2 Consider a long ladder or pole that is moving forward lengthwise at a high rate of speed, like a javelin. The pole enters a building — a barn or a garage or something like that, with doors open at both ends — and then goes out again the other side. If the building is 5 meters long, and the pole is 6 meters long (both of these lengths are measured at rest), you would not expect that the pole could fit entirely inside the building at any specific moment. But because of relativity, if it is moving fast enough, it can.

a) Compute the velocity the pole would need to have to fit inside the building.

b) Explain why using the post-Newtonian approximation is not a good idea for this problem.

c) Now let’s think about this from the point of view of someone riding along on the pole. From this observer’s point of view, the building should contract. Given the result of part a, compute the length of the building from the polerider’s point of view. This creates a bit of a problem, in that the building is now even smaller compared to the pole, so the pole certainly doesn’t fit. But how can it both fit inside, and not fit inside? That’s the basis of the so-called “ladder paradox”. We’ll resolve this difficulty later in the course. For now, just do the calculations and keep the apparent contradiction in mind for later.