On the Ehrenfest Paradox.
Comment on V. Varicak's Paper
by
A. Einstein
Physikalische Zeitschrift 12 (1911): 509-510]
(Translation from Collected Papers of Albert Einstein. Volume 3: The
Swiss Years (English Translation). p. 378.
Recently V. VariCak published in this journal some comments [footnote:
This jour. 12(1911): 169] 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)