I went to bed last night and couldn't stop thinking about this, and upon further reflection, I realized that time travel into the past is not possible.
This is because there is no past or future, but only the present.
Time is relative, so, a person could decrease the rate of change for him or herself while the rate of change continued at normal pace on Earth, and it would appear as though that person had traveled to the future, but in actuality, that person never left the present. What is being manipulated, in the scenario, is not a timeline, but the object in time.
The most extreme example of time manipulation can be found in a black hole, where time ceases to exist, or in other words, there is no rate of change. Upon entering the black hole, time begins to slow down more and more until all objects would simply freeze in place. There would never be an effect of "reversing" time, however. Although this is a linguistic error, because time is not a line moving forward and therefore can not be reversed. Time is simply the rate of change of one single moment, relative to all objects in space.
In conclusion, time (the rate of change for an object) can be increased or decreased, but it is not a line on which we could travel forward or backward.