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Relativity Express

  1. Oct 19, 2007 #1

    dot

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    As an example to demonstrate the relativity of simultaneous events Einstein used the train thought experiment. The argument envisages a very long tran moving at constant velocity with respect to an infinitely long embankment. A lightning strikes the embankment at a point A coincident with one end of the train, while a second lightning strikes at a point B coincident with the other end of the train. The lightning strike events are deemed to be simultaneous by an observer standing on the embankment at point M which is at the middle of the distance A to B. Another observer is sitting in the middle of the train at point M' coincident with point M when the lightning bolts strike. The argument concludes that the observer in the train will not see the two flashes of light simultaneously, because by the time the flashes reach the observer, the train would have moved a distance closer to one of the flashes and the same distance away from the other flash.

    My difficulty is in reconciling this conclusion, when one considers the situation from the point of view of the observer sitting in the train only, or in other words if the embankment is removed. Without the embankment, the train can be considered stationary as there is no way of deciding whether the train is moving or not. In this scenario, using essentially the same argument used for the earth bound observer above, the two lighting flashes hitting the ends of the train would be seen as being simultaneous by the observer sitting in the train at point M' midway along the train. Obviously these two results are contradictory. What am I missing?
     
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  3. Oct 19, 2007 #2

    HallsofIvy

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    You said "A lightning strikes the embankment at a point A coincident with one end of the train, while a second lightning strikes at a point B coincident with the other end of the train." That was relative to the observer on the enbankment. By doing away with the embankment and assuming "A lightning strikes the embankment at a point A coincident with one end of the train, while a second lightning strikes at a point B coincident with the other end of the train" is still true relative to a person on the train you have changed the situation.
     
  4. Oct 19, 2007 #3
    hello dot

    When i first came across this thought experiment i too fell into the same trap as you and many others. You must remember that to the observer on the train ( and on the embankment ) the movement of the other observer is irrelevant. If the strikes were simulataneous in the train frame then the light fronts would meet at the centre of the train , whatever its motion, and not at the embankment observer. The key is to realise ( this is where i went wrong ) that to an observer in the train frame the ends of the train remain central to the light spheres propagating from the flashes and this is also true to the observer in the embankment frame. This seems to be against common sense but this is how it must be visualized. It is as though the points central to the spheres of light travel with all the observers in all frames. I am afraid this is not very eloquently or rigorously put but once you realise how to see it this way you it will come to be second nature. There are many forum members better qualified than me to explain this so i would advise you take notice of them. The last poster, HallsofIvy is of course correct in his explanation.

    Matheinste.
     
  5. Oct 19, 2007 #4

    JesseM

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    The basic physical fact here (i.e. the frame-independent fact) is that the light from the two strikes reaches the observer on the middle of the train at different times (from the point of view of the guy on the embankment, this is because both strikes happen simultaneously and the light from both moves at the same speed c towards the center, but the guy in the center is moving towards the position of one strike and away from the position of the other). In the train-observer's own rest frame, since he's at the middle and the strikes happened at either end, they must have happened an equal distance apart--and since he must assume that the light from each strike travels towards him at c in his rest frame, the only way to explain the fact that the light from one strike reached him earlier than the light from the other is by concluding that one lightning strike happened at an earlier time than the other.
     
  6. Oct 22, 2007 #5

    dot

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    Thank you very much for your answers. However I remain unconvinced.

    HallsofIvy said that the situation has been changed. I can't see how. Eistain's argument assumes that the

    embankment is at a standstill and arrives at the conclusion that the person on the train sees the flashes at different times.

    My argument assumes that the train is at a standstill and arrive at the conclusion that the person on the train sees the

    flashes at the same time.

    matheinste takes the point of view of the observer on the train and arrives at the same conclusion as I did, that this person

    sees the flashes at the same time. He ignores what he stated in his own argument that the person on the embankment would in

    this case see the flashes at different times, and that this contradicts the assumption made by Einstain that the person on the

    ground sees that flashes at the same time. How can we predict which is the true version?

    JesseM simply asserts what Eisnstan said and fails to check if the argument remains true when the tables are turned around. He assumes that there is a "physical" fact when this is just the result of a logical argument.

    I have searched the net and found several people that have exactly this same problem, and in this I take small comfort. Has anyone made any real (not thought) experiment to verify what really happens in practice?
     
  7. Oct 22, 2007 #6

    Mentz114

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    Two different observers may not agree that two events are simultaneous. There's no 'true' version, simultaneity depends on relative velocities. That's the point of the example. Do you know how to draw a space-time diagram ? It's clear from that.

    So what ? You can find anything if you search the web including flat-earthers.
     
  8. Oct 22, 2007 #7

    Ich

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    You must realize that "coincident" is not enough. You have to state in which frame the events are coincident.
    If they are coincident in the embankment frame, the rays will hit M' at different times.
    That's how the paradox is formulated and resolved.
    If they are coincident in the train frame, the rays will hit M' at the same time.
    But that's not what you formulated, it is a very different setup. It is a setup where the lightnings strike at different times in the embankment frame.
     
