I have seen the classical twin paradox before. It uses a twin stationary on Earth and the other traveling away and back. I have seen many contradictory solutions for it, some use general relativity, others use special relativity, either way, I am still troubled by it. They always try to break the symmetry through the traveling twin's acceleration and deceleration, but never quite succeed.
So, let's do away with the classical twin paradox and let's explain a much simpler, perfectly symmetrical version of it where both twins are moving towards each other.
So imagine we have Twin A in a spaceship, and Twin B in another, a light year apart from each other at the beginning of the experiment. They both start traveling at the same speed towards each other when the first light of one twin since the beginning of the experiment reaches the other, so they effectively start moving one year into the experiment.
If I understand relativity properly:
- From Twin A's frame of reference, he's stationary and Twin B is moving at a constant speed towards him, therefore, because of time dilation, Twin B's clock is ticking slower.
- From Twin B's frame of reference, he's stationary and Twin A is moving at a constant speed towards him, therefore, because of time dilation, Twin A's clock is ticking slower.
Regardless of what their observations might be because of the Kepler effect and what not, time dilation dictates that a moving clock will absolutely tick slower than a stationary one. So, because Twin B is moving relative to Twin A, Twin B's clock is absolutely ticking slower than Twin A's. The same is supposed to be true the other way around. This is obviously a contradiction.