A stick of proper length L moves at speed v in the direction of its length. It p

Question

A stick of proper length L moves at speed v in the direction of its length. It passes over an infinitesimally thin sheet that has a hole of diameter L cut in it. As the stick passes over the hole, the sheet is raised so that the stick passes through the hole and ends up underneath the sheet. Well, maybe... In the lab frame, the stick's length is contracted to L/gamma, so it appears to easily make it through the hole. But in the stick frame, the hole is contracted to L/gamma, so it appears that the stick does not make it through the hole (or rather, the hole doesn't make it around the stick, since the hole is what is moving in the stick frame). So the question is: Does the stick end up on the other side of the sheet or not?

Explanation / Answer

Both the ends of the stick have to simultaneously pass through the hole for that reach the other end of the sheet. In special relativity, simultaneity is relative to each observer and therefore whether the stick ends up on the other side of the sheet is a question which has a different answer for different observers.

According to an observer in the lab frame, the stick will make it through the hole and it won't for an observer in the stick frame. There is no paradox in this situation.

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