304

THE

RELATIVITY PRINCIPLE

to E, and

if

the

clocks

and

measuring

rods

we use

for

measuring

the time

and

length

are

identical

with those

used

for the

measurement of

time

and

space

in

nonaccelerated

systems. Thus

the principle

of constancy

of

the

velocity of

light

can

be used

here

too

to

define simultaneity

if

one

restricts

oneself

to

very

short light

paths.

We now

imagine

that the clocks of

E are

adjusted, in the

way

described,

at

that time

t

=

0

of

S at

which

E

is

instantaneously

at rest

relative

to S.

The

totality

of

readings

of the clocks

of

E

adjusted

in

[96]

this

way

is called the "local time"

a

of

the

system

E.

It

is

immediately

evident

that the

physical

meaning

of

the local time

a

is

as

follows. If

one

uses

the local

time

a

for the

temporal

evaluation

of

processes

occurring

in

the individual

space

elements of

E,

then the

laws

obeyed

by

these

processes

cannot depend

on

the position

of

these

space

elements,

i.e.,

on

their

coordi-

nates,

if

not only

the

clocks,

but also the other

measuring

tools

used in

the

[97]

various

space

elements

are

identical.

However,

we

must not

simply

refer

to

the local

time

a

as

the

"time"

of

E, because according

to

the definition

given

above, two point

events

occurring

at

different points of

E are

not

simultaneous

when

their local times

a are

equal.

For

if

at

time

t

=

0

two

clocks

of

E

are

synchronous

with

respect

to

S

and

are

subjected

to

the

same

motions, then

they

remain

forever

synchronous

with respect

to S. However,

for this

reason,

in accordance with

§4,

they do

not

run

synchronously

with

respect to

a

reference

system

S'

instantaneously at rest

relative

to

E

but in

motion relative

to

S,

and

hence

according to

our

definition

they

do

not

run

synchronously

with respect

to

E

either.

We now

define the "time"

r

of

the

system

E as

the

totality

of

those

readings

of the

clock situated

at

the coordinate

origin of

E

which

are,

according to

the

above

definition,

simultaneous with the

events which

are

to

be

temporally

evaluated.1

We

shall

now

determines the relation

between

the time

r

and

the local

time

(j

of

a

point

event.

It follows

from

the first of

equations

(1)

that

1Thus

the

symbol

"r" is

used

here

in

a

different

sense

than

above.