So far as I can understand it, the travelling twin is not affected by his
velocity, but by his
acceleration. One of the twins is accelerated, the other isn't, and so far as I understand it, that's the difference between them.
Now I'd like to make a couple of points.
First, Einstein's ideas have been borne out by meticulous experiments: his ideas may sound crazy, but they're
right.
Second, I'm a mathematician. Of the two of us, I am much, much closer to being able to understand the math of general relativity. Nonetheless, I can't be bothered. There is so much more interesting stuff to learn and do that I shall live and die without bothering to learn what it was Einstein was trying to tell us, and on my deathbed I won't be saying "Damn, I should have spent more time learning about General Relativity", I'll be saying "Damn, I should have spent more time having sex".
This is kind of a serious point. The people who study physics know that Einstein was right, and they know
why Einstein was right. Unless we're going to try to become physicists, and learn the math, we might as well shrug our shoulders and say "yeah, it's weird, but apparently it's true".
Edited by Dr Adequate, : No reason given.