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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Question A Question | Comment 1 of 11

How is the tunnel positioned relative to the train?  Is the train inside the tunnel, or outside but parallel, or perpendicular?

For example,

()-------)   Tunnel

    ^
    |
    |        Train
    |
    |
 
         *OR*
 
(------()    -------->
  Tunnel        Train

(Please excuse the poor illustrations.)  Anyway, I think this makes a big difference.  In any case, I assume the answer has something to do with the time the light leaves the various parts of the tunnel in order to arrive at the camera lens at the same time, but without knowing the orientation of the train and the tunnel I'm having a hard time putting my ideas into action! :)

Any clarification, or am I completely off track here?


  Posted by tomarken on 2006-05-26 16:19:54
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