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A relativity problem (train & platform)

  1. Sep 28, 2006 #1
    This is a "paradox-type" relativity problem that I cannot figure out. Hope it's OK to post this here. Sorry for English errors, it's not my native language. Here it goes:

    Railway. Platform (1 km) by side of it. Train (100m).

    Train approaches platform very high velocity, so that (in train's reference frame) the platform is only 10m long. The personnel in train can calculate the moment when the mid-point of train is exactly at the mid-point of the platform. Train brakes are set to operate at that moment. All cars of the train will start braking at the same time (all cars "live the same time", at least until the braking). No messages need to be passed at the time of the braking. Deceleration is very strong, but not "infinitely" strong (we can allow a small stopping distance for the train, few centimeters for example).

    Now, what is happening from the viewpoint of different observers?

    An observer at the platform will see very short train approaching, braking and stopping at the mid-point of the platform, and "stretching" to its original 100m length.

    But an observer at the first car of the train will observe very different event. Short (10m) platform approaches and passes him by. No braking yet. Instead, the passenger sees terrain beyond the platform. He can even leave mark there (say, toss a candy paper out of the window). After a short but non-zero period of time, braking starts. Then he finds himself in a train, at halfway of 1km long platform.

    How can it be? In platform's reference frame train never passed the platform, not even reached the end of the platform. In passenger's reference frame train went past the platform, and the passenger even left a mark there. The mark (candy paper) should be there. How can it be, if the train never passed platform? What went wrong?
  2. jcsd
  3. Sep 28, 2006 #2
    You have no problem understanding the "stretching" of the train, but you have a problem with the "stretching" of the platform and terrain. Why?
  4. Sep 28, 2006 #3
    Stretching (when the length contraction ceases) of the platform or terrain is not itself a problem. However, I find it strange that the train passes by the platform in one reference frame, and not in another. The train even leaves a mark on the "other side" of the platform. From the platform's perspective, the train never was there.
  5. Sep 28, 2006 #4
    Ooke: Think in terms of a plane. When the plane is travelling fast, imagine it's flying high. The runway down below looks small, maybe 10m long, because of perspective. And the plane when viewed from the runway also looks small, maybe 1m long. When the plane is exactly halfway along the runway (not beyond the runway), it stops very quickly. This is like descending rapidly to the ground. Then the runway looks 1000m long and the plane looks 100m long. The perspective has gone, and now everything looks normal sized. Your relativistic train exhibits a different type of "perspective" to the plane, but it doesn't create a paradox.
    Last edited: Sep 28, 2006
  6. Sep 28, 2006 #5
    I hope that I am not misunderstanding you. But I see a perfect symmetry between the platform and the train.

    Paradoxed notwithstanding, I like the fact that you are exploring how frames "snap back" to a rest frame. But personally I don't feel comfortable starting out with such a complicated example.
  7. Sep 28, 2006 #6
    The plane-analogy may work, if we think the length contraction just "seen" (more or less imaginary) phenomenon. But if I've understood correctly, the length contraction is real, as real as can be. The front-end of the train really goes past the platform (in train's frame). This is not the case with the plane.
  8. Sep 28, 2006 #7
    Sure the length contraction is real Ookke. But the front of the plane didn't go beyond the runway, and the front of the train didn't go beyond the platform. The train stops half way along the platform, like you said.
  9. Sep 28, 2006 #8

    Doc Al

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    "At the same time" only in the frame of the train.
    According to the platform observers, clocks in different parts of the train are wildly out of synch. Platform observers see the rear of the train brake long before the front brakes engage. (According to platform observers, when the rear brakes are applied, the front of the train is still moving fast as if nothing happened.)
  10. Sep 28, 2006 #9
    Farsight: The front of the train never goes beyond the platform, in platform's reference frame. But how about the train's frame?
  11. Sep 28, 2006 #10


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    The front of the train certainly does pass the end of the platform--as you said, a rider at the front could even leave a mark at some point past the end, different frames cannot disagree about events which occur at a single place and time like the front of the train reaching a particular spot on the ground past the platform. Doc Al gave you the correct answer, it has to do with the fact that simultaneous braking in the train's frame doesn't look simultaneous in the platform's frame. (are you familiar with the relativity of simultaneity?) In the platform's frame, the back of the train starts braking before it even reaches the platform, the midpoint of the train starts breaking right as it passes the midpoint of the platform, and the front of the train starts breaking well after it has passed the platform.
  12. Sep 28, 2006 #11
    No doubt there are out-of-sync issues, but I cannot see how the relativity of simultaneity is involved here.

    Shouldn't the question "Does the front of the train go beyond the platform" be yes or no? Distances may be relative, but either it goes or not. Now it seems to do both.
  13. Sep 28, 2006 #12


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    Yes, it should be and it is. All frames agree that the front of the train goes past the platform, because in the platform's frame the different parts of the train begin braking at different times, and the front doesn't begin until long after the middle began, at which point the front has actually passed the end of the platform completely.
  14. Sep 28, 2006 #13
    Now it makes sense! Everything is not relative: the front of the train goes beyond the platform, in all frames. We might even say that the front takes some "reverse" during braking, of course a point-of-view issue.

    I'd like to watch this kind of train arrival! :smile:
  15. Sep 28, 2006 #14

    I quote myself...
  16. Sep 28, 2006 #15
  17. Sep 28, 2006 #16
    Unless I skimmed it too quickly, that's not the same thing at all! Ookle's idea is waiting until the train is in the tunnel and then SLAMMING ON THE BRAKES! What a cool idea! The lorentz contraction stops suddenly and the train busts out of both ends of the tunnel! We could call it the Lorentz explosion!
  18. Sep 28, 2006 #17


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    Well, in the frame of the tunnel, the train wouldn't bust out of both ends, instead the back end would begin to brake before it had entered the tunnel, the middle would begin to brake as it passed through the middle of the tunnel, and the front end wouldn't begin to brake until it had already passed completely through the tunnel and come out the other side. How exactly the train would stretch in this period would depend on the details of how it was accelerating--a "natural" way to do it might be to have the train accelerate in such a way that its length in the instantaneous inertial rest frame of its midpoint at any given moment was always 100m, and also to accelerate in such a way that the G-forces felt by an observer sitting in the middle of the train would feel constant throughout the acceleration. In this case I think the problem would be one of "Born rigid motion" discussed by pervect in post #22 of this thread and analyzed in more detail here:

  19. Sep 28, 2006 #18
    A further simplification would involve two unconnected moving observers with synchronized clocks agree to 'slam on the brakes' at a predetermined time. After that phenomenon is analyzed, you could introduce some rod in the rest frame and play around with it.
  20. Sep 28, 2006 #19
    If there is a wall at the end of the platform, and the brakes are set as described (operate when mid-points meet), what will happen?

    Front of the train never makes it to braking (collides, instead), the rest of the train brakes. After full-stop, the train is at midway of the platform, with broken nose. Right?
  21. Sep 28, 2006 #20
    If you look at my simplification, you will see that you are assuming the
    train is rigid. That is an invalid assumption.
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