Here's the impossible scenario I THINK I understand, from the train/platform thought experiments and the "twin paradox"... I prefer to use spaceships: We are in Spaceship A - this shall be our Frame of Reference (F.O.R.). At some time prior in our F.O.R., Spaceship A and B are synchronized. Spaceship B flies by us at relativistic speed. In our F.O.R. clocks on Spacehip B run slower. In the F.O.R. of the crew of Spacehip B, our clocks are running slower. If someone in Spacehip B could suddenly jump back into our F.O.R. after they pass us by, their clock would show an earlier time than ours. If we could suddently jump into their F.O.R. after they pass us by, our clocks would show an earlier time than theirs. Hopefully, there's nothing wrong with the above statements (the impossibility of shifting F.O.R. instantly aside - and yes, I know even the term "instantly" is ambiguous in this context - let's take it from a "common sense" perspective). If there are other issues I'm sure someone will let me know. When I try to get specific and make it more "realistic" by adding acceleration and deceleration into the mix is when I have a total failure to understand. Say Spaceship A and Spaceship B are next to each other in space and we synchronize our clocks. Lets even say we calculate how much time will pass for them as they venture to some specific point to give them time to accelerate.. Spaceship B takes off and accelerates, reaching a speed of 0.986c (this gives a Lorentz factor of 6, if I'm not mistaken) just as it passes us and it maintains that speed for the rest of its journey. It ventures out 4.5 ly, turns around and comes back (I don't even want to consider the consequences of that turnaround right now - lets ignore that for right now and just consider the acceleration/deceleration at the end and I'll ask about the turnaround later). At the moment when it passes us by in our F.O.R. 9.13 years have passed by for us (3331.6 days - ignoring the turnaround time), but only 1.52 years (555.3 days) have passed for the crew of Spaceship B. OK, so far I think I've got it. Now here's where it gets weird for me: If, instead of merely waiting for Spaceship B to pass by, we do some calculations to plot an intercept course to accelerate to .986c and rendezvous w/Spaceship B (which would have to happen at some point after Spaceship B passes our initial position) and then we compare times - who's clock says what? As we accelerate towards their F.O.R. the differences in our clock speeds would get smaller (they would also be decelerating towards us from our F.O.R. in fact, we'd be decelerating towards them in their F.O.R. as well). To us, their clocks would always be slower than ours, so I would think the difference would be similar to to the 9.13 years vs. 1.52 years above, with a slight difference. To them, OUR clocks would always be slower than theirs. they only see 1.52 years pass by before our F.O.R.s begin to meet, so we should have less than 1.52 years pass on our clocks. (This all assumes we can accelerate to .986c in a trivial amount of time (days?) and the numbers are ignoring this time... is this my wrong assumption?) BUT... more than 9 years have passed to us in our F.O.R. before we try to accelerate to the same F.O.R. as Spaceship B - so our clocks would have to have progressed at least that much - we wouldn't suddenly start going backward in time in our own F.O.R. even if our F.O.R. is changing. Does the changing time dilation between the two F.O.R.s during acceleration make up for the difference (just using SR alone, or including the gravity equivalence of GR)? Did we have to travel much farther and take longer (space dialation?) to accelerate from their F.O.R. than ours? Or is there something else I'm completely missing (I'm pretty sure this is the case)? How do I resolve these two scenarios? What happens as we accelerate and change F.O.R.s? And, what the heck WOULD our clocks say? Depending on the answers to these questions, I have more questions - but this is already a long post so I'll stop it here.