World Science Scholars
24.14 Lorentz Transformation: Examples

Module 24: Lorentz Transformation: Examples - Problem 9

In this problem, you’ll analyze how, in a particular example, an observer moving on a train makes sense of a platform observer’s claim that the train is Lorentz contracted.

Here’s the set up: A train whose resting length is 1,000 feet rushes by a platform at speed $v=\frac{3}{5}c$. The platform observers measures the train’s length to be contracted by a factor of $\gamma=5/4$, namely 800 feet. To prove to everyone that this is the train’s length, the platform observers make an 800 foot bronze statue of the train, and place it right next to the tracks. The next day, the train rushes by the platform again and as it does platform observer F, situated at the front of the statue, and platform observer R, situated at its rear, agree that at one moment in time the train and the statue exactly align, showing that the train is in fact 800 feet long.

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