11.45. Through the hole? A stick of proper length L moves at speed v in the dire
ID: 2268846 • Letter: 1
Question
11.45. Through the hole? 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/y, so it appears to easily make it through the hole. But in the stick frame, the hole is contracted to L/y, 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
In the frame of hole the concept of simultaneity is followed but in the frame of stick the simultaneity is violated. Relatively shows that simultaneity is no longer preserved between the reference frames as long as events are space like separated, then observers can disagree on what order the events occur.
For hole frame of reference the two ends of the stick are seen simultaneously.
For the stick frame of reference the events of entering of stick into the hole and leaving the hole are two events which are not simultaneous. In stick frame when one sees the two ends of the stick simultaneously, one end will be seen inside and other outside. For the hole observer, the simultaneous measurements by the stick observer are not simultaneous but are separated by a finite time interval in his own frame that is why he knows stick does not fit inside the hole according to stick observer.
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