Note that however authoritative I may sound, I'm thinking about it as I go along. I like to think about these things, but I don't have a degree in it.

Quote Originally Posted by blade5x View Post
The difference between our times - that makes sense. But how would that apply to person traveling near the speed of light who witnesses only 10 years pass by, while I witness 20 years pass by, and yet we still end up in the same time frame?[/b]
He passes through two time frames other than yours, and loses some time by doing so. He isn't really back in your time frame until he slows down to your speed.

A time frame is like a six-dimensional location (three coordinates space, three coordinates velocity). They cross each other in weird ways that can lose time through too many changes, but when we're in approximately the same place traveling at approximately the same speed our time frames are approximately the same.

Quote Originally Posted by blade5x View Post
I know Einstein's T=T/sqrt(1-(v/c)^2))... but why does this work? How did he prove this? Does time just become independent for every observer - like there is the universal time, that we pretty much usually experience, and then there is the internal time, separate of the universal time, which is dependent on how fast you are moving? Maybe all time frames already exist?[/b]
He didn't prove it - he made up something that sounded good, wrote some equations to describe it and turned out to be right. Much of science is creativity. Very little is solidly proven - it goes through hypothesis (cool idea), and eventually gets to theory (cool idea that really seems to work).

Quote Originally Posted by blade5x View Post
I don't know see how traveling faster than someone has any affect on how long it takes their light to reach my eyes. I'm not sure this principle applies anymore for larger speeds. (doppler shifts do not apply because you can either see something speed up or slow down depending on which direction you'd be moving)[/b]
It doesn't change the speed of light. The light will take exactly the same amount of time to reach your eye no matter how fast the source is traveling, but the distance does change the time. A red shift is the light coming to you more gradually than it was transmitted - not taking longer altogether, but longer delays between the parts because the source's location is changing mid-transmission. The light's lower-frequency because it's more spread out.