Perception vs. Reality-relativity of time

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I am new to physics, and have been especially persistent in trying to understand relativity. After a few days of research and Q & A, I understand relativity, and its effects on observations, however one thing continues to bother me. A few people that I have talked to all say that time really does slow down when the observer is traveling at greater velocities; that they age more slowly.

More specifically, this is my question; there are two twins, one standing on earth, and one who becomes an astronaut. The astronaut travels through space for a significant amount of time at a very high speed. When he returns, will he and his twin be the same age? In other words, does velocity effect the reality of aging?

Most of the people I have asked have said that the astronaut will be younger than his twin, but I cannot wrap my mind around that. I am becoming confused and frustrated with this concept, please help me sort this out. As I stated earlier; I am new to physics, so it would help me a lot if the replies use simple terminology so that I do not have to research the more complex vocabulary that is used by more experienced and versed physicists. Thank you =)
 
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BuddyPal said:
More specifically, this is my question; there are two twins, one standing on earth, and one who becomes an astronaut. The astronaut travels through space for a significant amount of time at a very high speed. When he returns, will he and his twin be the same age? In other words, does velocity effect the reality of aging?
If one twin moves inertially (doesn't change speed or direction) while the other moves away from him for a while, then accelerates to turn around and returns, the twin who accelerated will be younger when they reunite. This is known as the "twin paradox", there's a lot of detailed info here:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
 
the answer is 'the sheep are black on one side'.

most confusion with relativity is a result of not understanding 'relativity of simultaneity'.
 
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I like the link provided by JesseM above. It is important that you also know that this is not optical illusion, but instead has been verified experimentally to high precision: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

The way I prefer to think of this is in geometric terms. You know that if you have two points on a piece of paper then the shortest path between those two points is a straight line. Similarly with relativity, where a straight line is an inertial objest's path. But the distance formula is Minkowski's instead of Euclid's so that the longest interval between two events is a straight line. Clocks measure this interval, not "coordinate time".