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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 board the spaceship will not appear to pass more slowly.

If two events 1 and 2 occur at the points in spacetime with coordinatesand 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 thatthen the distance between the two events isin 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 writewhereandare the lengths of the ruler in O and O' respectively.