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Train thought experiment (SR)

  1. Apr 30, 2010 #1
    I am having problems with this presentation of the train thought experiment. I actually think it's incorrect, but I'm not sure.

    From Ray D'Inverno's book:
    Imagine a train
    travelling along a straight track with velocity v relative to an observer A on
    the bank of the track. In the train, B is an observer situated at the centre of
    one of the carriages. We assume that there are two electrical devices on the
    track which are the length of the carriage apart and equidistant from A.
    When the carriage containing B goes over these devices, they fire and activate
    two light sources situated at each end of the carriage (Fig. 2.13). From the
    configuration, it is clear that A will judge that the two events, when the light
    sources first switch on, occur simultaneously. However, B is travelling
    towards the light emanating from light source 2 and away from the light
    emanating from light source 1. Since the speed of light is a constant, B will see
    the light from source 2 before seeing the light from source 1, and so will
    conclude that one light source comes on before the other.

    [PLAIN]http://img144.imageshack.us/img144/2363/traing.jpg [Broken]

    - two sources of light (one on each end of train)
    - B sits in the middle of train
    - A sits on the platform (with same x-coord as B when the lights fire off)
    - B sees the light first

    Is it me, or is this a really bad treatment of the problem? The two lights that fire off at the same time...you can't really say something like that before simultaneity is understood surely.

    My main problem is - B should see both flashes at the same time, if we reverse the situation (train stationary, A moving backwards).

    I guess the author is saying "A sees the light flashes hit B at different times"?

    If I am wrong (which I probably am), can someone explain what B observes and why?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 30, 2010 #2


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    Science Advisor

    Well, you can understand that the flashes happen at the same time coordinate in the track frame, and that light must have a coordinate velocity of c in the track frame, and then if you use the second postulate to conclude the light must also have a coordinate velocity of c in the train frame, that shows that the flashes must have had two different time coordinates in the train frame.
    That would be a physically distinct scenario. Only one of the two can be true in any given scenario--either the flashes were simultaneous in the frame where the track observer was at rest and the train observer was moving, or they were simultaneous in the frame where the train observer was at rest and the track observer was moving.
    Different frames can disagree about the simultaneity of events which happen at different locations, but they can never disagree about whether two events coincide at the same point in space and time...if one frame says that both flashes didn't reach B's position at the same moment, all frames must agree on this. After all, B could be holding a bomb with light-detectors on either side that would only go off if both detectors were activated in a very narrow time window...different frames couldn't disagree about whether B was killed in an explosion or not! Different frames aren't parallel universes, there just different ways of labeling the same events in spacetime. So, in the particular physical scenario they describe where the flashes were simultaneous in the track frame (not in the train frame), all observers agree that the light reached B at different times. But B's own explanation for this is not that he was moving towards one flash and away from the other, since in his frame he was at rest...therefore, if the light from one flash hit him earlier than the other yet he says both flashes happened at equal distances and the light from each one traveled at c, he must conclude that one flash actually happened at an earlier time in his frame.
  4. May 2, 2010 #3
    Oh okay, thanks. Got it now.
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