A 20-meter pole is carried at toward a 10-meter barn with doors at both ends. The farmer says: contracted to 10 meters, the pole fits — slam both doors simultaneously, and for an instant it is entirely inside. The runner says: the barn is contracted to 5 meters, and the pole never fit at any moment. Both cannot be right about the doors — can they?
Solution
Both are right, and the doors never contradict either of them.
“The pole fits” secretly means “both ends are inside at the same time” — it is a simultaneity claim, not an invariant statement. The two door-slams are simultaneous in the barn frame only. In the runner’s frame the rear door slams and reopens before the front end of the pole reaches the far door; the slams happen in sequence, and at no moment is the pole enclosed. The two events are spacelike separated, so their time-order is frame-dependent, and no door ever touches the pole in either account.
The paradox only acquires teeth if you demand the pole stop inside the barn — and then Problema I collapses it: the pole cannot stop rigidly. The front stops first, a compression wave runs back, and what ends up enclosed in the barn is a genuinely shortened, crumpled pole in every frame.
Deeper in the notebook: 02. The Ladder (Pole-and-Barn) Paradox · 01. Timelike, Null and Spacelike Separation; the Causal Order