06 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=c we should have eq. 06a ,
and for stiII greater velocities the square-root 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.
Of course this feature of the velocity c as a limiting velocity also
clearly follows from the equations of the Lorentz transformation, for
these became meaningless if we choose values of v greater than c.
If, on the contrary, we had considered a metre-rod at rest in the
x-axis with respect to K, then we should have found that the length of
the rod as judged from K1 would have been eq. 06 ;
this is quite in accordance with the principle of relativity which
forms the basis of our considerations.
A Priori it is quite clear that we must be able to learn something
about the physical behaviour of measuring-rods and clocks from the
equations of transformation, for the magnitudes z, y, x, t, are
nothing more nor less than the results of measurements obtainable by
means of measuring-rods and clocks.
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