I was looking at this archived thread Two watches, one thrown in the air., that was also mentioned in the 'hard questions' thread recently. Reading the long and detailed discussion it struck me that there was a simple approach that seemed to have been overlooked. To briefly describe the situation, two clocks are held on the surface of the earth (or on a constantly accelerating spaceship, the two situations are equivalent). One is thrown up (ahead) and once it has fallen back to the clock that stayed 'stationary' (with respect to the thrower on the earths surface or ship) the question is asked about which, if either, clock has run slower. I would say, very simply that the thrown clock is following a geo-desic path and hence by definition maximizes the proper time experienced between two points [tex] (t_1,x_1) \to (t_2,x_2) [/tex] that the paths of both clocks intersect. Of course this dosn't give you the quantitative result straight out, but I think it's the best conceptual place to start from.