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?
(In reply to Solution
by Ken Haley)
"At that instant, the light from the tunnel's exit reaches the camera
since it's right there. At a later point in time, the light from the
the other end of the tunnel (its "entry") reaches the camera."
But a camera is only going to take a picture of the light that appears at the instant when it is clicked. I'm not sure I understand exactly what you are saying. "At a later point in time", the picture has already been taken...
As I alluded to in my first post, I think you have the right idea, but perhaps worded incorrectly. It's not that the light from the tunnel arrives to the camera at different points in time (because then they would not show up in the same picture) but that the light that does arrive at the camera at the instant the picture was taken had to leave the various parts of the tunnel at different times (to all arrive at the camera at the same instant).
I'm still having trouble wrapping my head around the idea well enough to explain exactly how this affects the photograph, however. :)
Posted by tomarken
on 2006-05-29 07:41:03