The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity. If a ladder travels horizontally it will undergo a length contraction and will therefore fit into a garage that is shorter than the ladder's length at rest. On the other hand, from the point of view of an observer moving with the ladder, it is the garage that is moving and the garage will be contracted. The garage will therefore need to be larger than the length at rest of the ladder in order to contain it.
Figure 1: An overview of the garage and the ladder at rest.Suppose we have a ladder that is longer than the length of the garage, but it is traveling at a fast enough speed that, from the frame of reference of the garage, its length is contracted to less than the length of the garage. Then from the frame of reference of the garage, there is a moment in time when the ladder can fit completely inside the garage, and during that moment one can close and open both front and back doors of the garage, without affecting the ladder.
Figure 2: In the garage frame, the ladder undergoes length contraction and will therefore fit into the garage. Figure 3: In the ladder frame, the garage undergoes length contraction and seems too small to contain the ladder.However, from the frame of reference of the ladder, the garage is much shorter than the length of the ladder (it is already shorter at rest, plus it is contracted because it is moving with respect to the ladder). Therefore there is no moment in time when the ladder is completely inside the garage; and there is no moment when one can close both doors without it hitting the ladder. This is an apparent paradox.
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