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Greene's example is from pages 46-47 First Vintage Books Edition March 2000.

Slim has bought a car. He measured the car's length in the showroom with a tape measure. Jim is standing on a track and is going to measure the length of the car while it is in motion (relative to Jim) as it passes by him. He does this by starting his stop watch as the front bumper of the car is even with him and stops the watch as the rear bumper is even with him. Greene states: "From Slim's perspective, (Slim is driving the car) he is stationary while Jim is moving, and hence Slim sees Jim's clock as running slow. As a result, Slim realizes that Jim's indirect measurement of the car's length will yield a shorter result than he measured in the showroom, since in Jim's calculation (length equals speed X elapsed time) Jim measures the elapsed time on a watch that is running slow. If it runs slow, the elapsed time he finds will be less and the result of his calculation will be a shorter length. Thus Jim will perceive the length of Slim's car, when it is in motion to be less than its length when measured at rest.

I am lost on 1 critical point. I understand that Slim will see Jim's clock running slow--and using Slim's perspective of the elapsed time on Jim's watch, Slim would calculate that the measured length of the car in motion will be less than he previously measured in the showroom when the car was at rest. But, doesn't Jim see his own clock running "normally" from his (Jim's) perspective? He won't measure "less time" from his (Jim's) perspective. Jim's calculation of length (speed X elapsed time) will NOT be based on Slim's perspective of Jim's watch, it will be based on Jim's perspective of Jim's watch. How then, will Jim measure the car as shorter than Slim's measurement? I thought the point was that the two different observers in relative motion will disagree about their length measurements from their two different perspectives. But in this example, if Jim uses his own watch, which is not running slow to him, and does his own arithmetic, why won't Jim calculate the length of the car when it is in motion as being identical to the length Slim measured at rest in the showroom?

I'd I appreciate anyone taking the time to explain this to the slow member of the class.

Thanks.