I have a version of the twin paradox which I am completely stumped by. There is a similar question on the forum but this particular version is unanswered. I really hope someone a lot better at physics than me is able to solve it!
Imagine two twins (Max and Tony) which are accelerated at birth in two opposite directions equally (at exactly the same rate of acceleration) for a long time, and then decelerated (at the exact same rate) until they are at rest with respect to each other far, far apart. Since they both accelerated the same amount, they are now the same age (say 20) in the same inertial reference frame.
Then, they accelerate towards each other until their relative speed is .99c, at which point they stop accelerating and are both travelling at constant velocity in an inertial (non-accelerating) reference frame (special relativity now applies).
At .99c, let's say they pass each other after say 30 years (or we can just stipulate a number of years x). The time dilation factor for .99c is about 1/7, so, when they pass, Max will see Tony at age 20+(30/7) = 24.3 years, and Max will see himself (Max) at age 20+30 = 50 years.
However, by the symmetry of special relativity the same goes for Tony: when they pass, each twin will see the other as 50 - 24.3 or about 26 years younger (or just (6/7x) years younger where x is the number of years travelled at .99c).
Finally, suppose they both accelerate (by decelerating, accelerating and decelerating equally and oppositely) into the same reference frame and come to rest together. Since they accelerate equally, they should age equally (say by y years) to each other. All other acceleration throughout their lives has been equal so no aging differences should have occurred at any point other than when they are travelling at constant speed of 0.99c (when special relativity applies). However, this means that both twins are now both 24.3+y and 50+y years at the same time by the symmetry of special relativity. How can this possibly be?
I’m sure there is a very simple explanation for this but I have no idea how to resolve it. I would expect that both twins are exactly the same age but how do you get round the fact that under special relativity each twin can absolutely legitimately claim the other is younger?