Question on General Relativity

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I am by no means an educated scholar in the field of Einstein's theory of relativity, so introducing myself into this topic is rather green. After watching a couple videos on time travel, I noticed something that came to me as contradictory:

In this video, it very simplistically explains how travelling at high speeds slows your time respectively. So in essence, you are travelling into the future by approaching such speeds. This empirical thought is backed up by satellite clocks that need to adjust themselves due to their orbit in space.

However at the same time this video states:
http://www.youtube.com/watch?v=JPk7imosxRg&feature=related
Skip to 7:28. In this video, it explains that as you approach the speed of light, by Einstein's theory of relativity it is Albert's stationary rocket that is moving. Thus, his "light clock" takes a longer time to hit each mirror in Bertand's relative position. Following this logic, as Bertand approaches the speed of light, Albert's "light clock" would stop all together, and in fact go back in time if Bertand breaks the speed of light.

My question is simply how do these contradictory theories coexist? How can travelling at speeds approaching the speed of light send you into the future and simultaneously into the past? This cognitive dissonance hasn't been fully explained where I looked, so hopefully I will have some answers here.
 
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LeonhardEuler
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Your question is a good one. It can be restated another way. If two observers are moving relative to each other, they both think that time is moving more slowly for the other. Who is right? If they meet again, who will be older?

This is known as the twin paradox, and it has been a well known counter-intuitive result of the theory of relativity since the beginning of that theory. Rather than going into a long explanation, you can read about it: http://en.wikipedia.org/wiki/Twin_paradox
 

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