Relativity of Length: Mind Games

The Pole Vaulter “Paradox”

Imagine that Peter has a small shed with doors on both sides. His friend Maria, a pole-vaulter, has a pole that’s somewhat longer than the width of Peter’s shed. One day, Maria runs very quickly through the shed carrying her pole. She runs, so fast, in fact, that she’s traveling at a more than half the speed of light. As Peter observes her, it seems to him that the entire pole fits inside the shed.

Maria disagrees with Peter, however, so they decide to do an experiment: First, Peter figures out how to close both doors at the same time, and then quickly open them. Then Maria runs through the shed and Peter operates the doors. From Peter’s frame of reference, Maria and her pole are inside the shed when the doors are closed. But according to Maria, the doors don’t close and open at the same time while she’s inside the shed. She sees the door in front of her close and open first, so that her pole is already sticking out of it by the time the other door closes behind her. Now Peter and Maria disagree about two things: the length of the pole and when each door closes and opens.

What Maria Observes

What Maria Observes

What Peter Observes

What Peter Observes

Is this story a paradox—is there really a contradiction here? Perhaps surprisingly, the answer is no. Within their own frames of reference, both Maria and Peter have been accurate observers. And both frames are equally valid. Physicists would explain the situation in terms of simultaneity: Two events, such as the closing of the shed doors, may occur simultaneously in one frame of reference but occur at different times in another frame of reference.

 


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