Length contraction is another of the strange consequences of special relativity. Moving bodies appear to be shorter than stationary bodies. Of course, if the moving body is a spaceship, it will not appear shorter to the astronauts on board the spaceship, just as time on board the spaceship will not appear to pass more slowly.
If two events 1 and 2 occur at the points in spacetime with coordinates
and
and these are the measuring of the ends of a ruler which is stationary in O', and we assume that these events happen at the same time in O so that
then the distance between the two events is
in O'. We can use the Lorentz transformation to find the distance between the two events as measured in O.
(1)
(2)
(2)-(1) gives
Hence we can write
where
and
are the lengths of the ruler in O and O' respectively.