I don't know why this problem just occurred to me- sorry if it's a silly question: Why is it that there isn't a limit to how high the gamma factor can be? How can you ever have a gamma factor which is more than 2, for example? Although if you plug the numbers into the equation for gamma it makes sense that you can have as high a gamma factor as you want, when you look at the problem visually as follows it seems impossible: If a moving frame S1 has a light clock aboard his ship which is one light second high, that light clock will be the same height in the stationary S frame, and the vertical side of the right triangle which represents the light clock will be one light second high. From S's point of view, the base of the right triangle can't be any longer than 1 light second because S1's ship can't be traveling faster than light speed. The longest the base of the right triangle can be is slightly less than 1. So, assuming that the height and base of the right triangle are equal, the hypotenuse will never be more than double the height of vertical side. Since the length that S observes the light beam traveling can never be more than double what S1 observes, how can there ever be a gamma factor of more than 2?