I Pole-Barn Paradox: Is My Understanding Correct?

[Grasshopper]

I want to make sure I have this right, and whatever I have wrong I would like to fix it.

Part I:

So in particular, I’m referring to a fast moving pole along the x-axis of an observer who is at rest with respect to the barn (the barn is a few feet away from the observer), and when the pole is at rest with respect to the barn and observer, it is longer than the barn. The pole goes through and fits completely inside the barn for a moment.

So my understanding of the situation is that, yes there is length contraction, however, to the pole, the barn is contracted as well. So what really matters is that the two ends are only in the barn simultaneously from the frame of reference of the observer standing next to the barn. For the pole, there is no such situation where both ends are in the barn simultaneously.

Part II: This time the doors of the barn are closed the moment both ends of the pole are inside.

This time, the observer sees both ends of the pole inside the barn at the same time, and the pole is crushed (because the sudden stop slows it down so that it is no longer length contracted).

But for the pole, first the door it is moving towards closes, it crashes into it, and then the signal of the sudden crash perpetuates through the pole at less than c, and when the back end the pole catches up so that it is inside the barn, THEN the back door closes.In summary, the solution to this apparent paradox is the relativity of simultaneity.

How close is that to correct? What did I get incorrect?

Thanks as always!

 

[Ibix]

however, to the pole, the barn is contracted as well.

I'd say "the barn is contracted instead", since the pole is not contracted in its rest frame. Other than that piece of pedantry what you wrote looks fine to me.

 

[PeroK]

That looks right. You can nail it even further by describing the sequence of events in each frame with some specific numbers.