That space station question

Friday 15 May 2015

My HL students thought that paper 3 was good but were concerned about one part of the relativity question and I have to admit it is confusing. It's the bit about two lights seen to flash simultaneously on the space station. The problem is the rocket is to the left of the space station so the light from the nearest light will arrive at the rocket first, the rocket observer will therefore see this light flash first however this is not the light that actually flashed first in the rockets frame of reference. Both observers must agree that the two flashes of light arrive at the space station observer at the same time, now the rocket observer will see the space station travelling to the left so the light from F has travelled a shorter distance than the light from B, for the two flashes to arrive simultaneously light B must have flashed first. This is obvious if you draw a space time diagram so its a good job that they have been introduced into the course.

Here the two events are represented by the points on the x axis. The origin of the Station frame is midway between the points. The yellow lines represent light travelling from these events, the events will be observed in S' when the light crosses the t' axis. The time of these events in S' can be found by drawing a line parallel to the x' axis. So you can see F is seen to flash first even though it actually was lit after B. All very well for me sitting at home thinking about this but well done to anyone who worked this out in the exam.