| MadSci Network: Physics |
In the barn-and-the-pole "paradox", you're right that different observers have different ideas of what is simultaneous, and this explains the paradox.
But it also explains what happens when the doors are shut. Someone in the pole's frame thinks that the front end of the pole hits the door *before* the back end of the pole enters the barn. Someone in the barn's frame thinks that the front end of the pole hits the door *after* the back end of the pole enters the barn.
One complication here is that there's no such thing as a rigid rod in relativity; what happens to one end of the pole cannot be "known" by the other end of the pole, except via information that travels down the pole at lightspeed. So even after the front end hits the door, both observers agree that the back end of the pole is not affected in any way for some finite duration. During that duration, the back end of the pole will continue to move forward, so both observers will still agree that the back end of the pole enters the barn, even if the front end is stopped in its tracks.
If the front end of the pole doesn't punch through the barn, and the pole doesn't break, then the pole must compress (in order for the back end of the pole to keep moving forward). When the pole compresses, it actually gets short enough to fit inside the barn, so if two superstrong doors are used, it would theoretically be possible to trap the pole inside the barn in a compressed state. (But after the pole is at rest the compression isn't due to relativity, it's due to the forces from the doors pushing on each end!)
Read the above link for another explanation.
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