Thought experiment 2:
Same basic setup as before. Ships A and B pass each other each in their own inertial frame but at a relative velocity of 0.866 c.
Both ships send out an encoded time signal by laser burst every second towards the other ship.
Each ship will see via this signal the other ships's clock advancing one second for every two seconds of their own time, correct? At least they will when they account for the distance the signals had to travel.
After traveling time.. let's say 1.866 t, they'll each be receiving signals that were sent time t ago, correct? (Sent at time/distance t, and in the time it took those signals to travel distance t at c the ships have moved another 0.866t, right?)
The time signal they are getting will claim it's from time t/2 though, right? Or am i thinking about this wrong?
Now, because these are magic thought experiment ships they have more reaction mass than god and inertial compensators to match. Ship A accelerates up to 0.866c to bring themselves to rest in relation to Ship B in the space of about half a second.
So now... the distance between them is cut in half so the signals start coming twice as often?
But the important issue is that just before the course change they received a signal saying "it is now time x:y:z." They are now going to be getting a signal saying it is now time x:y:z + 1" Being the ones that made the course change should have put them in the "we're younger than Ship B" frame, but nothing seems to have changed. Earlier evidence would have told both ships that they other one was aging half as fast, but now they both see the other as aging at the same rate and although the rate at which they're getting signals has changed they haven't suddenly switched to a new time so what's the discrepancy?
(Where did i put my Helliwell book??? =P)