Problem
The barn and the pole. A pole is longer than a barn in the frame in which both are at rest. Thrown along the barn’s axis at a speed close to , the pole appears contracted and would “fit” inside the barn. From the pole’s point of view, it is the barn that is contracted, so the pole should not fit. Who is right? The paradox is resolved by recalling the relativity of simultaneity: how? Argue without calculations, describing the events “ends of the pole crossing the doors”.
Solution
The crux: it is not a genuine paradox. Both observers are right in their own frame, because there is no absolute fact on which they could disagree. The question “is the pole entirely contained inside the barn?” requires comparing two events:
- Event 1: the front tip of the pole reaches the rear door (exit);
- Event 2: the tail of the pole enters through the front door (entrance).
Saying “the pole is inside” means these two events are simultaneous (at that instant both ends are between the doors).
In the barn’s frame. The pole is contracted and shorter than the barn: the two events are simultaneous, and for a brief instant the pole is entirely contained. (If we imagine closing both doors at that instant, the pole fits.)
In the pole’s frame. The barn is contracted and shorter than the pole: the pole cannot fit all at once. But here the two events are not simultaneous: the tail enters through the front door after the tip has already exited through the rear door. There is no instant at which the pole is entirely inside.
Resolution.
The two observers do not describe the same fact in a contradictory way: they describe the temporal order of two events at different points, and this order depends on the frame. It is the relativity of simultaneity that dissolves the paradox.
Links
Topics: Relatività ristretta Concepts: Contrazione delle lunghezze · Relatività della simultaneità Skills: Cambio di sistema di riferimento