Yes, this is just wrong. But sorry, it has nothing to do with acceleration/deceleration. Look at it from the point of view (frame of reference) of the traveler. He sees his twin go away, but then he has to CATCH UP with him. This is where the Lorentz transformation kicks in. You cannot just add velocities! (If you could it would be simple as pie to exceed the speed of light.) When you run the equations, the twin catches up much more quickly than you would expect in a Newtonian world (which by the way allows for doppler shifts). The sped up clock does not have enough time to cancel out the initial slowness. Thus the traveler is younger.

Better than the equations, IMHO, is the Minkowski diagram. Then it is clear as a bell. Check out the diagram at: .