4.2 The "Car and Barn Paradox" (Relativity and FTL Travel)
Description
This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
4.2 The "Car and Barn Paradox" (Relativity and FTL Travel)
The "Car and Barn" paradox deals with the question of "whose lengths
are shorter?" We have a barn whose front and back doors can be quickly open
and closed. There is also a car which is just long enough so that if you try
to fit it in the barn, and the barn doors close, they would close down on
the front and back bumpers of the car. Now, an observer in the car (say,
Carol) speeds the car towards the barn at a significant fraction of the
speed of light. One might then argue the following: from the point of view
of an observer sitting in the barn (say, Bob) the car will be length
contracted, and at some point it will be completely inside the barn. Bob
then reasons that he can close and open both barn doors while the car is
completely inside the barn. However, Carol will argue that it is the Barn
which moving with respect to here, and thus it the barn which is length
contracted. So, she argues, if Bob tries to close both doors at the same
time as the car goes through the barn, then the doors will smash into the
car.
We thus want to ask whether or not the barn doors do smash into the car
if Bob tries his idea, and how does each observer explain the outcome.
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