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The Polevault Paradox

I have a favourite Gedankenexperiment for illustrating the peculiarities of LORENTZ CONTRACTION: picture a polevaulter standing beside a 10 foot long barn with a 10 foot polevault pole in her hands. Tape measures are brought out and it is confirmed to everyone's satisfaction that the pole is exactly the same length as the barn. Got the picture? Now the barn door is opened - no tricks - and our intrepid polevaulter walks back a few parsecs to begin her run up.

Suppose we permit a certain amount of fantasy in this Gedankenexperiment and imagine that Superwoman, a very adept polevaulter, can run with her pole at a velocity  u = 0.6 c. (Thus $\beta = 0.6$ and $\gamma = 1.25$ -- check it yourself!) This means that as she runs past a stationary observer her 10 foot pole turns into a 8 foot pole due to LORENTZ CONTRACTION. On the other hand, in her own reference frame she is still carrying a 10 foot pole but the barn is now only 8 feet long. She runs into the barn and the attendant (Superman) slams the barn door behind her.

From Superwoman's point of view, the following sequence of events occurs: first the end of her pole smashes through the end of the barn, and then^23.9 (somewhat pointlessly, it seems) the barn door slams behind her. A few nanoseconds later she herself hits the end of the barn and the whole schmier explodes in a shower of elementary particles - except for Superwoman and Superman, who are (thankfully) invulnerable.

Superman sees it differently. He has no trouble shutting the barn door behind Superwoman before her polevault pole hits the other end of the barn, so he has successfully performed his assignment - to get Superwoman and her polevaulting skills hidden away inside the barn for the two nanosecond period that the scout for the Olympic Trials happens to be looking this way. What happens after that is pretty much the same as described by Superwoman.

Imagine that you have been called in to mediate the ensuing argument. Who is right? Can you counsel these two Superbeings out of a confrontation that might devastate the surrounding landscape? Or will this become the Parent of all Battles?

Well, if they want to fight they will fight, of course; but the least you can do is point out that objectively there is nothing to fight about: they are both right! When you think about it you will see that they have both described the same events; it is only the sequence of the events that they disagree on. And the sequence of events is not necessarily the same for two observers in relative motion! It all comes back to the RELATIVITY OF SIMULTANEITY and related issues. For Superwoman the pole hits the wall before the door slams, while for Superman the door slams before the pole hits the wall. Both events occur for both observers, but the sequence is different.^23.10