How Does the Twin Paradox Illustrate Time Dilation and Aging Differences?

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The idea is as follows:

My (imaginary) twin and I were born at the same time, thus just as old. Now, my twin made his own spaceship in the backyard, one day, and decided to go for a ride. It had only room for one person, so I had to stay behind.
Now, my twin went out of the Solar System and came back after 6 months.

Because gravity affects our age, my twin would be "younger" than I was, although we had lived for just as long (actually, we wouldn't). I think has something to do with the General Theory of Relativity.


My question is: Would staying at high speed (up to speed of light) have the same effect, as time would go slower? And, in what way would he get younger? As in live longer? He would look like he'd been aging, right?

I'm sorry, this is a little hypothetical, but I'm fascinated by time.
 
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