Before I go onto the relativity shattering example of the reverse analysis of .6c return trip, I decided to quickly do the example of Alice stopping wrt Bob at t'=4.
The world's chief scientainer on relativity, Prof Brian Greene would say the age difference is instantaneously established by the swing in Alice's present line to horizontal. He would show all present lines between Bob and Alice show Alice has aged 1 yr less than Bob in all cases past t'=4. This is the kind of malarkey that has brought up generations of confused relativists for over a century. If you apply the same reasoning as was presented in the .6c return trip example for ralfativity, you will get the correct answer how age difference unfurls and when the difference in aging ends. I'll just copy and paste it here with the necessary corrections in
red.
The pink line from t'=4 (the transition point tp) takes 3 Bob years or
3 Alice years to reach Bob so Alice ages from 4 to
7 yrs. Her line of present at t'=
7 intersects Bob at t=8. So Alice is
1 of her years younger than Bob in her years which converts to
1 Bob years younger that Bob
since they are both in the 0 relative velocity frame.. This is the correct answer
at the same time relativity arrives at the same answer
notwithstanding Brian Greene's ridiculous analysis. But how does it unfurl?
We need to work backwards from t=8. We know the light signal from t'=4 took 3 Bob years to propagate which means Bob was t=5 when Alice was t'=4. We can see from Bob's yellow light line at t=3.2 that Alice aged from t'=4 to t'=
5.2 (1.2 of her years) when Bob aged from t=2 to t=3.2 (1.2 of his years). Similarly we can see when Bob aged from t=3.2 to t=5 (1.8 Bob years), Alice aged t'=
5.2 to 7 (1.8 of her years).
Now let's use this data to reconstruct Bob and Alice's aging from t=2 where the light signal from Bob reaches Alice at t'=4 and Alice ages from t'=2.5 to 4 while Bob ages from t=2 to t=5. When Alice ages from t'=4 to t'=
5.2, Bob ages 1.2 of his years from t=5 to t=6.2. When Alice ages from t'=
5.2 to 7, Bob ages 1.8 of his years from t=6.2 to t=8. This is how the age difference unfurls during the the transition period from t'=4 to t=8. Relativity only cares about the age difference at the end of the spacetime path when
t=8. Ralfatity, for once agrees with this end result but would probably disagree with how relativiy would unfurl it if that info was available to be seen.
Unfortunately I don't know when I'll have the time to continue with this as I must spend some time looking for a job. Fortunately my ex-boss just handed me an extra $2000 2 months after he fired me. Don't know why.