EINSTEIN ON

LENGTH

CONTRACTION IN THE

THEORY OF RELATIVITY

Three themes

are

relevant

to

Einstein's brief

polemical

paper

which

appears

here

as

Doc. 22:

the

concept

of

the

rigid body

in the

theory

of

relativity,

the

question

of

whether the Lorentz contraction

is

real

or

only apparent,

and the role of accelerated

motion

in

the

theory

of

relativity. Although

Einstein 1911f

(Doc.

22)

explicitly

ad-

dresses

only

the second of these

themes, it

responds

to

a

paper

by

Varicak[1]

that

was

part

of

a

controversy

on

the definition of

a

rigid body

in

the

theory

of

relativity during

the

years

1909-1911.

The

controversy began

with Born's

proposal

of

a

relativistically

invariant definition

of

a

rigid

body.[2]

At

that

time,

the definition claimed interest

not

only

as

the

general-

ization of

a

concept

from classical

physics

to

relativity

but

also,

as

Born

pointed out,

because of its

promise

to

help

in

explaining

the

dynamics

of

the electron. Born's

proposal

was

followed

by a

short

paper

in

which Ehrenfest

gave

a

different but

equivalent

definition of

a

rigid body, as

well

as

his

discovery

that

both definitions lead

to

a paradox.[3]

Ehrenfest noted

that

the radius of

a rigid

disk

in

uniform rotation

about

its

central

axis

would have

to

satisfy

two

contradictory requirements:

it would have

to

be

con-

tracted

to

accommodate the Lorentz contraction of the

circumferentially

directed

elements of the

disk,

but

it

would also have

to

remain

unchanged

because the radial

elements,

oriented

normally

to

the rotational

motion,

would

be

uncontracted. This

re-

sult,

which

shortly appeared

in

more

elaborate form

in

the work of Gustav

Herglotz[4]

and Fritz

Noether,[5]

became the

focus

of much

discussion.[6]

By

1911

Ehrenfest's

paradox

had become the

starting point

for several

arguments

which convinced

physicists

that the

concept

of

a

rigid body

is

problematical

in

the

theory

of

relativity.

Laue,

in

particular,

showed

that

any

definition of

a

rigid body

would be in conflict

with the

theory

of

relativity's implication

that

no

signal velocity

can

exceed the

veloc-

ity

of

light.[7]

One of the

participants

in the

rigid body controversy,

Waldemar

von

Ignatowsky,

had

attempted

to

explain away

Ehrenfest's

paradox by claiming

that,

according

to

the

theory

of

relativity,

the Lorentz contraction is

only

an

artifact of

a

particular

mea-

[1]Varicak

1911.

[2]See Born 1909.

For

a

brief historical

discussion,

see

Einstein

1907h

(Vol. 2,

Doc.

45),

note

8.

[3]Ehrenfest

1909.

[4]Herglotz

1910.

[5]Noether

1910.

[6]See

Abraham

1910,

Born

1910a, 1910b,

Planck

1910b.

For

an

overview,

see

Miller

1981,

chap. 7.

[7]See

Laue

1911.