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# The Pole and Barn Paradox

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The Pole and Barn Paradox
A very fast runner holds a 20m long pole in front of a 10m long barn. Can he fit the pole fit in the barn? What happens if he runs toward the barn at 0.87c? In the barn’s frame of reference the pole contracts in the direction of motion: Yes, it fits. You could close the barn doors for an instant with the pole entirely inside. In the runner’s frame of reference the barn contracts in the direction of motion: No, it doesn’t fit, the doors would hit the pole. This is a paradox, how can we resolve it?

The Pole and Barn Paradox
Let’s look at this from the barn’s frame of reference and close the doors for an instant when the pole is inside the barn. Now let’s look from the runner’s frame of reference, what is different? The doors do not close at the same time, why does the right door close first?

The Pole and Barn Paradox
The runner is going toward the right door so it closes first in his frame of reference. The paradox is resolved because the runner does not have to fit the 20m pole in the 5m barn with both doors closed. The left door does not close until the left end of the pole has entered the barn. But what would happen if we keep the right door closed?

The Pole and Barn Paradox
Watch the animation again from the runner’s frame of reference. A pulse of light will be released when the pole hits the right door. Can you explain why keeping the right door closed does not create a new paradox? The runner is well inside the barn before he knows the pole has hit the right door. The pole is inside the barn before the left end knows the pole has hit the right door. Nothing travels faster than light, even the information that the right end of the pole has stopped! Does that make your brain hurt?

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