EINSTEIN ON LENGTH
CONTRACTION
479
surement
technique.
Von
Ignatowsky's
treatment
of the
rigid body problem
became
the
starting point
of
a
dispute
with
Ehrenfest.[8]
Vladimir Varicak's
paper
on
Ehrenfest's
paradox is
a
reply
to
Ehrenfest's
first note
on von
Ignatowsky's
work.
Elaborating
on
his
earlier
thought experiment,
Ehrenfest
imagined
that the
rotating
disk
was
covered
with
markers and
that
their
positions
were
traced
onto
tracing paper
in
the
rest
frame with the disk both
at
rest
and
in
uniform
rotation,
with the latter
tracings
conducted
at
a
fixed
instant
in the
rest
frame.
The radius of
the two
images
must be
the
same,
even
though
the
circumference
of
the
latter would
be
shorter-a
contradictory
requirement.[9]
Varicak,
on
the
other
hand,
claimed that the
two
images
would
be identical, since he
believed
that
relativis-
tic
length
contraction
was
not
a physical
fact but
a
psychological
one,
arising
from the
manner
in
which
we regulate
clocks
and
measure lengths.
It arises
if
we measure
the
length
of
a moving
rod
by
timing
reflected
light
signals,
but
not if
we
measure
that
length
from
a tracing-paper
image
made
at
some
instant in the
rest frame.
Einstein wrote
Ehrenfest
in
April
1911,
noting
that
a
reply
to
Varicak
was neces-
sary
"to
avoid
creating
confusion"
and
asking
if Ehrenfest would write
it.[10]
Since
Ehrenfest had
already
announced
his
disagreement
with Varicak and had
proposed
to sort out
the
disagreement by letter,[11]
Einstein took the task
upon
himself.
In his
paper
he first
emphasized,
as
he
had done
on
other
occasions,[12]
that
there
is
no
difference between his and Lorentz's
conception
of
length
contraction
as
far
as
the
physical
facts
are
concerned. He
rejected
the characterization of
length
contraction
as
a
subjective appearance,
and
finally
turned
to
the role of
the measurement process in
explaining
the contraction. In order
to
clarify
that
this
phenomenon
does
not
essen-
tially depend
on
signaling procedures
for
regulating clocks,
a
brief
thought experi-
ment is
discussed
in
which
a
contraction
effect
results without
invoking any
such
procedures.[13]
In
spite
of
its
title,
Einstein's
paper
does
not mention Ehrenfest's
paradox.
This
is
all
the
more
surprising
as
there
is
evidence
that
Einstein and Born had
independently
recognized
Ehrenfest's
paradox
at
the
meeting
of the
Gesellschaft Deutscher Natur-
forscher und Ärzte
in
September 1909.[14]
In
fact,
Einstein
never
did
publish
on
the
topic
of
the
definition of
a
rigid body
in
the
theory
of
relativity.
Nevertheless,
since the
time of
his
discussion with
Born,
the relativistic
analysis
of
rigid
rotation stood
out in
[8]Ignatowsky
1910, 1911, Ehrenfest 1910,
1911a.
For
a
historical
discussion,
see
Klein,
M.
1970, pp.
152-154.
[9]Ehrenfest
1910,
p.
1129.
[10]"damit
keine
Verwirrung gestiftet
werde,"
Einstein to Paul
Ehrenfest,
12 April
1911.
[11]See Ehrenfest 1911a,
p.
413,
fn.
Text dated
15
March
1911;
submitted
17
March
1911.
[12]See, e.g.,
Einstein
et
al. 1911
(Doc.
18),
pp.
V-VI.
[13]For
a
later
review
of the
controversy,
see
Pauli
1921, p.
557.
For
a
discussion of
its
philosophical
aftermath,
see
Hentschel
1990, pp.
412-414.
[14]See
Born
1910a,
p.
233, fn. 2. Ehrenfest
1909
was
dated
September
1909
and submitted
29
September
1909.