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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.