Verified answer

As you approach the speed of light, time "dialates", it moves more slowly for you relative to a stationary observer. Thus if you travel, say, fast enough to slow the passage of time by half, if you were to do so for one year (by your clock), two years would have passed for the stationary observer. It's not time travel in the strictest sense of the term. You are just slowing down the passage of time, not moving around in time as if it were a fourth dimension that you could traverse as you can the other three.

This dialation of time is required by the fact that the speed of light is the same no matter how fast you are moving relative to the source of light. So if a beam of light is sent out from a stationary observation point, the observer at that point will measure its speed as 'c', then if you were to travel in the same direction at near the speed of light, intuitively you would measure that beam of light at a much slower speed since you are traveling nearly as fast as it is. But that's not the case according to Einstein's theories, you would still see that beam of light move at 'c', the same speed as the stationary observer does. So the only way that can be explained is if time is moving more slowly for you, thus the beam of light can go further in one of your longer seconds.

The easiest way to think about it is to imagine some absolute time axis T, and the velocities you observe are vx, vy, vz, and vt (your "speed" through time with respect to T, ie. dt/dT). The magnitude of your speed through Time (capital T) must always be the same.

The fastest way to travel thru time is then to stand still (ie vx=vy=vz=0). Likewise, if you travel close to the speed of light (eg. vx=vy=0, vz=0.99*c) then your "speed" thru time will decrease to about dt/dT = 0.01.

These values are by no means mathematically correct, but the concept itself is (as it applies to special relativity. the case assumes that you are accelerating to change velocities)