I think one catch in Twin Paradox was about the big acceleration that can turn back the traveling twin from light speed outward bound, to become light speed inward bound.
What if there is strictly no acceleration?
- Peter is on a space ship, traveling 99% of light speed. He is exactly 20 years old.
- Michael is on Earth (or a planet similar to Earth, but with a radius so small that any centripetal acceleration is negligible... or consider him standing just on a piece of concrete in space with an oxygen supply)
- Michael is also exactly 20 years old.
- According to time dilation, Peter's clock in the spaceship is slower than Michael's clock.
- According to time dilation, Michael's clock on Earth is slower than Peter's clock. (since motion is relative, if we consider Peter to be stationary, and Michael is traveling)
- Peter's spaceship is traveling towards Michael.
- After 30 years on Earth, Peter's spaceship went past Michael's face, so Peter and Michael are 1 cm apart, face to face and eye to eye.
- Now, would Peter see Michael quite older than him, and also, Michael sees Peter quite older than him?