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Thought experiment in relativity of simultaneity

  1. Jan 3, 2007 #1
    My text reads thus (the part which is bolded is that which I don't understand, I just reckon that the rest is needed for the context) :


    This seems very wrong to me. Am I incorrect in saying that Mavis must see the two flashes simultaneously, and also must conclude that they happened at the same time? She can't take into account her movement towards one of the flashes, because that only happens in Stanley's reference frame. She's at rest with respect to the two sources in her own frame, surely?
     
    Last edited: Jan 3, 2007
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  3. Jan 3, 2007 #2

    Doc Al

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    Yes, that would be an incorrect conclusion.

    Every observer sees the light flash moving at speed c with respect to them. All Mavis directly observes is the flashes reaching her at different times. But we can certainly take advantage of Stan's viewpoint and deduce what Mavis will see: From Stan's viewpoint (which is perfectly legitimate) Mavis moves towards the incoming light flash. Since she knows that she is equidistant from the flash sources (the ends of the train) she is forced to conclude that the lightning flashed at different times according to her clocks.

    Of course, from the train observer's viewpoint, it is Stan who is moving away from the light flashes. Mavis agrees that the light flashes reach Stan simultaneously, but she is forced to conclude that something is wrong with Stan's clocks--they are not synchronized according to Mavis.
     
  4. Jan 3, 2007 #3
    Oh right. Thanks a lot for the help.
     
  5. May 10, 2009 #4
    I think the relativity of simultaneity deduction is incorrect.

    If two people are at each end of the train and they run toward the center, they will reach the center at the same time (assuming the same speed) because their speed is bound to the moving train; but light emitted from each end of the train will not reach the center at the same time because light is not bound to the movement of the train. The person in the center of the train should adjust his calculations of simultaneity for things like light that are not bound to the center of the train.
     
  6. May 10, 2009 #5

    Doc Al

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    What do you mean by the speed being "bound to the moving train"? If the two people move at the same speed with respect to the train and start at the same time according to train clocks, then they will meet at the center of the train. Everyone (in any frame, not just the train frame) will agree.
    Why is that? The same reasoning applies to light.
    You haven't even introduced a second frame, so you haven't yet deduced anything about the relativity of simultaneity. First understand what happens in the train frame, then see what that implies for another frame (the track frame, for instance).
     
  7. May 10, 2009 #6

    JesseM

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    In the relativity of simultaneity thought-experiment, light doesn't reach the observer at the center of the train simultaneously; light from one lightning strike reaches her before light from the other lightning strike. But it's a basic postulate of relativity that light must move at the same speed of c in every frame, so in the train frame, the light from the lightning strike at the front must have moved towards the center as the light from the strike at the back. This means that from the perspective of this frame, the only way to explain the fact that the light from each strike doesn't reach the center at the same time is to conclude that the lightning strikes themselves must have occurred at different moments in this frame. Meanwhile the light from each strike does reach the observer on the ground simultaneously, and they also occurred at equal distances from him, so in his frame we must conclude they occurred simultaneously (and in the thought-experiment it's also assumed that in his frame the strikes occurred at the same moment that his own position was lined up with that of the center of the train).
     
  8. May 10, 2009 #7
    Thanks for the quick reply, but I still believe the deduction is incorrect. If the distance from the center of the train to either end is the same and the speed of light is constant, and the observer sees the light from one end before the other, the observer has 2 possible deductions. The observer can conclude that the light from one end was emitted before the light from the other end (as everything I've read concludes); or the observer can conclude that he moved toward one light while moving away from the other light. I don't understand why the observer concludes the former.
    If the distance from the center of the train to either end is 1000, and the train moves forward at a rate of 1 in the same amount of time it takes the light to travel 1000, the man on the train can conclude that he moved toward one light beam so it had to travel 999 and the other light beam had to travel 1001. Since one light beam had to travel farther, he should expect to see one light beam before the other.
    If the man believes he is not moving, he will conclude that one beam struck before the other; but if the man is aware that he is moving, he should compensate his calculation and realize the lights were emitted simultaneously.
     
  9. May 10, 2009 #8

    JesseM

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    Because there is no absolute notion of "moving" in relativity, for any non-accelerating object you can choose an inertial frame where that object is at rest, and the two basic postulates of special relativity are 1) the laws of physics will be observed to work identically in every inertial frame, and 2) the speed of light is always c in every inertial frame (which naturally must include the frame where the train is at rest). These are just postulates of course, experimental data could prove them wrong, but so far all the evidence is consistent with the idea that all the fundamental laws of physics are "Lorentz-symmetric" and thus will obey the same equations in the different inertial frames given by relativity (whose coordinates are related to one another by the 'Lorentz transformation', hence the name). In any case, the point of the thought-experiment is not to prove the postulates must necessarily be true in the real world, but just to show that if the two postulates are true, then simultaneity must be relative.
     
