DOC.

23

141

basis of Maxwell's

theory

for bodies

at rest.

The

introduction of

a

"light

ether"

will

prove

superfluous, inasmuch

as

in accordance with the

concept to

[6]

be developed

here,

no

"space at

absolute

rest"

endowed

with

special properties

will

be introduced,

nor

will

a

velocity

vector be

assigned

to

a

point

of

empty

space

at which electromagnetic

processes are

taking

place. [7]

Like

every

other

electrodynamics,

the

theory

to be

developed

is

based

on

the kinematics of the rigid

body,

since assertions

of

each

and

any

theory

concern

the relations

between

rigid bodies

(coordinate

systems),

clocks,

and

electromagnetic processes.

Insufficient

regard

for this circumstance is

at

the

root

of the difficulties with

which

the

electrodynamics

of

moving

bodies

must presently grapple.

I.

Kinematic

Part

§1.

Definition

of

simultaneity

Consider

a

coordinate

system

in

which

the

Newtonian

mechanical

equations

are

valid.

To

distinguish

it

verbally from

the coordinate

systems

that will

[8]

be

introduced later

on,

and to

visualize it

more

precisely,

we

will designate

this

system

as

the

"system

at

rest."

If

a

material

point

is at rest

relative

to

this coordinate

system,

its

position

relative

to

the latter

can

be

determined

by means

of rigid

measuring

rods

using

the

methods of

Euclidean

geometry

and

can

be

expressed

in

Cartesian

coordinates.

If

we

want

to

describe the

motion

of

a

material point,

we

give

the

values of its coordinates

as a

function of time.

However,

we

should

keep

in

mind

that for

such

a

mathematical description

to

have physical

meaning,

we

first

have to

clarify

what

is

to be

understood here

by

"time."

We

have to

bear in

mind

that all

our

propositions

involving

time

are

always

propositions

about simultaneous

events.

If, for

example,

I

say

that "the train arrives

here

at

7

o'clock,"

that

means,

more or

less,

"the

pointing

of the small

hand

of

my

clock

to

7

and

the arrival of the train

are

simultaneous events."1

1We

shall

not

discuss here the

imprecision

that is inherent in the

concept

of

simultaneity of

two events

taking

place

at

(approximately)

the

same

location

and

that also

must

be

surmounted

by

an

abstraction.