When you say in the problem that the positron moves from a high voltage region to a low voltage region, how do you determine the charge and how did it get that way? Is the high voltage region of space charged by lack of electron (positive) or many electrons (negative)? Or did you mean it is high...
If you were traveling near the speed of light time would be just fine, your clocks running, to an observer you'd be literally glowing and no way to read out the clock at that speed!