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Relativistic snapshot (Posted on 2006-05-26) Difficulty: 3 of 5
The Theory of Relativity is not required to solve this problem.

The Lightway Express boasts half the speed of light. According to the advertisements, this relativistic speed literally shortens long trips. This is true. At one point, the train goes through a tunnel of about 111.8 km, but from the train's point of view, it is exactly 100 km long.

As a curious tourist, I resolved to experience relativistic speeds, and furthermore, bring home memories in photo form. So while I was riding the Lightway Express, I pointed my camera out a window, and took a picture of the entire 100 km tunnel. Later, when I examined my excellently timed photo, I was disappointed to find that the picture showed a tunnel that was much longer than 100 km.

How long is the tunnel in my photo, and why is it longer than I expected? Was I looking out the front or the back window of the train?

See The Solution Submitted by Tristan    
Rating: 3.3333 (3 votes)

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Solution dfntly nt th sltn | Comment 9 of 12 |

Tristan et al,

  The first statement of the problem indicated that the Theory of Relativity is not required for this problem.  The fact is that it is. Time dialation and Length Contraction and all the stuff inherent to Relativity make the assumptions of the problem incorrect. From no point of view will the tunnel appear longer.


  Posted by Leming on 2006-06-12 16:53:23
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