relativity lesson #3

Our third Relativity point would be the one I mentioned in passing on my Einstein post:moving things shrink.

How does this happen? For example, take a train that measures 12 meters. By the way, relativity-obsessed people are gaga about trains. Mainly because it provides the perfect conditions for the theories. Or at least that’s what I think. Anyways, there wouldn’t be a problem measuring the trains if it’s stationary. But what if it’s moving?

Take your 12 meter train along with four friends. Two of them you station inside the train while the other two stays outside. All of them are equipped with clocks that they’ve set to perfect synchronization. For the two inside the train, one of them stand on one end of the train and fires a ray gun (nothing deadly, not the YuYu Hakusho-type) to the other one on the other end. They record the time as say, 0.00000004 seconds. Those two outside does the same time recording. However, they get 0.000000037 seconds.  The two pairs work out the train’s length like this:

Train length = speed of light x time difference

The first pair gets 12 meters but the second gets 11 meters! How does this happen?

Yey, it's this photo again!

While the light ray is traveling to the other end of the train, it had some time to move a bit meeting the light ray on its way. So, for the ones outside the train, it’s shorter than those inside it. In other words, if a train is moving past, it’s shorter than if it isn’t.

P.S. There’s an equation for this principle which goes like this: moving length = normal length x square root of 1 minus s^2 over c^2. I don’t know what the s is, I’m sorry. Maybe the time elapsed?


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A shy and quiet person who loves anime, books and Japanese food.

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