Tensors and Relativity: Chapter 1

Length contraction

Length contraction

next up previous index
Next: The twin paradox Up: Consequences of the Einstein Previous: Time dilation

Now suppose the observer tex2html_wrap_inline1118 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. tex2html_wrap_inline1458 and tex2html_wrap_inline1460 .

  figure488
Figure 1.12: Length contraction

The Lorentz transformations give:

eqnarray844

so the length is

eqnarray846

since tex2html_wrap_inline1462 [ instantaneous measurement by tex2html_wrap_inline1118 ]. Writing this result in terms of v and c we have:

equation849

Note that this is not a physical effect on the rod but an effect of spacetime itself.