grav

2009-May-30, 06:03 PM

I am having trouble wrapping my head around something all of a sudden. We all know the twin paradox for a barn / polevaulter experiment, but what about light itself? Let's say we have two lights set up at a large distance outside of either end of a ten light-second long ship and an observer outside the ship that is always stationary to the lights while the ship is also stationary for the time being. Observers are placed at every light-second within the ship with synchronized clocks, so eleven in all, nine within the ship and one at each end. Now the light at one end of the ship is flashed. The ship observers record the times that they receive the flashes, one per second, and a short while later reproduce the flashes to the outside observer, one per second, and that is the rate the outside observer receives them. Then the same thing is done from the other end.

Okay, now let's say the ship has a relative speed of .6 c to the stationary observer. All of the clocks within the ship are again synchronized to each other. The outside observer remains stationary with the lights. The experiment is repeated. According to the ship observers, light from either direction still passes each observer at c, passing one observer per second, and so a short while later, the ship observers flash their own light to the outside observer once per second in both cases also, as far as I can tell. The ship is time dilated to the outside observer by a factor of .8, so the flashes are received by the outside observer once per 1.25 second each in both cases, so after the initial pulse, all pulses will be received in 12.5 seconds according to the outside observer in either case.

Now let's look at what the outside observer measures. The light coming from behind the ship is travelling through the ship at c, while the ship moves forward at .6 c, and the ship is contracted by .8, so that ray should take t = (8 light-seconds) / (c - .6 c) = 20 seconds to travel through, and that is how the pulses from the ship observer should also be received, since they match the rate the pulses pass each observer. From in front of the ship, the light should take (8 light-seconds) / (c + .6 c) = 5 seconds to travel through the ship and that is mimicked by the ship observers, so the pulses from the ship observer should be received in that amount of time to the outside observer. So neither case matches what should be observed, although the sum of the times is the same. What's going on?

Okay, now let's say the ship has a relative speed of .6 c to the stationary observer. All of the clocks within the ship are again synchronized to each other. The outside observer remains stationary with the lights. The experiment is repeated. According to the ship observers, light from either direction still passes each observer at c, passing one observer per second, and so a short while later, the ship observers flash their own light to the outside observer once per second in both cases also, as far as I can tell. The ship is time dilated to the outside observer by a factor of .8, so the flashes are received by the outside observer once per 1.25 second each in both cases, so after the initial pulse, all pulses will be received in 12.5 seconds according to the outside observer in either case.

Now let's look at what the outside observer measures. The light coming from behind the ship is travelling through the ship at c, while the ship moves forward at .6 c, and the ship is contracted by .8, so that ray should take t = (8 light-seconds) / (c - .6 c) = 20 seconds to travel through, and that is how the pulses from the ship observer should also be received, since they match the rate the pulses pass each observer. From in front of the ship, the light should take (8 light-seconds) / (c + .6 c) = 5 seconds to travel through the ship and that is mimicked by the ship observers, so the pulses from the ship observer should be received in that amount of time to the outside observer. So neither case matches what should be observed, although the sum of the times is the same. What's going on?