Now suppose the observer 
wants to measure the length of the
spaceship. He can only do this by making an instantaneous measurement
of the spatial coordinates of the end of the ship i.e. 
and
.
Figure 1.12: Length contraction
The Lorentz transformations give:
so the length is
since 
[ instantaneous measurement by ].
Writing this result in terms of v and c we have:
Note that this is not a physical effect on the rod but an effect
of spacetime itself.