I PLACE a metrerod in the x'axis of k'
in such a manner that one end (the beginning) coincides with the point
x' = 0, whilst the other end (the end of the rod) coincides with
the point x' = 1. What is the length of the metrerod relatively
to the system K? In order to learn this, we need only ask where
the beginning of the rod and the end of the rod lie with respect to K
at a particular time t of the system K. By means of the first
equation of the Lorentz transformation the values of these two points at
the time t = 0 can be shown to be
the distance between the points being
But the metrerod is moving with the velocity v relative
to K. It therefore follows that the length of a rigid metrerod
moving in the direction of its length with a velocity v is
of a metre. The rigid rod is thus shorter when in motion than when
at rest, and the more quickly it is moving, the shorter is the rod. For
the velocity v = 0 we should have
and for still greater velocities the squareroot becomes imaginary.
From this we conclude that in the theory of relativity the velocity c
plays the part of a limiting velocity, which can neither be reached nor
exceeded by any real body.

1 
Of course this feature of the velocity c as a limiting
velocity also clearly follows from the equations of the Lorentz transformation,
for these become meaningless if we choose values of v greater than
c. 
2 
If, on the contrary, we had considered a metrerod at rest in
the xaxis with respect to K, then we should have found that the
length of the rod as judged from K' would have been
this is quite in accordance with the principle of relativity which
forms the basis of our considerations.

3 
A priori it is quite clear that we must be able to learn
something about the physical behaviour of measuringrods and clocks from
the equations of transformation, for the magnitudes x, y, z, t,
are nothing more nor less than the results of measurements obtainable by
means of measuringrods and clocks. If we had based our considerations
on the Galilei transformation we should not have obtained a contraction
of the rod as a consequence of its motion. 
4 
Let us now consider a secondsclock which is permanently situated
at the origin (x' = 0) of K'. t' = 0 and t'
= 1 are two successive ticks of this clock. The first and fourth equations
of the Lorentz transformation give for these two ticks:
and 
5 
As judged from K, the clock is moving with the velocity
v; as judged from this referencebody, the time which elapses between
two strokes of the clock is not one second, but
seconds, i.e. a somewhat larger time. As a consequence of
its motion the clock goes more slowly than when at rest. Here also the
velocity c plays the part of an unattainable limiting velocity.

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