1. The problem statement, all variables and given/known data On my ever hopeful quest to come to a personal understanding of special relativity, I have stumbled upon a question while following my textbooks explanation of deriving an equation for length contraction. My textbook word for word: S' is moving at v relative to S Consider a rod at rest in frame S' with one end at x'2 and the other end at x'1. The length of the rod in this frame is its proper length Lp = x'2-x'1. Some care must be taken to find the length of the rod in frame S. In that frame, the rod is moving to the right with speed v, the speed of frame S'. The length of the rod in frame S is defined as L = x2 - x1, where x2 is the position of one end at some time t2, and x1 is the position of the other end at the same time t1 = t2 as measured in frame S. to calculate x2 - x1 at some time t, we use these equations x'2=γ(x2-vt2) x'1=γ(x1-vt1) subtracting leads to x'2-x'1 = γ(x2-x1) Okay... So I understand all that.. what I DON"T understand is why using the inverse equations doesn't lead to the same result.. you are relating all the same variables to each other, shouldn't the answer be the same? But of course when you do the inverse equation of x2=γ(x'2+vt'2) x1=γ(x'1+vt'1) you end up with (x'2-x'1)γ=x'2-x'1 Are t'2 and t'1 not equal to each other? Why would the same variables give different answers? Does it have to do with "perspective"/"What frame your looking from" or something like that? And if so shouldn't that information be inside of the equation somewhere? I hope somebody understands the dilemma i'm seeing here... I just feel like the equations aren't being consistent.. Does it have something to do with maybe t'2 doesn't equal t'1 so they don't cancel in this situation? If so why don't they equal?