## Length contraction

Once the concept of time becomes suspect, the concept of length must also be reinvestigated. Think of how we measure the length of an object. We measure the positions of the two ends and take the difference between the two positions. For this procedure to have any meaning, the measurements must be carried out simultaneously. (If I measure the position of the front of an airplane, when it is in NY, and the position of the tail 6 hours later when it is in LA, I should not conclude that the airplane is 5000 km long.) Unfortunately, we have seen that observers in different inertial frames cannot agree on the simultaneity of events separated in space.

It is therefore not surprising that lengths will appear different to observers in different inertial frames. In fact, physicists had been playing with this idea before Einstein's 1905 paper. H. Lorentz had proposed it as a way around the results of the Michelson-Morley experiment. He said that the ether could be saved if the lengths of objects depended in a particular way on their state of motion.

In considering changes in length, we look separately at lengths perpendicular to and parallel to the direction of motion. We can first show that there can be no length changes perpendicular to the direction of motion. Let's assume that there were such a change and that moving objects shrink. We now consider an experiment. Two people of identical height are standing, as in Fig. 7.6.

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