PeroK said:
Too many words, not enough calculation!
Let's do some calculations.
Assume we have two planets ##15## light years apart. They have synchronised clocks between them (over the course of a few decades). A rocket passes the first planet, A, and synchronises its clock with planet A. The rocket travels to planet B at a speed of ##\frac 3 5 c## and compares its clock with the clock at planet B when it gets there.
We know is that the ##\gamma## factor between the rocket frame and the planets' frame is ##\frac 5 4##, hence the planets are ##12## light years apart in the rocket frame. And the journey takes ##20## years according to the rocket clock.
The clocks on planets A and B are dilated by a factor of ##\frac 5 4##, as measured in the rocket frame, so the clock on planet B advances only ##16## years during the journey, as measured in the rocket frame.
But, in the planets' frame, the journey takes ##25## years, so this is what B's clock reads when the rocket arrives.
The immediate conclusion is that B's clock must have read ##9## years ahead in the rocket frame at the start of the journey. That tells us that we must have a loss of simultaneity of ##9## years in this case.
Can we confirm this conclusion by another method? Let's assume that when the rocket reaches the midpoint between the planets it fires a light signal in each direction. The signals should reach the planets simultaneously in their frame, as they were fired from the midpoint. The planets may use this to synchronise their clocks.
In the rocket frame, planet B is moving towards the light signal, so the signal reaches planet B after only ##3.75## years (##6## light years divided by ##(1 + \frac 3 5)c##.
Planet A is moving away from the light signal, so the signal reaches planet A after ##15## years (##6## light years divided by ##(1 - \frac 3 5)c##.
That gives a difference of ##11.25## years in the rocket frame. But, planet B's clock is dilated in the rocket frame, so advances only ##\frac 4 5 \times 11.25 = 9## years.
Hence, we obtain the same result that the clock on planet B (if synchronised with the clock on planet A in their rest frame) is ##9## years ahead as measured in the rocket frame.
This is how a careful analysis of simultaneity resolves the twin paradox and related problems.