352

DOC.

18

DISCUSSION OF

DOC.

17

perception

of

time.

The

difficulties start

only

when it

comes

to the

fixing

of

temporal

events at

places

removed

from

us.

In

view

of

this

circumstance

Einstein introduced

and

carried

out

the

radical

expedient

of

measuring

and

fixing

times

by making

them

measurable

by means

of

light paths,

because,

in

the

end,

he

always comes

to

perceive

the

world around

us by way

of

light signals.

He

makes times

measurable

by light

paths

and

lays

down

the

postulate,

which has

recently emerged

from

our

experience,

that

equal

distances must

be traveled

in

equal

times. This

postulate

makes it

possible

to

compare

clocks with

each

other,

and

this in turn makes it

possible

to resolve

the

question:

How

do clocks

run

if

one

of them

is

located

in

a system

at

rest,

and

the other

in

a

moving

system?

Quite

stringent arguments

show

that these

clocks do

not

run

synchronously.

It

turns out

that the notion of

time

as something

absolute

in

the

old

sense

cannot

be

maintained,

but

that,

instead,

that

which

we

designate

as

time

depends

on

the

states

of

motion.

Something

similar

obtains for the

spatial

coordinates

by

means

of

which

we

usually

represent

spatial

relations.

They

prove

to

be

dependent on

the

state

of motion.

This

also

seems

to

be of

a

revolutionary

character insofar

as we

used

to

think of

length

as

something absolute,

i.e.,

something independent

of

velocity.

Upon

closer

examination,

the

matter

of

this

fixity

and

peculiar

definiteness of the

spatial

coordinates

is not

all

that

simple.

I would

say

that the

relativity

principle

brings us only a

clarification and not

some-

thing

that

is

fundamentally new.

Now Mr.

Einstein

has shown

that,

based

on

the

assumption

of the

constancy

of the

velocity

of

light

and

the

relativity principle,

some

simple

relations

exist

between the coordinates of

space

and

time

for

systems moving

relative to

each other. If

we

introduce into the mathematical

expressions

of

laws

that

are

valid with

respect

to

a

coordinate

system

k the

space

and time coordinates of

another

reference

system

k', which

are

connected

with

those of

k

by

the

simple

equations

peculiar

to

the

theory

of

relativity, we

arrive at laws

of the

same

form. This

is

the

property

that, above all

else,

made the

relativity

principle

creditable

to

the mathemati-

cians.

They recognized

that

this

invariability

for these

systems

involves

something

with

which

they

are

familiar,

a

special case

of the

invariance

they

occasionally

observe in

the

structures

of

projective

geometry.

The observation that

something

well known in its

mathematical formulation

is already

finding

application

in

reality

has

helped

gain

credit

for the

relativity

principle.

As for the

physicist,

when the

admissibility

of

such

a principle

is

being discussed,

he

is

wont to

keep just

to

arguments

of

a more

physical

character. The

consequence

of the

relativity

principle

that motion results

in

a change

of

shape is

to

us

of much

greater

importance.

In other

words,

this

consequence

yields

the result that

rigid

bodies

in the

usual

sense

of

the word

do

not exist.

A

body

moving

in

a

certain direction

gets

flattened,

it

becomes

an ellipsoid

in

the direction of motion.

Thus, rigid

bodies do

not

exist,

because

all

bodies

are

in

motion.

This

is something

that

runs

counter to

the

naive