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.