  9. Oct 22, 2007 #8

    JesseM

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    But then you're just dealing with an entirely different physical situation. Look, people in different frames can't disagree about physical facts which are localized to a single point in spacetime, like whether or not two photons hit a given clock at the same moment (according to that clock's own readings)--if they did, then that would lead to absurd differences, like if the clock had light-sensors on both sides that detected whether they both went off at the same moment, and if they did it would cause a bomb to explode, killing the person standing next to the clock...do you imagine different frames would disagree on whether the guy was dead or not? Different "frames" are just different coordinate systems for describing the same events in the same spacetime, they can't disagree on local facts like this.

    So, if you want to imagine a physical situation where the physical facts are different, and the light waves from the two flashes do reach the observer at the center of the train at a single moment, that's fine. In this case, you're right that the observer at the center of the train concludes the lightning strikes happened simultaneously in his frame. But in this case, the observer on the embankment would conclude they were non-simultaneous, and would agree the light from both sides reached the observer at the center of the train (who in the embankment frame is moving towards one flash and away from the other) at the same moment. So this is just a different physical situation than the one Einstein describes in his thought-experiment, with different conclusions about simultaneity from both observers.
    There certainly must be a physical fact about all local truths like whether two light beams arrive at a clock at the same moment--see my bomb argument. Again, the issue is that your version of "turning the tables around" just involves creating a different physical situation than the one Einstein was considering, rather than viewing the same physical situation he talked about from a different frame.
     
  10. Oct 23, 2007 #9

    Zan

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    But the fact is the train isn't stationary -- it's moving toward one lightning bolt and away from the other.
     
  11. Oct 23, 2007 #10

    JesseM

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    There is no "fact" about whether it's stationary, that just depends on your choice of reference frame--in the train's rest frame it is, in the embankment's rest frame it isn't. You can analyze the problem equally well in either one.
     
  12. Oct 25, 2007 #11

    dot

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    Thanks JesseM for your explanation and I agree with it perfectly: According to the STR
    1. If M sees the flashes simultaneously then M' must see them at different times.
    2. If M' sees the flashes simultaneously then M must see them at different times.

    What I don't agree with is that the statements are describing different situations. There is only one objective situation defined by: "when M and M' are coincident the lightnings strike the two ends of the train." As you said, an objective situation cannot have two contradicting interpretations. I am strongly suspecting the problem lies with the constant speed of light in all frames of reference.
     
  13. Oct 25, 2007 #12

    Doc Al

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    You assume that this statement unambiguously defines an objective situation. But it doesn't. Rephrasing the statement for clarity: At the same time that M and M' coincide, lightning strikes the two ends of the train. We must ask: At the same time, according to who? In the pre-Einstein, Newtonian view of things, the simple answer would be: According to everybody. Now we know different. Unless one specifies who observes the simultaneous lightning strikes, the statement is ambiguous.
    Most definitely! It is the strange fact that the speed of light is the same in all frames that allows us to deduce that simultaneity is relative.
     
  14. Oct 25, 2007 #13

    JesseM

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    No, that statement is not enough to determine the objective physical situation. After all, wouldn't you agree that the following two statements describe different objective situations similar to your 1 and 2?

    --"in the frame of M, the two lightning bolts strike the two ends of the train at the same time that M and M' coincide".

    --"in the frame of M', the two lightning bolts strike the two ends of the train at the same time that M and M' coincide".

    You do understand that the frame of M and the frame of M' have different definitions of simultaneity, right? So to say the two lightning strikes happen at the same time-coordinate in the frame of M means they happen at different time-coordinates in the frame of M', and vice versa.
     
    Last edited: Oct 26, 2007
  15. Oct 25, 2007 #14
    dot: Let me see if I can help you eliminate your confusion.
    When it is stated that lightning has struck points A and B it’s important to state if those are two points on the embankment or the two ends of the train. The problem set up, as I remember it, stipulates that the two lightning bolts hit points A and B on the embankment in such a way that they are seen simultaneously by an observer stationed midway between A and B. (Note that this stipulation breaks any symmetry which you might imagine exists between embankment and train observers.)

    Having fixed A and B in the embankment frame, you can truly say that the train observer is moving toward the front positioned emitter, A, and away from the rear one, B. (If A and B were points fixed on the train, then you would claim that the rear emitter, B, moves toward the embankment observer while the front emitter, A, moves away.)

    Continuing with the first setup (where A and B are fixed in the embankment frame), though the speed of the emitted light wave is the constant c for all observers, the train observer’s motion toward A and away from B dictates that she will receive the A signal before receiving the B signal. This will still be the outcome even if you want to think of the train as being stationary with the embankment in motion.