  10. May 10, 2009 #9

    diazona

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    Not to step on JesseM's toes, but I think this point is worth highlighting: it is a postulate of relativity that all observers see light traveling at the same speed. Intuitively, yes, the man on the train may think that one light beam had to travel at speed 999 and the other at speed 1001 (in your notation). But according to Einstein, that is flat-out wrong. Light always travels at speed 1000. Strange but apparently true. Anyway, if you accept that light always travels at the same speed, then the notion of time (simultaneity) has to change to keep the physical picture consistent - that's what relativity is all about.
     
  11. May 10, 2009 #10
    If we have a really long train, and if the train is NOT moving, and the distance from either end of the train to the center is 1000, we may calculate that it takes 6 seconds for the light from each end to reach the center and we would deduce that the lights were simultaneous.
    However, if the same train is traveling at 1/2 the speed of light; then the center of the train and the light emitted from the front of the train will travel toward each other and they will meet in 4 seconds. The light from the front end of the train will have traversed two-thirds the distance (666.6) while the center of the train moved forward one-third the distance (333.3). The train keeps moving and at 12 seconds the light emitted from the rear of the train has traveled 2000, the train has moved forward 1000, and the person in the center of the train sees the 2nd light.
    Are those numbers correct from the perspective of the man on the train, or is the time a value other than 4 seconds because the man's perception of time is slowed due to his speed?
     
  12. May 10, 2009 #11

    Doc Al

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    I'm not sure what units you are using, but it's certainly true that if the light from each end reaches the middle of the train at the same time, then the folks on the train can conclude that the lights flashed simultaneously according to train observers. Note that this is true whether the train is moving or not.
    Here you are having the lights flash simultaneously according to track observers. The details of your calculation aside, it's certainly true that the light from the front of the train will reach the person in the middle of the train before the light from the rear of the train, since the train is moving towards one light beam and away from the other. Since the speed of light is the same for all observers, the train observer concludes that the lights were flashed at different times in his train frame.
     
  13. May 10, 2009 #12
    Instead of lights, if a horn sounded at the front of the train, and a bell rang at the rear of the train, and both sounds occurred at the same time from the perspective of someone watching the train go by; then the rider would hear the horn before he heard the bell. Would he therefore conclude that the horn sounded before the bell rang? Or would he consider the possibility that his motion caused him to hear the horn before the bell?
     
  14. May 10, 2009 #13

    JesseM

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    You don't seem to understand that there is no such thing as absolute velocity in relativity--all velocities are relative to your choice of frame, something moving at 1/2 the speed of light in one frame will be at rest in another frame, and in another frame it could be moving at 3/4 the speed of light or something. And again, it's a basic postulate of relativity that light moves at c in every inertial frame, and that all the other laws of physics work the same way in every inertial frame too.
     
  15. May 10, 2009 #14

    JesseM

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    No, because it's not a basic postulate of relativity that the speed of a sound wave should be the same in every inertial frame. You could construct a weird set of coordinate systems such that it was, but the laws of physics would not obey the same equations in different members of this set. On the other hand, if you construct coordinate systems under the assumption that the speed of light should be the same in every frame, you find that the laws of physics obey the same equations in all of these frames because they have the property of Lorentz-symmetry.
     
  16. May 10, 2009 #15

    Doc Al

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    The problems with using sound for such an experiment are: (1) Sound requires a medium (air) to travel; is the air stationary while the train is moving? (2) The speed of sound is not the same in each frame. (3) The speed of sound is small compared to the speed of light.

    So the observer knows that his motion effects the speed of the sound waves with respect to him. But if you did the experiment with mythical super-precision, the observer on the train would once again conclude--after careful calculation--that the two sounds did not chime at the same time in his frame. But this is more difficult to analyze than the experiment with light flashes--the fact that the speed of light is the same in every frame makes the thought experiment easy to analyze.
     
  17. May 10, 2009 #16
    Thanks for taking the time to reply to me. I think I am about to give up. But if I was riding on a train with my son, and the noon-time horn blew from the front of the train and the noon-time bell rang from the rear of the train, and we heard the horn first, and he asked me why both noon-time sounds did not occur at the same time; I would explain that we are moving toward one sound and away from the other. Later, if we were on a really fast train, and the noontime light shined from the front of the train, and the noontime light shined from the rear of the train, and we saw the noontime light first; I would use the same reasoning I used with sound to explain why we saw the light from the front of the train first. What I seem to read in the explanations is that same reasoning cannot be applied for light as for sound, even though both reasonings have the same result.
     
