The very famous ladder paradox says that if you take a ladder of length $l$ and a barn of length $l + dl$ and put the ladder on a cart traveling toward the barn, you can fit the ladder inside the barn if the cart travels fast enough. This is due to length contraction, which says that a person in a non-moving reference frame will measure the length of moving objects to be shortened. However, Penrose and Terrell showed that one can not observe any such shortening when viewing a moving object. Furthermore, the object does not physically change length. So now suppose you have the technology to try and conduct the ladder paradox experiment; you have the cart that can travel up to 0.99c, you have the ladder, and you have the barn, and you want to try and fit the ladder into the barn. You start up the cart and get it going to 0.99c with the ladder attached. Since you measure the ladder to be shorter, you know you should be able to close both barn doors while the ladder is inside the barn, at some point in time. But you also know that you can't ever physically see the ladder contained inside the barn. Suppose, then, that you say that what you see isn't really what's happening at that instance; maybe at some point you see the ladder sticking out of the barn, but it is really contained fully inside the barn, and maybe you can close the doors then (you are assuming that some weird optical effects are happening while trying to find a solution to the issue). Well, that doesn't solve the problem because this "solution" implies you would have to see the doors cutting through (or hitting the ends) of the ladder, which obviously makes no sense. So the only solution that is really left is that you see the ladder fully outside the barn, you calculate that at that moment it is actually fully contained inside the barn, and you close the doors at that moment. But now what if you have cameras installed at the two sets of doors, and you have the cameras take a picture as soon as the doors close? What do they see? If they see the ladder fully contained inside the barn, then the ladder has actually become shorter, which of course can't happen. But since they can't see the ladder partially sticking out of the barn (the doors are closed!), this means they must capture an empty barn. So the ladder really isn't inside the barn at that time, which suggests that while you can measure the ladder to be fully inside the barn at some time t, it cannot actually ever be fully contained inside the barn (which could of course be seen without this whole discussion by noting that length contraction does not actually happen).
The conclusion, then, seems to be that you can measure that an event happens even though it never actually happens. Is this the correct conclusion, or am I missing something? It seems like a pretty big conclusion that isn't discussed very often, which is why I'm uncertain of its validity. I'm not sure what parts of what I said would be incorrect though. I think my arguments rest on three main assumptions; length contraction can be measured, it can't be observed, and it doesn't physically happen. I'm near certain these are correct assumptions, so I'm not sure where else my arguments fail.