There is a pole m long and a barn m deep. Standing still, the pole does not fit in the barn.
Run the pole at . Then , and in the frame of the barn the pole's length contracts to m.
At the moment the rear end of the pole reaches the entrance, its front end is exactly at the exit. Close both doors at that moment and the whole pole is inside the barn.
Seen from the frame of the pole, it is the barn that moves, and so it is the barn that contracts.
The barn is m and the pole is still m. The pole sticks out at both ends and is never entirely inside at any moment.
In the frame of the barn the pole fits; in the frame of the pole it does not. This disagreement is called the pole and barn paradox.
In the frame of the barn the two doors were closed at the same time. The phrase the whole pole is inside also contains simultaneity: it means both ends are inside at the same time.
On a spacetime diagram, the two door closings lie on a horizontal line, the barn's line of simultaneity. The pole's line of simultaneity has slope , and read along it the far door closes first.
Since simultaneity differs between frames, so does the statement that the whole pole is inside. It is true in the barn frame and false in the pole frame, and neither measurement is mistaken.
In the frame of the pole, the pole is at rest and the m barn moves toward the left.
First the far door closes, at the moment it coincides with the front end of the pole, and opens again at once. At that moment the rear end of the pole is m outside the entrance.
When the barn has moved another m, the rear end is exactly at the entrance and the near door closes. Covering m at takes nanoseconds, and by then the front end is m outside the far door.
Each door closes at the instant an end of the pole is exactly at it. In neither frame does a closed door block the pole partway along.
On a spacetime diagram, the strip between the world lines of the two ends is where the pole is in spacetime. There is one strip, and it does not change with the frame.
Cut the strip along the barn's line of simultaneity and it measures m on the barn's scale. Cut it along the pole's line of simultaneity and it measures m on the pole's scale.
The same strip is being cut along different lines of simultaneity; no force has pressed the pole shorter.