I'm having trouble reconciling two different versions of the Pole and Barn paradox.
Version 1: Consider a pole 10 m long and a barn 5 m long with a front and rear door. A runner carrying the pole (frame S') moving with respect to the barn and a farmer (frame S) runs into the barn. The farmer will see that the pole fits into the barn if the runner is moving at a speed:
gamma = Lp/L = 10/5
v = 0.866c
But according to the runner, the barn is moving towards him. The barns length contracts to:
L = Lp/gamma = 5/gamma = 2.5 m
How is it possible for a 10 m pole to fit in a 2.5 length contracted barn? Basically by drawing a spacetime diagram it becomes apparent that the pole doesn't fit. From the farmers frame, the front of the 5 m length contracted pole gets to the rear door of the barn simultaneously as the end of the pole enters the front door. But in the runners frame, these events are not simultaneous and the pole does not fit into the barn (the front end of the pole leaves the back door before the end of the pole enters the front door).
Version 2: Consider the same situation, but the rear door is replaced with an armor plate. From the farmers frame, when the pole fits into the barn, he shuts the front door (in the next instant, assuming the pole doesnt break, the pole must bend or break through the armor plate). From the runners frame, the front end of the pole hits the iron plate, with 7.5 m of the pole still outside of the barn. If information travels down the pole at speed of light c, it would take 10/c to reach the back of the pole. The barn on the other hand must reach the back of the pole in 7.5 / (0.866*c), which is less time than the time it takes for the info to travel down the pole. Thus, the runner is in agreement with the farmer, and the 10 m pole is contained within the 2.5 m barn.
Question: How is it that the pole fits into the barn in version 2, but not in version 1?
Question: My book says, as a part of version 2, "since this is relativity, the runner must come to the same conclusion in his rest frame [as the farmer] as the 2.5 m barn races towards him at v = 0.866c." But in version 1, the runner didnt come to the same conclusion?