Suppose you're traveling on a space ship at 9/10 the speed of light (.9c). You have a high-powered rifle that shoots bullets at the same speed. Suppose you shoot the bullet perpendicular to your direction of travel.
It appears that the bullet would travel at a 45-degree angle (northeast, if the ship is traveling north and the bullet is shot eastward), at about 1.2728c which is faster than light. Why is this wrong, and what would the actual speed and direction be?
(In reply to
Solution by Jay Schamel)
Nice analysis, Jay. Your solution matches mine exactly, and I don't think I could have explained it any more clearly.
It's true. Understanding special relativity is based on accepting two postulates (which have been empirically verified many times): (1) Constant velocity is relative. An object moving in a straight line at a constant speed may be considered to be at rest, and the observer be considered to be moving in the opposite direction. (2) The speed of light is constant in all non-accelerating reference frames.
Using these two facts and high school math, you can arrive at all the perplexing consequences that we call Special Relativity--time dilation, length contraction, trailing clocks run ahead, etc. It's remarkable to me that such astounding results can be derived so simply.
re: Solution
