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24.13 Lorentz Transformation: Examples

Module 24: Lorentz Transformation: Examples - Problem 8

Consider two frames of reference, Team Train and Team Platform. From the perspective of Team Platform, Team Train is moving east at speed $v=12c/13$. Each team properly synchronizes their clocks, and sets things up so that when the clocks at the origin of each frame of reference pass one another, they both read 4 PM. (Usually, we set things up so these clocks both read 0 or 12 noon, but all such choices are valid and arbitrary.) Use $c=1$ light-hour per hour and express all answers in the units of hours for time and light-hours for distance.

With this more or less usual set-up, let’s now imagine that a devastating crime is committed: President Backwardland, riding along in Team Train, is assassinated. (As in the earlier example of the treaty signing ceremony, President Backwardland is facing backwards in the train, i.e. he is located at the front of the train and is facing the rear.) An observer in Team Platform, who happened to be situated where the assassination took place, notes that the clock in Team Train (at the location of the crime) reads 2 PM when the crime was committed. This same observer notes that the clock in Team Platform (at that same location) reads 4 PM when the crime was committed.

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