  18. May 10, 2009 #17

    JesseM

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    In the Earth's rest frame you are moving towards one sound and away from the other. In your own rest frame, you aren't moving at all, but the sound wave from one horn moved faster towards you than the sound from the other (sound waves only travel at the same speed in the rest frame of the air, and your rest frame is different from the rest frame of the air). There would also be a slight difference in simultaneity if you were using SR frames (related by the Lorentz transformation) rather than Newtonian frames (related by the Galilei transformation), but at low speeds this effect is of negligible importance, from the perspective of the train rest frame the main reason for the difference in times the sounds reach you is the difference in speeds.
    This would imply you are using the inertial frame where the ground is at rest but the train is moving, and your reasoning would be correct for that frame. But if you want to analyze things from the frame where the train is at rest, your reasoning must be different, just as it was for the sounds.
    In both cases you are free to use either the rest frame of the ground or the rest frame of the train--each frame will have a different explanation for why one signal reached you before the other, regardless of whether you're talking about sound or light. And each frame must be equally valid in relativity. Your explanations above aren't wrong, it's just that they are only correct in the rest frame of the ground, whereas the whole point of this thought-experiment is to compare what's true in the ground frame with what's true in the train frame.
     
  19. May 10, 2009 #18
    Rob,

    Try thinking about it this way.

    You talked about a noon horn and a noon bell at the front and rear of the train, but gave no more information than that. But what will make a difference is where the horn and the bell are located.

    Put them inside the train, and the sound propogates in the air of the train, which is at rest with respect to the train. As a result, you should hear them together, assuming that the train is not fast enough for relativistic effects to manifest noticeably. As an example if you have a really long, very fast train, say 50km and Mach 2, you would have a relativistic delay of 0.1ns (nanoseconds). - this delay is according to a track observer, not the train observer. See Saw's comment in a later post.

    Put them outside the train, and the sounds propogates in the air outside the train, which is not at rest with respect to the train. In this case, you will never hear the bell from the back of the train (at Mach 2, twice the speed of sound, the train will leave the sound waves from the bell well behind).

    With no medium for propogation, light won't be affected the same way. - Perhaps better stated "with no medium required for propogation".

    cheers,

    neopolitan

    (I'm still away, just having a few quiet moments to scan the forums.)
     
    Last edited: May 11, 2009
  20. May 11, 2009 #19

    Saw

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    Neopolitan, for completeness and for the orientation of Rob, I think we should add the following:

    If the horn and the bell are at rest with the train, the sound travels through air at rest with the train, the clocks travelling with the horn and the bell have been synchronized in the train frame (following the Einstein convention) and sound departs from both at the same time in the train frame, then the two sounds (in accordance with SR) will reach Rob at the same time, no matter how fast the train is moving with regard to the ground, even if it is travelling at 0.99 c. That is what relativity means: you cannot detect that you are moving relative to another frame through any experiment, no matter how high the relative speed, no matter whether the experiment is done with an electromagnetic object (light waves) or a mechanical one (a sound wave or a tennis ball).

    If the bell is at rest in the ground frame and the ring travels through air at rest with the ground, yes, it will not reach Rob if he is on a train escaping away faster than sound. But I do not think that this rules out that light propagates through a medium. Sound will not reach Rob because the train travels at supersonic speed, which is possible. If instead we talked about a light signal, the latter would forcefully catch Rob because his train cannot travel faster than light. So this way we are simply stating that superluminal speeds are not feasible, but this has nothing to do with the question whether light travels though a medium or not. (And if it had, I am inclined to think that it would be the other way round, but that's another story...)

    I agree that the great advantage of SR versus Lorentz Relativity is that it explains things on the basis of a clear and easy principle (principle of relativity = the laws of physics work the same in all inertial frames) without resorting to a medium for light propagation, on whose existence and nature endless discussions might arise. But there is no logical argument that can rule out that medium. It simply happens that such medium is undetectable and, if it existed, would be useless (so far), but it may exist or not.

    Rob, I initially had the same concerns as you have with the concept of relative of simultaneity of SR but have finally declared myself fully satisfied with it. In the thread The show of the duel you can see a tortuous account of my “conversion”. If you want a summary, please let me know.
     
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