378

DOC.

22

EHRENFEST PARADOX

Doc. 22

On the Ehrenfest Paradox.

Comment

on

V.

Varicak's

Paper

[1]

by

A.

Einstein

[Physikalische Zeitschrift

12

(1911):

509-510]

Recently

V. VariCak

published

in this

journal

some

comments1

that

should not

go

unanswered because

they

may cause

confusion.

The author

unjustifiably

perceived

a

difference

between Lorentz's

conception

and

[3]

mine

with

regard

to

the

physical facts.

The

question

of whether the Lorentz contraction

does

or

does

not exist in

reality

is

misleading.

It

does not exist "in

reality"

inasmuch

as

it

does

not exist

for

a moving

observer;

but

it

does

exist "in

reality,"

i.e.,

in such

a way

that,

in

principle,

it

could be detected

by physical means,

for

a

noncomoving

observer.

This

is just

what

Ehrenfest made clear

in such

an

elegant

way.

We obtain the

shape

of

a

body moving

relative to

the

system

K

with

respect

to

K

by finding

the

points

of K

with which

the material

points

of the

moving body

coincide

at

a

specific

time

t

of

K.

Since

the

concept

of

simultaneity

with

respect

to

K that

is

being

used

in this

determination

is completely defined, i.e., is

defined

in such

a way

that,

on

the

basis

of

this

definition,

the

simultaneity can,

in

principle,

be established

by

experiment,

the Lorentz contraction

as

well

is

observable

in

principle.

Perhaps

Mr. VariCak

might

admit-and thus

in

a

way

retract

his

assertion-that the

Lorentz contraction

is a

"subjective

phenomenon."

But

perhaps

he

might cling

to

the

view

that the Lorentz contraction

has its roots

solely

in

the

arbitrary stipulations

about

[4]

the "manner of

our

clock

regulation

and

length

measurement." The

following

thought

experiment

shows to what extent this view cannot be

maintained.

Consider

two

equally long

rods

(when

compared

at

rest)

A'B' and

A"B",

which

can

slide

along

the

X-axis

of

a

nonaccelerated coordinate

system

in

the

same

direction

as

and

parallel

to

the

X-axis.

Let A'B' and A"B"

glide

past

each other

with

an

arbitrarily

large,

constant

velocity,

with

A'B'

moving

in

the

positive,

and A"B"

in

the

negative

direction of the

X-axis.

Let the

endpoints

A' and A"

meet at

a

point

A*

on

the

X-axis,

while

the

endpoints

B' and B"

meet

at

a

point

B*.

According to

the

theory

of

relativity,

the

distance A*B*

will then

be smaller than the

length

of either of

the two

rods A'B'

and

A"B",

which fact

can

be established

with

the

aid

of

one

of the

rods,

by laying

it

along

the stretch

A*B* while it

is

in

the

state

of

rest.

Prague, May

1911. (Received

on

18

May 1911)

[2]

1

This

jour.

12

(1911):

169.