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?

Holy cow, you're right!  What was I thinking?  (or drinking?)

After thinking about it some more, I think the effect is actually just the opposite of what I said.  The tunnel will appear longer as we approach it, and shorter as we leave it.

When the tourist is 50km away from the tunnel's entrance, (and 150km away from the tunnel's exit), light from the tunnel's exit begins it's journey to the camera.  A very short time later the camera covers the 50 km to the tunnel's entrance arriving at the same time the light from the tunnel's exit reaches the entrance.  Since the distance between the camera and the tunnel's exit was 150km when the light left the exit (going through the tunnel), it will appear on film to be 150km away. 

Similar reasoning would show that the tunnel appers shorter than 100m if we photograph it from the rear of the train as it recedes. 

Does that sound better?  (Now that my confidence is shaken, I'm waiting to hear if other arguments shoot down this reasoning.) 

Edited on May 30, 2006, 9:46 pm

Posted by Ken Haley on 2006-05-30 02:05:05