Barn-pole paradox
A textbook puzzle in which a pole longer than a barn at rest fits inside the barn at relativistic speed because length contraction shortens it in the barn frame, while in the pole frame the doors open and close non-simultaneously. Two observers, two stories, no contradiction — once the relativity of simultaneity is taken seriously.
Definition
The barn-pole paradox is a textbook puzzle that dramatises the relativity of simultaneity. Take a pole of proper length L₀ flying at relativistic speed v through a barn of proper length L_b < L₀. In the barn's rest frame, the pole is length-contracted to L₀/γ; if γ is large enough, L₀/γ < L_b and the pole fits inside the barn entirely. The barn-frame observer slams both doors shut simultaneously while the pole is wholly inside, then re-opens the front door before the pole exits the back. The pole-frame observer sees the barn length-contracted to L_b/γ < L₀, far smaller than the pole — there is no instant at which the pole fits.
Both stories are correct because the two door-closings are spacelike-separated events whose temporal ordering is frame-dependent. In the barn frame they are simultaneous; in the pole frame they happen sequentially — back door first (then immediately re-opens), front door second — and the pole is always partly outside the barn at any given instant in its own frame. The relativity of simultaneity is the substance of the resolution: there is no frame-independent answer to the question "is the pole inside the barn?" because "inside at the same time" presupposes a simultaneity slicing of spacetime that observers in relative motion do not share. The "paradox" dissolves once you stop demanding that fact.