The Behaviour of Measuring-Rods and Clocks in Motion
I place a metre-rod 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 metre-rod relative 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
x(beginning of rod) = 01 − v 2
x(end of rod) = 1.1 − v 2
1 − v 2
c2 . But the metre-
v2/c2 of a metre. The rigid v = c we should have 1 − 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.