

system

K, we

directly obtain

the

electrodynamic equations

of

moving

bodies for

the

case

that the velocity of

the

matter

is spatially

and temporally

constant.

Obviously,

the

equations

so

obtained hold

at

least in first

approximation

also

in the

case

when

the distribution

of velocity of

the

matter

is arbitrary.

[2]

This

assumption

is also partly justified

by

the fact that the result obtained

in this

way

is strictly valid in the

case

of

a

number

of bodies

moving

with

different uniform velocities that

are

separated

from each

other

by vacuum

interspaces.

When

referred

to

the

system

K',

the

vector

of the electric force will

be

denoted

by

(£', that

of

the

magnetic

force

by

V',

that of the dielectric

displacement

by

©', that

of the

magnetic

induction

by

,

that of

the

1H.

Minkowski, Gottinger

Nachr.

1908

[1]