I think I get it, but I'm still a bit confused, because both A' and A'' are moving forward at the same rate, which means since A'' started off older, A' will never really "catch up to" and become A'', because A'' continues to age. A'' is still three hours older than A', right, forever and ever?
To consider a weird example, what about a six hour old baby going back in time to witness her own birth? Once the fetus comes out, wouldn't there just be two babies, one six hours older than the other? Since they're both there and they're both experiencing time at a normal forward rate of one second per second, can't they just both grow up like siblings? If the baby that was just born waited an hour and went back to witness her own birth, she would see her six hour older version there watching her get born, and she would also see the newborn come out, and then there'd be three babies, age 0, age six hours, and age twelve hours, right?
How exactly would the "witnessing your own birth" thing play out with time travel? I think your explanation implies that there will never be multiple copies running around for any length of time, but why does A'' cease to exist once A' ages three hours? A'' has also aged three hours and become someone else in the meantime, right?
A' doesn't become A'' by catching up to him, he becomes A'' when he uses his time machine to jump back 3 hours.
There would be three babies for 6 hours, but then the youngest two would use their time machines and disappear into the past.
A'' doesn't cease to exist. A' "ceases to exist" because his time machine sends him back into the past to become A''.
r/Fitness does a weekly "Moronic Monday", a judgment-free thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. I thought this seemed like a useful thing to have here - after all, the concepts discussed on LessWrong are probably at least a little harder to grasp than those of weightlifting. Plus, I have a few stupid questions of my own, so it doesn't seem unreasonable that other people might as well.