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24.13 Lorentz Transformation: Examples
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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/13v=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=1c=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.

  1. 1. Question

    According to those in Team Train, when the President was assassinated what was the reading on the clock in their frame of reference that is located where the crime was committed?

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  2. 2. Question

    According to those in Team Train, what was the reading on the clock at the origin of Team Train when the crime was committed?

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  3. 3. Question

    According to those on Team Platform, what was the reading on the clock at the origin of Team Platform when the crime was committed?

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  4. 4. Question

    According to those on Team Platform, what was the reading on the clock at the origin of Team Train when the crime was committed?

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  5. 5. Question

    According to those on Team Train, what is the reading on the clock at the origin of Team Platform when the crime is committed?

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  6. 6. Question

    Determine where, according to Team Train, the origin of Team Platform was located when the crime was committed. Express your answer in light-hours from the origin of Team Train.

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  7. 7. Question

    Determine where the assassination took place according to those on Team Train. Express your answer in light hours from the origin of Team Train.

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  8. 8. Question

    Similarly, determine where the assassination took place according to those on Team Platform.

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  9. 9. Question

    When the observer on Team Platform situated at the location of the assassination sees the crime committed, he immediately sends a light signal to the observer at the origin of Team Platform, alerting him to what happened. At what time does the observer at the origin of Team Platform receive the message?

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  10. 10. Question

    The observer on Team Train who happened to be located where the crime was committed also immediately sends out a light signal alerting his colleagues of the crime. At what time does the observer at the origin of Team Train receive the message?

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  11. 11. Question

    When the observer at the origin of Team Platform receives the message from his colleague that was located at the crime scene, he immediately tells the member of Team Train who happens to be passing him at that moment. What does this observer in Team Train say her clock reads at that moment?

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  12. 12. Question

    When the observer at the origin of Team Train receives the signal in part (j) (two questions before this one), how far away will he/she claim he/she is from the observer at the origin of Team Platform?

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  13. 13. Question

    If the observer at the origin of Team Train immediately forwards (via another light signal) the light signal she received (part (j), three questions before this one) to the observer at the origin of Team Platform, at what time will that observer say the signal arrived?

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  14. 14. Question

    Consider the clock in Team Train which, according to Team Platform, read 2 PM when the crime was committed. According to Team Platform, what time will it be on Team Platform's clocks when this train clock strikes 4 PM?

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