There are two well-known paradoxes involving manhole covers, which illustrate some unexpected implications of special relativity. In the first, a 2-foot manhole cover approaches a 2-foot manhole at relativistic velocity. Since the hole sees the cover as much smaller than two feet long, the cover must fall into the manhole. It does.

But what does the cover see? It sees a very small hole rushing at it. No way is this enormous manhole cover going to fit into this small hole!

The resolution of this paradox requires careful consideration of what it means for something to begin to fall, and is left to the reader.

There is also a higher-dimensional version of this problem, without the complication of falling, that is, without gravity. Suppose the manhole cover is flying to the right as before, but now the hole is in a metal sheet which is rising up to meet it. Again, from the point of view of the hole, the cover is very small and so — if the timing is right — the cover will pass through the hole. It does.

But what does the cover see? It again sees a very small hole rushing at it. How do you get a big object through a small hole? This time one must consider what it means for the cover to “pass through” the hole.

If you have successfully resolved these two paradoxes, you will realize that some properties of materials which we take for granted are quite impossible in special relativity!