A Level Physics Notes: Special and General Relativity – Length Contraction
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 boar the spaceship will not appear to pass more slowly.
If two events 1 and 2 have 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.