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Simultaneity; is it valid to deduce that events occur at the same time?

  1. Feb 7, 2009 #1
    Ok folks, this is my first post to this forum and I’m afraid that I might be asking an embarrassingly simple question!

    I’m reading Einstein’s book on SR and GR and I’ve reached a discussion of simultaneity that involves an observer attempting to decide if lighting strikes that occur ahead and behind of a moving train happen at the same time. This is how I understand the argument so far; due to the finite speed of light that has the same value in all reference frames, the information about the event that takes place ahead of the train will reach the observer in a shorter time that the information about the event that happens behind the train. As a result of this, it is not possible to reason that the simultaneous arrival of light from both events corresponds to both events happening at the same time in the rest frame of the train track. This idea is then developed to illustrate that events that are simultaneous in one intertial frame are not simultaneous in another. This all makes sense to me.

    As part of his exposition, Einstein asks the reader to think about how they could determine the simultaneity of such lightning strike events, and given the constand speed of light it is made clear that this cannot be done simply by reference to the light that arrives from the events.

    However, what if there were clocks placed as the sites of the lightning strikes? These clocks could be synchronised in the rest frame of the track. Wouldn’t the light / information from the lightning strike then arrive at the observer along with information about the state of the clock at the instance that the strike happened? Wouldn’t this then allow the moving observer to determine the simultaneity (or lack there of) in the rest frame of the track?

    I suspect that I’m missing something profound about relativity here, and maybe I’m thinking about measuring the wrong time or something. I was sure that this sort of question must come up all the time, but I can’t find a satisfying answer.

    Thanks for any replies.
  2. jcsd
  3. Feb 7, 2009 #2


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    But they are then out of sync in the train's rest frame. Similarly, if two clocks are placed on the train, at the ends, and synchronized in the train's rest frame, they are out of sync in the rest frame of the track.
  4. Feb 7, 2009 #3
    Yep! Although the events are not simultaneous in different frames, the different observers will always agree on what frame the events are simultaneous in. So the guy on the ground can observe the events to be simultaneous and the guy on the train can observe them not to be, but the guy on the train could calculate (or observe in your example) that the events are simultaneous in the ground's frame. Notice in your example that if the clocks are synchronized in the ground's frame then they are of course not synchronized in the train frame. The guy on the train observes the events to happen at different times (according to his wristwatch), but the clocks on the ground will read the same time according to him. Hopefully I just re-explained what you were thinking - you seem to have a good grasp on this.

    My guess is that Einstein is talking about absolute simultaneity (which of course doesn't exist in SR). There is no disagreement between the observers as to who sees the events as simultaneous.
  5. Feb 7, 2009 #4


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    I think that somewhere in here there is an answer to my long-standing confusion about entanglement (QM). A cause at one particle is said to have an "instantaneous" effect on the other. This means that a change happens to both particles simoultaneously, and I've always wondered (aside from the sloppy description of the Quantum Mechanicle event being sited), "simoultaneously to whom?"
  6. Feb 7, 2009 #5


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    Note also that there are lots of other threads about this specific scenario. You'll find a few of them if you do a search. (I haven't tried it, but I'm guessing that you'll have lots of hits if your search includes at least two of the words einstein, train and simultaneous).
  7. Feb 7, 2009 #6
    Ah ha! This is very much what I was thinking. In fact, my second quesiton was going to be about how we could just do away with the clocks and calculate the times at which the events occured in the rest frame by using our knowledge of the speed of light. It seems that the observer in the train can arrive at the rest frame timings but upon comparing these to his own clock finds that his times / sequence of events are different. I think I made the mistake of somehow thinking that an observer in the rest frame and the observer on the train are required to never agree on what's going on, when in fact (as you've stated) they can easily agree on the frame in which the events are simultanious.

    Thanks for all the replies and giving me a chance to think this one through!
  8. Feb 8, 2009 #7
    You dont need extra clocks to find the order of events.Before the motion of the train you can synchronize one clock on the train with one clock on the tracks. You dont even have to assume that the speed of light is constant in the train's reference frame. You just need to assume that the speed is constant in the track's frame. From your velocity and the red shift between the lightning A and B, you can calculate the time and therefore order of the lightning events.I dont see the point of this chapter as it is just regular galilean relativity.
  9. Feb 8, 2009 #8
    Hello Emreth

    This thought experiment is a used as a helpful illustration to teach the relativity of simultaneity. It works very well. Of course any better ideas that serve the same purpose i am sure would be very welcome.

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