hello. ok, In a philosophy class I'm taking the instructor went over the proof for time dilation using the pythagorean theorem and the distance=timexvelocity equation to end up with the equation http://hsc.csu.edu.au/physics/core/space/9_2_4/Image4.gif Based on measuring the pulse of light from the bottom to the top of a moving object, like a train. and I understood that. But what happens if you are measuring the light reflection from the back of the train to the front and from the front to the back? from the back to the front, it will appear to have travelled farther to an outside observer, implying time slows. But from the front to the back light would have appeared to have travelled a shorter distance. Doesn't that imply time speeds up? and these are happening at the same time, so I'm not sure what to think. I may just be thinking about this in some wrong way. Can anyone help in showing steps to a mathematical proof to this like the one above? I'm thinking that Distance = CxT+VxT going forward and Distance = CxT-VxT going back. c being speed of light, t being time, v being the velocity of the train. Not sure where to go from there though or how that could end up being equal to the original equation. So any help would be appreciated.