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Consider a scenario, a bus is about to pass over a bridge. The bridge is broken in the middle. Now according to ground observer the broken part is bigger than bus (because bus appears smaller to ground observer due to the motion of the bus) and hence bus will fall down the bridge.

Now for observer on the bus sees that the broken part is smaller because, according to him, the bridge is moving and not him and he thinks bus will remain on the bridge.

Whose prediction is right in this situation?

Kyle Kanos
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Vicky Shrimali
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  • This is a variation of the fast walker paradox of Rindler, as exposed in http://aapt.scitation.org/doi/abs/10.1119/1.1937789 – ZeroTheHero Dec 20 '17 at 00:40
  • This question does not show any research effort – Alfred Centauri Dec 20 '17 at 00:49
  • @Alfred Centauri Actually , i did some research and i saw the answer too, but i wasn't convinced with the explanation. I am seeking a better explanation, that's why i asked this question... – Vicky Shrimali Dec 20 '17 at 04:02
  • Then your question should focus on what prt of an explanation you do not understand. In addition to Rindler’s paper there is also a discussion of this in Leo Sartori’s book. See also https://physics.stackexchange.com/questions/197393/whats-the-name-for-the-relativistic-paradox-with-the-train-car-travelling-over/232127#232127 – ZeroTheHero Dec 20 '17 at 04:34
  • Here is the exact answer: https://en.m.wikipedia.org/wiki/Ladder_paradox#Man_falling_into_grate_variation – safesphere Dec 20 '17 at 08:39

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In the usual answer to this kind of puzzle (which more typically involves running with a ladder through a barn, or something similar), the solution is that whether the ladder is inside the barn is not a Lorentz-invariant statement, because it requires information about what is happening at two points with spacelike separations (the ends of the ladder, at equal times; whichever observer's time is used, the ladder ends are spacelike separated). So it is no surprise that different observers see the situation differently.

In this case, there is an additional mistaken assumption, which is that as long as part of the bus is on solid ground, it will not fall. The goal of this modification was presumably to try to make the outcome (whether or not the bus eventually falls) clearly invariant. And it is a Lorentz-invariant observation whether the bus falls or not. In fact, the bus does fall. This is obvious in the frame where the bus appears at some point to be completely unsupported. In the frame where the bus is slightly longer than the gap? Well, you trying driving a 65-foot bus across a 60-foot gap in the road, and let me know if you make it.

Buzz
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  • Why assume in the moving reference frame the bus is "slightly" longer than the gap. Its can be considerabally larger. – Vicky Shrimali Dec 20 '17 at 00:58
  • @VickyShrimali It doesn't have to be. I included it merely as an illustration. The full calculation in the frame of the bus requires studying how the gravitational torques act on the bus in that frame, which is a VERY tricky problem. It's much easier to see that, in the other frame, there is a period in which the bus has no viable means of support and conclude from there. – Buzz Dec 20 '17 at 01:04
  • I agree. But i just can't see whats wrong with the reference frame of bus. Its totally non intuitive to me to predict that bus will fall from the reference frame of bus – Vicky Shrimali Dec 20 '17 at 04:18