Einstein's pole in the barn paradox. In this video we talk about aspects of special relativity like length contraction and simultaneous events to solve Einstein's pole in the barn paradox.
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Today we dive into the weird and wonderful world of relativity with an Einstein Paradox:
There is a pole vaulter on a farm, and to get to the bar she needs to run through a barn. Earlier that day, she measured the length of her pole against the barn and found it was twice its length. Is there a way this pole vaulter can fit her pole inside the barn?
At any normal human speed, this would be impossible. But what if Alberta were running at nearly the speed of light? When objects are travelling at nearly the speed of light, they contract in length in a process known as length contraction.
So if Alberta is running toward the barn at near light speed, from your reference frame she contracts in length in the direction of travel. So it's perfectly possible her pole can fit inside the barn with both doors closed.
But this still isn't a paradox until we consider things from Alberta's reference frame, as all motion is relative. From Alberta's reference frame, she is stationary and the barn is moving, so the barn is what contracts in length. So there's no way she could fit inside, as it was already too small to begin with. So what's happening?
The solution lies in what we mean by "simultaneous events". Special relativity tells us that there is no absolute time, there are only reference frames. So from your reference frame, the timer goes off and the signal reaches both doors at the exact same time. But from Alberta's reference frame, the signal reaches the doors at different times, and so she experiences the doors closing and opening at different times. This is what allows both reference frames to coexist. That time is relative.