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?

    First off Einstein stated that no possible speed could ever exceed the speed of light;c. In this case the solution states the light is reaching the boat at 1.5c. This would ruin the framework of Relativity as we know it. In the famous theory of Relativity, an object whos speed increases must therefore compensate for the speed by increasing its mass and becoming smaller in size. An object whos speed increases becomes shorter in length. An observer in the Tunnel would witness the boats length decrease. while a witness on the boat would see the tunnel decrease in size. This all has to do with point of reference. The resulting photograph could be no longer than the original size of the tunnel; 111.8 km.

Posted by matt on 2006-08-06 12:39:31