    Eli
     
  16. Oct 26, 2007 #15

    Mentz114

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    The only problem is with your understanding at present. You can't seem to grasp, that there is no objective definition of simultaneity.
    False. Listen to JesseM.
     
  17. Oct 26, 2007 #16
    dot, as I reread the explanation I gave you, I become more and more dissatisfied with it. My emphasis on stating whether the points A and B were fixed in the embankment frame or the train frame was a poor way of implying that the outcome depends on which observer, M or M’, sees the lightning simultaneously. But I realize now that that is not where your confusion lies.

    You seem to think that there is symmetry between the two observers. There isn’t. M claims that when the lightnings simultaneously struck points A and B on the embankment, both train ends were coincident with those points. You seem to think that that also holds true for M’, that M’ also says that the train ends were coincident with points A and B when the lightning struck.

    In fact, When observers M and M’ are coincident (M’ just passing M) M’ notes that the front of the train is already beyond point A and the rear of the train has not yet reached point B.

    Since the train-front has passed A, then for M’ the front lightning strike took place earlier than the time of M and M’ coincidence.

    Similarly, since the train-rear has not yet passed B, then for M’ the rear lightning strike has not yet occurred.

    But since both strikes occur when the train ends are coincident with their respective points (A and B), then from the M’ point of view the front strike occurred earlier than the rear strike and therefore, with each signal traveling the same distance (half the train length) at the same speed, c, the signals arrived at M’ at different times.

    Whether you do the math assuming (as we usually do) that the embankment is at rest and the train is moving, or you assume vice-versa, the outcome will be the same.

    Eli
     
  18. Oct 27, 2007 #17

    dot

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    Thanks very much Eli for your last reply and it makes the most sense so far. I was going to answer your previous explanation, that it was really equivalent to saying that the speed of light was constant only with respect to the frame in which it originates and different for all other frames in relative motion. But now your revised explanation has a different meaning which I need to study more deeply.
     
  19. Oct 27, 2007 #18

    JesseM

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    dot, to repeat something I asked in my last post, do you understand that to say two events happened "at the same time" has no frame-independent meaning in SR, and that two events at different locations (like the two lightning flashes) which both happen at the same time-coordinate in one frame may have happened at two distinct time-coordinates in another frame? This is known as the relativity of simultaneity and it's a pretty key concept in SR.
     
  20. Oct 30, 2007 #19

    dot

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    After much thinking about this, I have some good news - finally what all you experts have been telling me has filtered through, and I have found the flaw in my argument that did not allow me to understand SR.

    My logic was

    1. The lightning bolts strike simultaneously in M frame (embankment)
    2. Since M is in the middle of the distance along the embankment, M sees the flashes simultaneously.
    3. The lightning also hit the train simultaneously (this is what threw me off, as this statement is without reference to a frame and is therefore meaningless in SR)
    4. Since M' is in the middle of train, and the speed of light is constant, he too must see the flashes simultaneously.

    In the above argument I made the implicit assumption that time was absolute! While the whole point of the SR thought experiment was to specifically to show that point 3 above cannot be true for the M' frame of reference.


    The SR argument follows a different logic, namely:

    5. M on the embankment sees two lighting flashes at the same instant (this is a given).
    6. The lighting that M sees hit both the ends of a passing train and the tracks.
    7. M later finds out that he was standing at the midpoint from where the lightnings had struck.
    8. M concludes that the lightning bolts in his frame of reference were simultaneous.
    9. M' on the train moves some distance with respect to M by the time M sees the flashes, therefore M' cannot see the flashes at the same instant.
    10. Since M' is sitting in the middle of the train, and assuming the speed of light in his frame is constant, M' concludes that the lighting had struck at different times and were NOT simultaneous.

    Thus the SR argument concludes that simultaneity is relative and what occurs at the same time in one frame of reference will not be simultaneous in the time of another frame in relative motion.

    I feel happy now because, thanks to all of you, for the first time in my life I have a glimpse of understanding of SR and what it means that time is not absolute. Going back to your previous comments, I can now see what you meant by your responses. I can also see the other side of the coin. If we reverse the tables, and assume that M' sees the flashes at the same instance, then M would conclude that the one lighting struck before the other. If such is reality, this would be awesome.

    I still harbour doubts. Specifically point 9 above seems to imply that the speed of light is NOT constant for M' on the train, when reckoned from the frame of reference of M on the embankment. If such is the case, M' would conclude that the flashes were in fact simultaneous and we have back absolute time - and this time without paradox. Given also considerations on how to reconcile the red/blue shifting of light with the postulate of a constant speed of light, I prefer not to feel too much exuberant.

    Thanks again for your help.
     
  21. Oct 30, 2007 #20

    Ich

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    This implication follows only when you assume that the speed of light for M' - call it c' - could be calculated like c' = c+v or c' = c-v. But this is only true with absolute time and space.
    In reality, you have to use the relativistic velocity addition formula. It allows you to correlate speeds in different frames.
     
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