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Itchy and Scratchy on a Train

  1. Aug 13, 2009 #1
    Howdy!

    In the middle of reading "The Fabric of the Cosmos" by some MIT physicist or something.

    I'll present the problem differently than he did because i like my presentation better and it doesn't change the meaning of the problem.

    There is, on a moving train, a pile of gunpowder. On each end of the train, there's a stopwatch that will start when it receives a signal from a light-sensitive monitor.

    There is an observer on the train and an observer watching the train go by.

    The gunpowder ignites and makes a small explosion! Both light sensors sense the light generated by the explosion and start their stopwatch.

    The observer on the train sees that both stopwatches started at the same time, as the speed of light is constant to any observer.

    The observer NOT on the train, however, sees the stopwatch at the caboose of the train start sooner. Light, traveling at a constant speed, does not get "pushed forward" by the fact that the explosion was not stationary as it happened. However, the sensor at the caboose of the train does get pushed forward by the fact that it is on a moving train! It gets pushed towards the explosion. Likewise, the sensor at the front of the train is being pushed away from the light generated by the explosion.

    The onboard observer, however, was at rest relative to the train and therefore the fact that the train was moving should not have affected the timing of the stopwatches at all.

    When the train stops and the two stopwatches are brought together...

    what the hell happens?
     
  2. jcsd
  3. Aug 13, 2009 #2

    JesseM

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    Yes, in the frame of the observer on the ground, the two clocks on the train are out-of-sync. This is known as the relativity of simultaneity--it's a basic property of inertial frames in SR that two events which are assigned the same t coordinate in one frame will be assigned different t coordinates in another.
    Assuming the train decelerates uniformly in the ground frame, and the two stopwatches are brought together at the same speed, then they will remain out-of-sync. Similarly, if you had two clocks which were synchronized in the ground frame, and in the train frame they were decelerated uniformly until they were at rest relative to the train and then brought together at the same speed, these clocks would be out-of-sync when they were next to each other.
     
  4. Aug 13, 2009 #3
    But, to the observer on the train, the two stopwatches started ticking at the same time, right?
     
  5. Aug 13, 2009 #4

    JesseM

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    Right, in his frame the events of the two stopwatches starting are simultaneous.
     
  6. Aug 13, 2009 #5
    And if, still on the train before it slows, he is able to see both stopwatches in his field of vision without moving, what would he see? That the stopwatches are synchronised?
     
  7. Aug 13, 2009 #6

    JesseM

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    If he's equidistant from the two clocks (at the midpoint between them where the gunpowder went off) he'll see both showing the same time, if he's closer to one he'll visually see that one as being ahead, but if he factors out the different times for light from each clock to reach his eyes based on the assumption that light moves at c in the train rest frame, he'll conclude they're "really" synchronized in his frame.
     
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