I'm doing some independent study with a professor at my university. He has taken one GR class and he said that it was not a good experience. So we are in a sense learning together as we pursue this.(adsbygoogle = window.adsbygoogle || []).push({});

We are using the book "A First Course in General Relativity" by Schultz. We are doing problem 17 in chapter 1. (It is the classic "pole in the barn" problem.)

The pole is 20 m and is moving at .8c. What is the length it has for a stationary person..? (I left out the details of the "setting" but this the gist of it.)

Now he and I both know how to do it using the standard old formula: L=L(o) sqrt(1-v^2/c^2)

But we were trying to get to the same answer using geometrical means. Even in the book Schultz tries to emphasize getting in this "geometrical way of thinking" but when he got to the length contraction part, he used the formula above instead.

I've attached an image that I made in Photoshop to demonstrate how we did it the geometric way. The tan(phi)= v came from the book. Also of course c=1 which would reduce the above formula to: L=L(o) sqrt(1-v^2)

But the problem we run into is that when we use the original equation we get 12. But when we do it the geometrical way we get 12.5. Now as far as "theoreticals" go, doing it two different way should give you almost the exact number. (Not off by .5)

I was wondering if any of you can point out what we are not taking into account or doing something fundamentally wrong.

Please, if you need more information just ask.

Thank you.

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# Question about length contraction (geometric way)

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