I got as far as this "Then two inconsistencies were found because of contradictory results." and then stopped because that's a misunderstanding that invalidates the rest of that section at least. There is no contradiction!
"This means that for each twin the other one age less. They both would see themselves with a long beard and the other one without it."
This is correct.
"Now from the referential at the mother-ship both twins are observed aging the same and in a different amount since for it they travel at velocity v and not w. The mother-ship would see both with a “half beard”."
Also correct. What's not correct is that this is in any way a contradiction. This is just the standard twin paradox that really shouldn't be called a paradox because it blatantly isn't one. For there to be a genuine contradiction, this: "This means that for each twin the other one age less.") would have to apply when the twins are back in the same frame of reference and that doesn't happen. If they accelerate equally so that they're back at rest with the mother ship then each sees the other aging rapidly to catch up with themselves and they're both the same age again when they're at rest relative to each other but both are younger than their triplet that stayed on the mother ship and didn't accelerate.
Well done for using the mothership. Too many thought experiments don't use an object in between the accelerating objects to compare to, makes it so much easier to illustrate what's going on.
Could be worded better...
"The mother-ship goes there, brakes and stops remaining there."
It stops remaining there? You mean 'The mother-ship goes there, brakes and stops, remaining there.' Leave it out because it's not needed. There's no such thing as absolute motion, it brakes (accelerates) relative to what? If it's inertial (not accelerating) then it's already at rest in that reference frame.
"After that, two small space-ships with twins"
Sounds like each ship has twins on board, or the two ships mated and had twins.
Never seen it written like that before, looks weird.
"may be synchronized by the mother-ship that is at equal distance from them"
Maybe's one word but it shouldn't be used here, using the mothership is the only way of doing it properly.
"After that, they turn their space-ships in the opposite direction and at some time (may be synchronized by the mother-ship that is at equal distance from them) they accelerate and travel back in a second symmetrical travel deviating a negligible little (to not collide) just to pass very near of them and the mother-ship at the same instant but they don't brake."
Not nice wording. Also don't say brake, there's no such thing in this context. They accelerate in the opposite direction.
Inertial reference frames, referentials sounds wrong even though it isn't.
""Now from the referential at the mother-ship both twins are observed aging the same and in a different amount since for it they travel at velocity v and not w. The mother-ship would see both with a “half beard”."
I should correct this. The mothership would see the twins with less than a full beard but more than a half beard because the time dilation and length contraction between the mothership's frame and the two twin frames is than than half of what it is between the twin's frames.
Edited by A-wal, 28 October 2016 - 01:10 AM.