When I first started to think about how much the home twin (she) ages during a light pulse's transit from her to the traveler (him) during his outbound leg, I was immediately struck by the fact that so MANY years pass during the lifetime of that pulse. So many years passing BEFORE his instantaneous velocity change occurs (IF it actually DOES finally occur). I was struck by the fact that she clearly does a LOT of ageing before we even KNOW if he goes through with his plan to change his velocity or not. That's when I started to suspect that my cherished belief in the CMIF method was doomed to the dustbin. The Minkowski diagram I described in my last posting has two light pulses in it which only differ infinitesimally. But we can imagine that they are distinct pulses, with one slightly "to the right" of the other. But remember that, "to the right of" on the diagram ACTUALLY means "later in time than". We should keep in mind that the two pulses are actually moving along essentially the same line in space. We can imagine ourselves following along behind the second pulse, and we would see the two pulses infinitesimally close together, traveling that way for MANY years. For me, that mental image makes the CMIF method IMPOSSIBLE to believe. Her ages when each of those pulses were emitted differ only infinitesimally. And her ageing during the transit of each of those pulses differ only infinitesimally. So her ages when he receives the two pulses (which is the sum of her age at emission, plus her ageing during the transit) differ only infinitesimally. The CMIF method says that difference is FINITE and LARGE. I conclude that the CMIF method is invalid.