1. The problem statement, all variables and given/known data How does one prove that, of all timelike worldlines connecting two events A and B, the accelerated one is the longest. 2. Relevant equations dT^2 = dt^2 - dx^2 (accelerated reference frames: t = (sinh aT)/a x = (cosh aT)/a c = speed of light = 1) 3. The attempt at a solution If there is no acceleration, then x = vt, therefore T = t(1 - v^2)^0.5 I don't know where to go from there. Conceptually, I understand this, however, I can't seem to prove this with mathematics. Any ideas?