Is it possible to speed up time using Special Relativity? I know that with special relativity when having more velocity than a stationary observer your time relative to the observer slows down. Is it possible using special relativity to increase your time relative to the observer? Is it possible for a observer to experience less time than you do? For example the observer experiences 1 second while you experience 10 seconds.
 A: I think the way you frame the problem leads to confusion. Why is the observer stationary and "you" are moving. That doesn't make sense, since "you" are always at rest relative to yourself, and it is the observer who is moving.
Moreover, everyone is an observer in SR. So really you have "You" at rest and "they" are moving. They do see your clock moving slower, and you see their clock moving slower, so the answer to your question is "yes". If they are moving at:
$$ v = \frac{\sqrt{99}}{10} c$$
you see them experience 1 seconds as you experience 10 seconds. 
However, from their point of view, the answer to your question is "No": as they experience 1 second, they see you experience 1/10th of a second.
Now if you want to consider non-internal world lines, then you have to invoke the twin paradox. They need to move away from you for 5 seconds at the aforementioned $v$, and then return at the same speed. The you will observed them observing you experiencing 10 seconds total, as they only experience 1 second themselves. Moreover, you will also agree that you experienced 10 seconds while they only had one.
A: All you need to do is to put them in a centrifuge with a tangential velocity of about 0.99 c. If you stood somewhere on the circumference of the centrifuge then you could compare clocks every time the observer passes by. Their clock would run slower than yours
